PCGrate-S(X) v. 6.1 & 6.2 Examples of Calculation Procedures » International Intellectual Group, Inc.

Introduction to v. 6.1

In order to use the program efficiently, it is necessary to get oneself acquainted with the description of parameters and calculation modes. This section presents seven step-by-step examples of brief calculations of frequently used grating efficiency problems with scanning in varied parameters. The examples with references to the HTML Help also illustrate the selection of a “pivotal” parameter, which must be selected (or toggled) to access the parameter setting properly. The information on saving and exporting the output data files and on preparing graphs and tables for the described samples is included. All the examples of input *.grt files are stored in the …/PCGrate-S*/Examples directory and can be run by the PCGrate-S v. 6.1 Complete Demo software.

On our website you can find more computation examples using the PCGrate-S(X) v. 6.1program with data files, plots, and tables.

Also, keep in mind !

IMPORTANT NOTE
If you change one Calculation Mode for another, all parameters of the grating except the scanning parameters will be set to their default values. Therefore, during the change of Calculation Mode you will see a confirmation window.

Example 1: Ruled Spherical Al/Al2O3 Grating for the TM Polarization in the VUV

Input specification:

General tab

Accuracy optimization:

Calculation mode: Normal

Type of low border conductivity: Finite

Green functions and their normal derivatives: Remainder term, accelerating convergence: On

Logarithmic singularity accounting: On

Profile curvature accounting: On

Phase jump accounting: On

Number of terms: 50 % of points N

Grating shape:

Type of grating shape: Spherical

Grating shape parameters: Grooved width: 50 mm

Groove height: 50 mm

Meridional radius: 200 mm

Number of plane sections: Meridional: 3

Sagittal: 3

Frequency: 3600 grooves/mm

Beam and mounting geometry:

Wavelength: 140 nm

Wave front type: Spherical

Wave radius: 97 mm

Type of diffraction: Classical (in-plane)

Type of polarization: TM(S)

Optical mount configuration: Littrow

Littrow order number: -1

Deviation angle: 0 deg.

Scanning options:

Scanning parameter: Wavelength

Scan range number: 1

Scan range start value: 90 nm

Scan range step value: 5 nm

Scan range end value: 190 nm

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Trapezoidal/Sawtooth

Left angle: 9 deg.

Classical ruled profile changing: On

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: Off

Layer 1:

Vertical shift between borders (layer thickness): 2 nm

Rms roughness: 0 nm

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: From library: Al2O3_Palik_handbook.ri

Type of inter/extrapolation: Linear

Layer 2:

Rms roughness: 0 nm

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: From library: Al_Palik_handbook.ri

Type of inter/extrapolation: Linear

Output specifications:

· Save the “Input parameters” and “Far field parameters” reports for a point of scan, 140 nm, as text files.

· Plot the Absorption (TM), and Efficiency (TM) of reflected order # -2, # -1, and # 0 functions vs. the Wavelength parameter.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application.

· Press the General tab in the lower left corner.

· Choose the Accuracy optimization item in the upper left corner.

· Press the Normal button in the Calculation mode group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Check the Remainder term, accelerating derivatives check box.

· Check the Logarithmic singularity accounting check box.

· Check the Profile curvature accounting check box.

· Check the Phase jump accounting check box.

· Enter “50” in the Number of terms, % of points N field.

· Choose the Grating shape item in the upper left corner.

· Choose the Spherical radio button in the Type of grating shape group in the upper right corner.

· Enter “50” and use the default unit in the Grooved width field in the Grating shape parameters group (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Enter “50” and use the default unit in the Groove height field in the group.

· Enter “200” and use the default unit in the Meridional radius field.

· Enter “3” in the Meridional field in the Number of plane sections group.

· Enter “3” in the Sagittal field in the group.

· Press the Frequency button in the unnamed group.

· Enter “3600” in the Frequency field.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “140” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Spherical button in the Wave front type group.

· Enter “97” and use the default unit in the Wave radius field in the group (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the TM (S) button in the Type of polarization group.

· Press the Littrow button in the Optical mount configuration group.

· Enter “-1” in the Littrow order number field in the group.

· Enter “0” in the Deviation angle field.

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Wavelength item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button.

· Use the default unit (to change a unit, choose the nm item in the Measurement unit combo-box on the right).

· Choose the Scan range 1 item in the Scanning parameters tree in the middle.

· Enter “90” in the Scan range start value field on the right.

· Enter “5” in the Scan range step value field.

· Enter “190” in the Scan range end value field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Trapezoidal button.

· Press the Sawtooth button.

· Enter “9” and use the default unit in the Left angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Check the Classical ruled profile changing check box.

· Press the Accuracy parameters tab.

· Press the Equal S-interval button in the Type of integration step group.

· Enter “100” in the Number of collocation points N field.

· Uncheck the Using half-segment shift check box.

· Choose the Layer 1 item in the tree on the left.

· Click the Clone selected item button on the Main toolbar, or choose the Edit/Layers & borders/Clone item on the Main menu, or right-click the Layer 1 item and, then, click the Clone item on the context menu.

· Delete a layer item having a number greater than 2, if any exists in the tree, by choosing it and clicking the Delete selected item button on the Main toolbar, or choosing Edit/Layers & borders/Delete item on the Main menu, or right-clicking the Layer # item and, then, clicking the Delete selected item command on the context menu.

· Repeat the previous step for all layer items having numbers greater than 2 and choose the Layer 1 item.

· Enter “2” and use the default unit in the Vertical shift between borders field in the Geometry of layer group in the middle (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Enter “0” in the Rms roughness field in the group on the right.

· Enter “0” in the Upper profile horizontal offset field.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “Al2O3_Palik_handbook.ri” file in the …/PCGrate* 6.1/RI directory using the Open dialog window.

· Click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Choose the Layer 2 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field in the Geometry of layer group.

· Enter “0” in the Rms roughness field in the group.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “Al_Palik_handbook.ri” file in the …/PCGrate* 6.1/RI directory using the Open dialog window.

· Click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Click the Check parameters button on the Main toolbar or choose the Calculations & Results/Check item on the Main menu and, then, click the OK button to see the memory requirements in the status pane.

· Open the PCGrate Solver window, clicking its icon on the system tray.

· Choose the Tools/Options item on the Main menu of the PCGrate Solver application.

· Uncheck the Save near field parameters check box in the PCGrate Solver Options dialog window and, then, click the OK button.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 1” as the name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

During the calculations you can see the status information on the solving process in the status pane of the PCGrate* 6.1 Main application (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.1 Solver application is on – see more in Computation Process).

The step-by-step instruction for saving output data files and preparing a graph containing the above listed functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the name of the currently solved problem Grating Example 1 in the tree (by default, the last file name) on the left and open it by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Text reports item in the tree.

· Choose the Input parameters in the Report type combo box in the right upper corner.

· Choose the 140.(0) nm item in the tree on the right.

· Press the Save button.

· Choose the Far field parameters in the Report type combo box.

· Press the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Add graph/table button on the Main toolbar, or choose the Graphs &Tables/Add item on the Main menu, or right-click the Graphs item and, then, click the Add item on the context menu.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Length item.

· Type a name in the Graph name field (or use the default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. length (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button on the right.

· Choose the Absorption (TM) item in the Plot of combo box and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order -2, reflected) item (type “-2” in the field) and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order -1, reflected) item (type “-1” in the field) and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order 0, reflected) item and, then, click the OK button.

· Click the Save graph(s)/table(s) button on the Main toolbar, or choose the Graphs &Tables/Save item on the Main menu, or right-click the saved Graph name item and, then, click the Save item on the context menu.

· Use buttons located to the left of the graph to change display modes of the graph.

Your output text-type files “Grating Example 1 Input Parameters (Wavelength, Range 1, Step 11).txt” and “Grating Example 1 Far Field Parameters (Wavelength, Range 1, Step 11).txt” for the wavelength of 140 nm are stored in the …/PCGrate* 6.1/Results directory. The main output data file “Grating Example 1.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 1 Graphs.dat” and “Grating Example 1 Orders.dat” files are also stored by default in this directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting table in Figure #32.

Example 2: Blazed Transmission Grating for the NP Polarization in the Visible

Input specification:

General tab

Accuracy optimization:

Calculation mode: Resonance

Type of low border conductivity: Finite

Green functions and their normal derivatives: Remainder term, accelerating convergence: On

Logarithmic singularity accounting: On

Profile curvature accounting: Off

Phase jump accounting: On

Number of terms: 50 % of points N

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 100 mm

Groove height: 50 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Frequency: 100 grooves/mm

Beam and mounting geometry:

Wavelength: 500 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: NP ((P + S)/2)

Optical mount configuration: Blazed

Scanning options:

Scanning parameter: Trapezoid left angle

Scan range number: 1

Scan range start value: 5 deg.

Scan range step value: 0.5 deg.

Scan range end value: 19.5 deg.

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Trapezoidal/Triangular

Left angle: 18 deg.

Right angle: 40 deg.

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: On

Layer 1:

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: From library: SiO2_Palik_handbook.ri

Type of inter/extrapolation: Linear

Output specifications:

· Export the “Input parameters”, “Far field parameters”, and “Near field parameters” reports for a point of scan, 18 deg., to MS Excel™.

· Plot the Efficiency of transmitted order function vs. the Order number parameter for scanning steps: 6 deg., 9 deg., 12 deg., 15 deg., and 18 deg.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application.

· Press the General tab in the lower left corner.

· Choose the Accuracy optimization item in the upper left corner.

· Press the Resonance button in the Calculation mode group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Check the Remainder term, accelerating derivatives check box.

· Check the Logarithmic singularity accounting check box.

· Uncheck the Profile curvature accounting check box.

· Check the Phase jump accounting check box.

· Enter “50” in the Number of terms, % of points N field.

· Choose the Grating shape item in the upper left corner.

· Enter “100” and use the default unit in the Grooved width field in the Grating shape parameters group in the upper right corner (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Enter “50” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Press the Frequency button in the unnamed group.

· Enter “100” in the Frequency field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Trapezoidal button.

· Press the Triangular button.

· Enter “18” and use the default unit in the Left angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Enter “40” and use the default unit in the Right angle field.

· Press the Accuracy parameters tab.

· Press the Equal S-interval button in the Type of integration step group.

· Enter “100” in the Number of collocation points N field.

· Check the Using half-segment shift check box.

· Delete a border item having a number greater than 1, if any exists, by choosing it and clicking the Delete selected item button on the Main toolbar, or choosing Edit/Layers & borders/Delete item on the Main menu, or right-clicking the Border # item and, then, clicking the Delete selected item command on the context menu.

· Repeat the previous step for all border items having numbers greater than 1.

· Delete a layer item having a number greater than 1, if any exists, by choosing it and clicking the Delete selected item button on the Main toolbar, or choosing Edit/Layers & borders/Delete item on the Main menu, or right-clicking the Layer # item and, then, clicking the Delete selected item command on the context menu.

· Repeat the previous step for all layer items having numbers greater than 1.

· Choose the Layer 1 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field in the Geometry of layer group in the middle.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “SiO2_Palik_handbook.ri” file in the …/PCGrate* 6.1/RI directory using the Open dialog window.

· Click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Press the General tab in the lower left corner.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “500” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the NP ((P + S)/2) button in the Type of polarization group.

· Press the Blazed button in the Optical mount configuration group.

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Trapezoid left angle item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button on the right.

· Use the default unit and choose the Border 1/Scan range 1 item in the Scanning parameters tree in the middle (to change a unit, choose the Border 1 item and, then, the deg item in the Measurement unit combo-box on the right).

· Enter “5” in the Scan range start value field on the right.

· Enter “0.5” in the Scan range step value field.

· Enter “19.5” in the Scan range end value field.

· Open the PCGrate Solver window, clicking its icon on the system tray.

· Choose the Tools/Options item on the Main menu of the PCGrate Solver application.

· Check the Save near field parameters check box in the PCGrate Solver Options dialog window and, then, click the OK button.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 2” as the name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

During the calculations you can see the status information on the solving process in the status pane of the PCGrate* 6.1 Main application (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.1 Solver application is on – see more in Computation Process).

The step-by-step instruction for saving output data files and preparing a graph containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the name of the solved problem Grating Example 2 in the tree (by default, the last file name) on the left and open it by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Text reports item in the tree.

· Choose the Input parameters in the Report type combo box in the right upper corner.

· Choose the 18.(0) deg item in the tree on the right.

· Press the Export to XLS button in the right upper corner, type a name in the field (or use the default name instead), and, then, click the Save button.

· Choose the Far field parameters in the Report type combo box.

· Press the Export to XLS button in the right upper corner, type a name in the field (or use the default name instead), and, then, click the Save button.

· Choose the Near field parameters in the Report type combo box.

· Press the Export to XLS button in the right upper corner, type a name in the field (or use the default name instead), and, then, click the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Discrete item.

· Type a name in the Graph name field (or use the default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. discrete (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button on the right.

· Choose the Efficiency vs. T. order number item in the Plot of combo box in the Add function to graph dialog window.

· Choose the 6.(0) deg item in the Scanning steps list in the Add function to graph dialog window and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item in the Plot of combo box.

· Choose the 9.(0) deg item in the Scanning steps list and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item.

· Choose the 12.(0) deg item and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item.

· Choose the 15.(0) deg item and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item.

· Choose the 18.(0) deg item and, then, click the OK button.

· Use the buttons located to the left of a graph to change display modes of the graph.

Your output Excel-type files “Grating Example 2 Input Parameters (Trapezoidal left angle, Item 1, Range 1, Step 27).xls”, “Grating Example 2 Far Field Parameters (Trapezoidal left angle, Item 1, Range 1, Step 27).xls”, and “Grating Example 2 Near Field Parameters (Trapezoidal left angle, Item 1, Range 1, Step 27).xls” for the triangular left angle of 18 deg. are stored in the …/PCGrate* 6.1/Exports directory. The main output data file “Grating Example 2.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 2 Graphs.dat” and “Grating Example 2 Orders.dat” files are stored by default in the …/PCGrate* 6.1/Results directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting graph in Figure #34.

Example 3: Non-conformal Au/Dielectric Grating for the NP Polarization in the Visible-IR

Input specification:

General tab

Accuracy optimization:

Calculation mode: Resonance

Type of low border conductivity: Finite

Green functions and their normal derivatives: Remainder term, accelerating convergence: On

Logarithmic singularity accounting: On

Profile curvature accounting: On

Phase jump accounting: On

Number of terms: 67 % of points N

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 100 mm

Groove height: 50 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Frequency: 1000 grooves/mm

Beam and mounting geometry:

Wavelength: 1000 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: NP ((P + S)/2)

Optical mount configuration: Littrow

Littrow order number: -1

Deviation angle: 10 deg.

Scanning options:

Scanning parameter: Wavelength

Scan range number: 1

Scan range start value: 700 nm

Scan range step value: 1 nm

Scan range end value: 850 nm

Scan range number: 2

Scan range start value: 850 nm

Scan range step value: 10 nm

Scan range end value: 1150 nm

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Sine trapezoidal/Sinusoidal

Depth: 125 nm

Accuracy parameters tab

Type of integration step: Equal X-interval

Number of collocation points N: 50

Using half-segment shift: Off

Layer 1:

Vertical shift between borders (layer thickness): 125 nm

Rms roughness: 0 nm

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 2

Im: 0

Border 2:

Function of border profile tab

Type of profiles: Sine trapezoidal/Sinusoidal

Depth: 175 nm

Accuracy parameters tab

Type of integration step: Equal X-interval

Number of collocation points N: 50

Using half-segment shift: Off

Layer 2:

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: From library: Au_Palik_handbook.ri

Type of inter/extrapolation: Cubic spline

Output specifications:

· Use the program’s caching in calculations.

· Save the “Input parameters”, “Far field parameters”, and “Near field parameters” reports for the whole scan range as text files.

· Plot the Efficiency of reflected order # -1, Efficiency (TE) of reflected order # -1, and Efficiency (TM) of reflected order # -1 functions vs. the Wavelength parameter and print the graph.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application.

· Press the General tab in the lower left corner.

· Choose the Accuracy optimization item in the upper left corner.

· Press the Resonance button in the Calculation mode group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Check the Remainder term, accelerating derivatives check box.

· Check the Logarithmic singularity accounting check box.

· Check the Profile curvature accounting check box.

· Check the Phase jump accounting check box.

· Enter “67” in the Number of terms, % of points N field.

· Choose the Grating shape item in the upper left corner.

· Enter “50” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Press the Frequency button in the unnamed group.

· Enter “1000” in the Frequency field.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “1000” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the NP ((P + S)/2) button in the Type of polarization group.

· Press the Littrow button in the Optical mount configuration group.

· Enter “-1” in the Littrow order number field.

· Enter “10” and use the default unit in the Deviation angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Wavelength item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button.

· Click the Add button on the right

· Use the default unit (to change a unit, choose the nm item in the Measurement unit combo-box on the right).

· Choose the Scan range 1 item in the Scanning parameters tree in the middle.

· Enter “700” in the Scan range start value field in the upper right corner.

· Enter “1” in the Scan range step value field.

· Enter “850” in the Scan range end value field.

· Choose the Scan range 2 item in the Scanning parameters tree.

· Enter “1150” in the Scan range end value field.

· Enter “10” in the Scan range step value field.

· Enter “850” in the Scan range start value field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Sine trapezoidal button.

· Press the Sinusoidal button.

· Enter “125” and use the default unit in the Depth field (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Accuracy parameters tab.

· Press the Equal X-interval button in the Type of integration step item.

· Enter “50” in the Number of collocation points N field.

· Uncheck the Using half-segment shift check box.

· Click the Clone selected item button on the Main toolbar, or choose Edit/Layers & borders/Clone item on the Main menu, or right-click the Border 1 item and, then, click the Clone selected item command on the context menu.

· Delete a border item having a number greater than 2, if any exists, by choosing it and clicking the Delete selected item button on the Main toolbar, or choosing Edit/Layers & borders/Delete item on the Main menu, or right-clicking the Border # item and, then, clicking the Delete selected item command on the context menu.

· Repeat the previous step for all border items having numbers greater than 2.

· Delete a layer item having a number greater than 2, if any exists, by choosing it and clicking the Delete selected item button on the Main toolbar, or choosing Edit/Layers & borders/Delete item on the Main menu, or right-clicking the Layer # item and, then, clicking the Delete selected item command on the context menu.

· Repeat the previous step for all layer items having numbers greater than 2.

· Choose the Layer 1 item in the tree on the left.

· Enter “125” and use the default unit in the Vertical shift between borders field in the Geometry of layer group in the middle.

· Enter “0” in the Upper profile horizontal offset field in the group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group.

· Choose the Refractive index item in the upper combo-box in the group.

· Enter “2.0” in the Re field.

· Enter “0” in the Im field.

· Choose the Border 2 item in the tree on the left.

· Press the Function of border profile tab.

· Enter “175” and use the default unit in the Depth field.

· Choose the Layer 2 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Press the Browse button and choose the “Au_Palik_handbook.ri” file in the …/PCGrate* 6.1/RI directory using the Open dialog window.

· Click the Open button.

· Press the Cubic spline button in the Type of inter/extrapolation group.

· Open the PCGrate Solver window, clicking its icon on the system tray.

· Choose the Tools/Options item on the Main menu of the PCGrate Solver application.

· Check the Save near field parameters check box in the PCGrate Solver Options dialog window.

· Check the Enable cache check box and, then, click the OK button.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 3” as a name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

The step-by-step instruction for saving output data files and preparing and printing a graph containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the name of the currently solved problem Grating Example 3 in the tree (by default, the last file name) on the left and open it by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Calculations & results/Full reports/Save text/Input parameters…item on the Main menu or right-click the Text reports item in the tree and, then, select the Save full report/Input parameters… item.

· Type a name in the field (or use default name instead) in the Save As dialog window and click the Save button.

· Choose the Calculations & results/Full reports/Save text/Far field parameters…item on the Main menu or right-click the Text reports item in the tree and, then, select the Save full report/Far field parameters… item.

· Type a name in the field (or use default name instead) in the dialog window and click the Save button.

· Choose the Calculations & results/Full reports/Save text/Near field parameters…item on the Main menu or right-click the Text reports item in the tree and, then, select the Save full report/Near field parameters… item.

· Type a name in the field (or use default name instead) and click the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Length item.

· Type a name in the Graph name field (or use default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. length (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button on the right.

· Choose the Scan range 1 item in the Against group in the Add function to graph dialog window.

· Choose the Efficiency (for order -1, reflected) item (type “-1” in the field) in the Plot of combo box in the dialog window and click the OK button.

· Click the Add function button.

· Choose the Efficiency (TE) (for order -1, reflected) item (type “-1” in the field) in the Plot of combo box and click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order -1, reflected) item (type “-1” in the field) and click the OK button.

· Click the Add function button and choose the Scan range 2 item in the group.

· Choose the Efficiency (for order -1, reflected) item (type “-1” in the field) and click the OK button.

· Click the Add function button and choose the Scan range 2 item.

· Choose the Efficiency (TE) (for order -1, reflected) item (type “-1” in the field) and click the OK button.

· Click the Add function button and choose the Scan range 2 item.

· Choose the Efficiency (TM) (for order -1, reflected) item (type “-1” in the field) and click the OK button.

· Click the Save graph(s)/table(s) button on the Main toolbar, or choose the Graphs &Tables/Save item on the Main menu, or right-click the Real vs. length (#) item and, then, click the Save item on the context menu.

· Use the buttons located to the left of the graph to change display modes of the graph.

· Click the Print button on the Main toolbar, or choose the File/Print item on the Main menu.

· Choose options in the Print dialog window (or use default options instead) and, then, click the OK button.

Your saved text-type files “Grating Example 3 Input Parameters.txt”, “Grating Example 3 Far Field Parameters.txt”, and “Grating Example 3 Near Field Parameters.txt” for the whole wavelength scan range from 700 nm to 1150 nm are stored in the …/PCGrate* 6.1/Results directory. The main output data file “Grating Example 3.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 3 Graphs.dat” and “Grating Example 3 Orders.dat” files are also stored by default in this directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting graph in Figure #35.

Example 4: Rough Sawtooth Mo Grating in Conical Mount for the Elliptically Polarized EUV

Input specification:

General tab

Accuracy optimization:

Calculation mode: Normal

Type of low border conductivity: Perfect

Green functions and their normal derivatives: Remainder term, accelerating convergence: On

Logarithmic singularity accounting: On

Profile curvature accounting: On

Phase jump accounting: On

Number of terms: 50 % of points N

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 100 mm

Groove height: 200 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Frequency: 5000 grooves/mm

Beam and mounting geometry:

Wavelength: 13.5 nm

Wave front type: Plane

Type of diffraction: Conical (off-plane)

Azimuth angle: 74.5 deg.

Type of polarization: General

Polarization angle: 45 deg.

Phase difference: 60 deg.

Optical mount configuration: General

Polar angle: 7.5 deg.

Scanning options:

Scanning parameter # 1: Azimuth angle

Scan range number: 1

Scan range start value: 72 deg.

Scan range step value: 0.1 deg.

Scan range end value: 78 deg.

Scanning parameter # 2: Trapezoid left angle

Scan range number: 1

Scan range start value: 5 deg.

Scan range step value: 0.1 deg.

Scan range end value: 10 deg.

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Trapezoidal/Sawtooth

Left angle: 7.5 deg.

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: Off

Layer 1:

Rms roughness: 5 Å

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: From library: Mo_CXRO_May_2006.ari

Type of inter/extrapolation: Linear

Output specifications:

· Export the “Input parameters” and “Far field parameters” reports for the whole scan ranges to MS Excel™.

· Draw a table for the Energy balance, Energy balance (TE), Energy balance (TM), Reflected energy, Reflected energy (TE), Reflected energy (TM), Efficiency of reflected order # -1, Efficiency (TE) of reflected order # -1, and Efficiency (TM) of reflected order # -1 functions (with four digits after a decimal point) vs. scanning parameters, export the table to MS Excel™, and print it.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application.

· Press the General tab in the lower left corner.

· Choose the Accuracy optimization item in the upper left corner.

· Press the Normal button in the Calculation mode group and, if necessary, click the OK button in the dialog window.

· Press the Perfect button in the Type of low border conductivity group.

· Check the Remainder term, accelerating derivatives check box.

· Check the Logarithmic singularity accounting check box.

· Check the Profile curvature accounting check box.

· Check the Phase jump accounting check box.

· Enter “50” in the Number of terms, % of points N field.

· Choose the Grating shape item in the upper left corner.

· Choose the Plane radio button in the Type of grating shape group in the upper right corner.

· Enter “100” and use the default unit in the Grooved width field in the Grating shape parameters group (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Enter “200” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Press the Frequency button in the unnamed group.

· Enter “5000” in the Frequency field.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “13.5” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Conical (off-plane) button in the Type of diffraction group.

· Enter “78.5” and use the default unit in the Azimuth angle Æ field in the group (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Press the General button in the Type of polarization group.

· Enter “45” and use the default unit in the Polarization angle ´ field in the group.

· Enter “60” and use the default unit in the Phase difference È field.

· Press the General button in the Optical mount configuration group.

· Enter “7.5” and use the default unit in the Polar angle ¸ field in the group.

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Azimuth angle item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button.

· Choose the Trapezoid left angle item in the Parameters available for scanning item.

· Click the “<” button.

· Use the default unit and choose the Scan range 1 item in the Azimuth angle parameter in the Scanning parameters tree in the middle (to change a unit, choose the Azimuth angle item and, then, the deg item in the Measurement unit combo-box on the right).

· Enter “78” in the Scan range end value field on the right.

· Enter “0.1” in the Scan range step value field.

· Enter “72” in the Scan range start value field.

· Choose the Border 1 item in the Trapezoid left angle parameter in the Scanning parameters tree and use the default unit (to change a unit, choose the deg item in the Measurement unit combo-box).

· Choose the Scan range 1 item in the Border 1 item.

· Enter “5” in the Scan range start value field.

· Enter “0.1” in the Scan range step value field.

· Enter “10” in the Scan range end value field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Trapezoidal button.

· Press the Sawtooth button.

· Enter “7.5” and use the default unit in the Left angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Press the Accuracy parameters tab.

· Press the Equal S-interval button in the Type of integration step group.

· Enter “100” in the Number of collocation points N field.

· Uncheck the Using half-segment shift check box.

· Repeat the previous step for all layer items having numbers greater than 1.

· Choose the Layer 1 item in the tree on the left.

· Right-click the nm unit near the Rms roughness field in the Geometry of layer group in the middle and, then, check the A unit on the context menu.

· Enter “5” in the Rms roughness field in the group.

· Enter “0” in the Upper profile horizontal offset field.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the Refractive Index Files In Additional Format (*.ari) item in the Files of type combo box in the Open dialog window.

· Choose the “Mo_CXRO_May_2006.ari” file in the …/PCGrate* 6.1/RI directory and, then, click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Open the PCGrate Solver window, clicking its icon on the system tray.

· Choose the Tools/Options item on the Main menu of the PCGrate Solver application.

· Uncheck the Save near field parameters check box in the PCGrate Solver Options dialog window.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 4” as a name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

During the calculations you can see status information on the solving process in the status pane of the PCGrate* 6.1 Main application (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.1 Solver application is on – see more in Computation Process).

The step-by-step instruction for saving output data files and preparing and printing a table containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose a name of the currently solved problem Grating Example 4 in the tree (by default, the last file name) on the left and open it by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Calculations & results/Full reports/Export to XLS/Input parameters…item on the Main menu or right-click the Text reports item in the tree and, then, select the Export full report to XLS/Input parameters…item.

· Type a name in the field (or use default name instead) in the Save As dialog window and click the Save button.

· Choose the Calculations & results/Full reports/Export to XLS/Far field parameters…item on the Main menu or right-click the Text reports item in the tree and, then, select the Export full report to XLS/Far field parameters…item.

· Type a name in the field (or use default name instead) in the dialog window and click the Save button.

· Choose the Tables item in the tree on the left.

· Click the Add graph/table button on the Main toolbar, or choose the Graphs &Tables/Add item on the Main menu, or right-click the Tables item and, then, click the Add table item on the context menu.

· Type a name in the Table name field (or use default name instead) in the Add table dialog window and click the OK button.

· Choose the <Table name> item in the tree on the left (the sub-graph of the Tables item).

· Click the Add rows button in the upper right corner.

· Open the name of the parameter Azimuth angle in the tree on the right in the Add rows dialog window by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Scan range 1 item in the Azimuth angle parameter.

· Click the “<” button in the middle of the Add rows dialog window.

· Open the name of the parameter Trapezoid left angle in the tree on the right by double-click on the name (or click the “cross” symbol on the left of the name).

· Open the name of the border Border 1 in the tree by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Scan range 1 item in the Border 1 item in the Trapezoid left angle parameter.

· Click the “<” button.

· Click the Ok button in the dialog window.

· Click the Adjust columns button on the right.

· Choose the Energy balance item in the Parameters list in the Adjust columns dialog window.

· Click the “<” button in the middle of the dialog window.

· Choose the Energy balance (TE) item in the Parameters list.

· Click the “<” button in the dialog window.

· Choose the Energy balance (TM) item.

· Click the “<” button.

· Choose the Reflected energy item.

· Click the “<” button.

· Choose the Reflected energy (TE) item.

· Click the “<” button.

· Choose the Reflected energy (TM) item.

· Click the “<” button.

· Choose the Efficiency of order item in the list and type “-1” in the (for order #, reflected) field below.

· Click the “<” button.

· Choose the Efficiency (TE) of order item.

· Click the “<” button.

· Choose the Efficiency (TM) of order item.

· Click the “<” button.

· Click the OK button in the dialog window.

· Right-click the Scan step button, choose the Digits item on the context menu, and click item 1.

· Right-click the Bal. button, choose the Digits item on the context menu, and click item 6.

· Right-click the Bal.(TE) button, choose the Digits item on the context menu, and click item 6.

· Right-click the Bal.(TM) button, choose the Digits item on the context menu, and click item 6.

· Right-click the Refl.En. button, choose the Digits item on the context menu, and click item 4.

· Right-click the Refl.En.(TE) button, choose the Digits item on the context menu, and click item 4.

· Right-click the Refl.En. (TM) button, choose the Digits item on the context menu, and click item 4.

· Right-click the Eff.(-1,R) button, choose the Digits item on the context menu, and click item 4.

· Right-click the Eff.TE(-1,R) button, choose the Digits item on the context menu, and click item 4.

· Right-click the Eff.TM(-1,R) button, choose the Digits item on the context menu, and click item 4.

· Click the Autosize columns button on the right or choose the same item on the context menu by right-click.

· Click the Save graph(s)/table(s) button on the Main toolbar, or choose the Graphs &Tables/Save item on the Main menu, or right-click the <Table name> sub-item in the Tables item in the tree on the left and, then, click the Save item on the context menu.

· Click the Export to XLS button, type a name in the field (or use the default name instead), and, then, click the Save button.

· Click the Print button on the Main toolbar or choose the File/Print item on the Main menu.

· Choose options in the Print dialog window (or use default options instead) and, then, click the OK button.

Your exported Excel-type files “Grating Example 4 Input Parameters.xls”, “Grating Example 4 Far Field Parameters.xls”, and “Grating Example 4 Table ‘Table #’” for the whole scan ranges are stored in the …/PCGrate* 6.1/Exports directory. The main output data file “Grating Example 4.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 4 Tables.dat” and “Grating Example 4 Orders.dat” files are stored by default in the…/PCGrate* 6.1/Results directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting table Figure #23.

Example 5: Real Groove Profile Echelle Grating for the TE Polarization in the Visible

Input specification:

General tab

Accuracy optimization:

Calculation mode: Resonance

Type of low border conductivity: Perfect

Green functions and their normal derivatives: Remainder term, accelerating convergence: On

Logarithmic singularity accounting: On

Profile curvature accounting: On

Phase jump accounting: On

Number of terms: 50 % of points N

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 258 mm

Groove height: 128 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Frequency: 112.96 grooves/mm

Beam and mounting geometry:

Wavelength: 577 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: TE

Optical mount configuration: General

Polar angle: 78 deg.

Scanning options:

Scanning parameter: Polar angle

Scan range number: 1

Scan range start value: 65 deg.

Scan range step value: 0.5 deg.

Scan range end value: 85 deg.

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Polygonal: RG_real_echelle.ggp

Number of segments: 99

Height (relative to period): 0.205298293

Profile scaling coefficient (polygonal): 1.0

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: Off

Layer 1:

Refractive index/Electric permittivity origin: Presetting

Refractive index: Re: 0

Im:

Output specifications:

· Export the “Table” report about the diffraction orders parameters for a point of scan, 78 deg., to MS Excel™.

· Plot the Efficiency (TE) of reflected orders # -30, # -29, and # -28 functions vs. Polar angle parameter.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application.

· Press the General tab in the lower left corner.

· Choose the Accuracy optimization item in the upper left corner.

· Press the Resonance button in the Calculation mode group and, then, if necessary, click the OK button in the dialog window.

· Press the Perfect button in the Type of low border conductivity group.

· Check the Remainder term, accelerating derivatives check box.

· Check the Logarithmic singularity accounting check box.

· Check the Profile curvature accounting check box.

· Check the Phase jump accounting check box.

· Enter “50” in the Number of terms, % of points N field.

· Choose the Grating shape item in the upper left corner.

· Enter “258” and use the default unit in the Grooved width field in the Grating shape parameters group in the upper right corner (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Enter “128” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Press the Frequency button in the unnamed group.

· Enter “112.96” in the Frequency field.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “577” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the TE (P) button in the Type of polarization group.

· Press the General button in the Optical mount configuration group.

· Enter “78” and use the default unit in the Polar angle field in the group (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Polar angle item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button.

· Use the default unit and choose the Scan range 1 item in the Scanning parameters tree in the middle (to change a unit, choose the Polar angle item and, then, the deg item in the Measurement unit combo-box on the right).

· Enter “85” in the Scan range end value field on the right.

· Enter “0.5” in the Scan range step value field.

· Enter “65” in the Scan range end value field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Polygonal button.

· Press the Load border profile button on the right (with the green arrow), choose the “AFM_real_echelle.grt” file in the Open dialog window and, then, click the Open button.

· Enter “1.0” in the Profile scaling coefficient field.

· Press the Accuracy parameters tab.

· Press the Equal S-interval button in the Type of integration step group.

· Enter “100” in the Number of collocation points N field.

· Uncheck the Using half-segment shift check box.

· Repeat the previous step for all border items having numbers greater than 1.

· Repeat the previous step for all layer items having numbers greater than 1.

· Choose the Layer 1 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field in the Geometry of layer group on the right.

· Open the PCGrate Solver window, clicking its icon on the system tray.

· Choose the Tools/Options item on the Main menu of the PCGrate Solver application.

· Uncheck the Save near field parameters check box in the PCGrate Solver Options dialog window.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 5” as a name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

During the calculations you can see status information on the solving process in the status pane of the PCGrate-* 6.1 Main application (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.1 Solver application is on – see more in Computation Process).

The step-by-step instruction for saving output data files and preparing a graph containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the name of the currently solved problem Grating Example 5 in the tree (by default, the last file name) on the left and open it by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Table report item in the tree.

· Choose the Reflected orders in the Report type combo box in the right upper corner.

· Choose the 78.(0) deg item in the tree on the right.

· Press the Export to XLS…button, type a name in the field (or use default name instead), and, then, click the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box and, then, choose the Angle item.

· Type a name in the Graph name field (or use default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. length (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button on the right.

· Click the Plot of combo box in the Add function to graph dialog window and, then, choose the Efficiency (TE) (for order -30 reflected) item.

· Click the OK button in the dialog window.

· Click the Add function button.

· Click the Plot of combo box in the Add function to graph dialog window and, then, choose the Efficiency (TE) (for order -29 reflected) item.

· Click the OK button.

· Click the Add function button.

· Click the Plot of combo box in the Add function to graph dialog window and, then, choose the Efficiency (TE) (for order -28 reflected) item.

· Click the OK button.

Your output Excel-type files “PCGrate Problem 5 Reflected orders (Polar angle, Range 1, Step 27.xls)” for the incident polar angle of 78 deg. is stored in the …/PCGrate* 6.1/Exports directory. The main output data file “Grating Example 5.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 5 Graphs.dat” and “Grating Example 5 Orders.dat” files are stored by default in the …/PCGrate* 6.1/Results directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting graph in Figure #37.

Example 6: Binary Phase High-Conductive Grating for the NP Polarization in the Near IR

Input specification:

General tab

Accuracy optimization:

Calculation mode: Resonance

Type of low border conductivity: Finite

Green functions and their normal derivatives: Remainder term, accelerating convergence: Off

Logarithmic singularity accounting: Off

Profile curvature accounting: On

Phase jump accounting: Off

Number of terms: 50 % of points N

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 2 mm

Groove height: 0.5 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Period: 2000 nm

Beam and mounting geometry:

Wavelength: 780 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: NP ((P + S)/2)

Optical mount configuration: Bragg

Bragg order number: 0

Deviation angle: 30 deg.

Scanning options:

Scanning parameter: Imaginary part of electric permittivity

Layer group: 1 (layers 1 to 1, step 0)

Scan range number: 1

Scan range start value: 0

Scan range step value: 1

Scan range end value: 40

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Electric permittivity: Re: 2.89

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Sine trapezoidal/Sinusoidal

Depth: 0 nm

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: Off

Layer 1:

Vertical shift between borders (layer thickness): 500 nm

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: Custom

Electric permittivity: Re: –100

Im: 0

Border 2:

Function of border profile tab

Type of profiles: Trapezoidal/General

Land: 1000 nm

Depth: 499.8 nm

Left angle: 89.99 deg.

Right angle: 89.99 deg.

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: Off

Layer 2:

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: Custom

Electric permittivity: Re: 1

Im: 0

Output specifications:

· Plot the Efficiency of transmitted order # -1, # 0, Efficiency (TE) of transmitted order # -1, # 0, and Efficiency (TM) of transmitted order # -1, # 0 functions vs. the Real part of electric permittivity parameter and export the plotted graph to MS Excel™.

· Copy the plotted graph to the clipboard in MS Metafile format.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application.

· Press the General tab in the lower left corner.

· Choose the Accuracy optimization item in the upper left corner.

· Press the Resonance button in the Calculation mode group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Uncheck the Remainder term, accelerating derivatives check box.

· Uncheck the Logarithmic singularity accounting check box.

· Check the Profile curvature accounting check box.

· Uncheck the Phase jump accounting check box.

· Enter “50” in the Number of terms, % of points N field.

· Choose the Grating shape item in the upper left corner.

· Enter “2” and use the default unit in the Grooved width field in the Grating shape parameters group in the upper right corner (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Enter “0.5” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Press the Period button in the unnamed group.

· Enter “2000” and use the default unit in the Period field.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “780” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the NP ((P + S)/2) button in the Type of polarization group.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Choose the Electric permittivity item in the upper combo-box in the Refractive index/Electric permittivity group.

· Enter “2.89” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Sine trapezoidal button.

· Press the Sinusoidal button.

· Enter “0” in the Depth field.

· Press the Accuracy parameters tab.

· Press the Equal S-interval button in the Type of integration step group.

· Enter “100” in the Number of collocation points N field.

· Uncheck the Using half-segment shift check box.

· Repeat the previous step for all border items having numbers greater than 2.

· Repeat the previous step for all layer items having numbers greater than 2.

· Choose the Layer 1 item in the tree on the left.

· Enter “500” and use the default unit in the Vertical shift between borders field in the Geometry of layer group in the middle (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Enter “0” in the Upper profile horizontal offset field in the group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group.

· Choose the Electric permittivity item in the upper combo-box in the group.

· Enter “-100” in the Re field.

· Enter “0” in the Im field.

· Choose the Border 2 item in the tree on the left.

· Press the Function of border profile tab on the right.

· Press the Trapezoidal button.

· Press the General button.

· Enter “89.99” and use the default unit in the Left angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Enter “89.99” and use the default unit in the Right angle field.

· Enter “1000” and use the default unit in the Land field (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Enter “499.8” and use the default unit in the Depth field.

· Choose the Layer 2 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field in the Geometry of layer group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group.

· Choose the Electric permittivity item in the upper combo-box.

· Enter “2.89” in the Re field in the group.

· Enter “0” in the Im field.

· Press the General tab in the lower left corner on the right.

· Press the Bragg button in the Optical mount configuration group.

· Enter “0” in the Bragg order number field in the group.

· Enter “30” in the Deviation angle field.

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Real part of electric permittivity item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button on the right.

· Choose the Layer group # item in the Scanning parameters tree in the middle, press it and, then, type “1” in the field.

· Enter “1” in the Layer interval start value field on the right.

· Enter “0” in the Layer interval step value field.

· Enter “1” in the Layer interval end value field.

· Choose the Scan range 1 item in the Scanning parameters tree (sub-item of the Layer group 1 item).

· Enter “0” in the Scan range start value field.

· Enter “1” in the Scan range step value field.

· Enter “40” in the Scan range end value field.

· Open the PCGrate Solver window, clicking its icon on the system tray.

· Choose the Tools/Options item on the Main menu of the PCGrate Solver application.

· Uncheck the Enable cache check box and, then, click the OK button.

· Uncheck the Save near field parameters check box in the PCGrate Solver Options dialog window and, then, click the OK button.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 6” as the name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

The step-by-step instruction for preparing, exporting, and coping a graph containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the name of the solved problem Grating Example 6 in the tree (by default, the last file name) on the left and open it by double-click on the name (or click the “cross” symbol on the left of the name).

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Real item.

· Type a name in the Graph name field (or use the default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. real (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button on the right.

· Choose the Efficiency (for order -1 transmitted) item in the Plot of combo box in the Add function to graph dialog window and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TE) (for order -1 transmitted) item in the Plot of combo box and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order -1 transmitted) item in the Plot of combo box and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (for order 0 transmitted) item in the Plot of combo box in the Add function to graph dialog window and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TE) (for order 0 transmitted) item in the Plot of combo box and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order 0 transmitted) item in the Plot of combo box and, then, click the OK button.

· Use the buttons located to the left of a graph to change display modes of the graph.

· Press the Export to XLS button on the right and, then, press the Save button in the Save As dialog window.

· Click the Copy button on the Main toolbar, or choose the Edit/Copy item on the Main menu, or right-click on the graph and, then, click the Copy item on the context menu.

Your exporting Excel-type graph “Grating Example 6 Graph `Real vs. Real (#)’” is stored in the …/PCGrate* 6.1/Exports directory. Your coping Metafile-type graph is stored in the Clipboard and you can place it into a file using the Paste command. The main output data file “Grating Example 6.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 6 Graphs.dat” and “Grating Example 6 Orders.dat” files are stored by default in the …/PCGrate* 6.1/Results directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting graph in Figure #38.

Example 0: Sawtooth High-Conductive Grating for the TE Polarization in the Near UV-IR

Input specification:

General tab

Accuracy optimization:

Calculation mode: Normal

Type of low border conductivity: Perfect

Green functions and their normal derivatives: Remainder term, accelerating convergence: On

Logarithmic singularity accounting: On

Profile curvature accounting: On

Phase jump accounting: On

Number of terms: 50 % of points N

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 100 mm

Groove height: 50 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Frequency: 1000 grooves/mm

Beam and mounting geometry:

Wavelength: 800 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: TE(P)

Optical mount configuration: General

Polar angle: 40 deg.

Scanning options:

Scanning parameter: Wavelength

Scan range number: 1

Scan range start value: 200 nm

Scan range step value: 25 nm

Scan range end value: 1500 nm

Layers tab

Layer 0:

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Trapezoidal/Sawtooth

Left angle: 15 deg.

Accuracy parameters tab

Type of integration step: Equal S-interval

Number of collocation points N: 100

Using half-segment shift: Off

Layer 1:

Rms roughness: 0 nm

Upper profile horizontal offset: 0

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 10

Output specifications:

· Convert the input parameters from the GUI format to the XML format.

· Run calculations from a command line using the ConsoleSolver.exe utility and view results using any XML browser.

The step-by-step instruction for exporting to XML the above listed grating and light parameters (in accordance with the input specification), running calculations using the command line, and viewing results follows further.

· Run (open) a new window (grating) of the Main application by clicking on its icon. The grating and light parameters in accordance with the input specification are running by default.

· Click the Export to XML button on the Main toolbar, or choose the File/Export to XML item on the Main menu.

· Choose …/PCGrate* 6.1/Console Solver as the saved directory and XML for the file type in the Save As dialog window and, then, enter “Grating_Example_0” in the File name field.

· Click the Save button in the dialog window and, if necessary, click the Yes button in the next dialog window to replace the existing file.

· Run the Start/All Programs/Accessories/Command Prompt command from the Windows Start menu.

· Type “cd c:\program files\I. I. G. Inc\PCGrate* 6.1\Console Solver” in the Command Prompt window and click the Enter button.

· Start the PCGrate* 6.1 Solver application by pressing the Check parameters button on the Main toolbar of the Main application, or choosing the Calculations & Results/Check item on the Main menu, or typing “consolesolver.exe -run” in the Command Prompt window and, then, clicking the Enter button.

· Type “ConsoleSolver.exe -s Grating_example_0.xml” in the Command Prompt window and, then, clicking the Enter button. The calculation starts using the Console Solver application.

· Find calculation results with the default name Grating_example_0_results.xml in the …/PCGrate* 6.1/Console Solver directory when the calculation finished.

· View the resulting XML-type file Grating_example_0_results.xml by clicking on it. Your default XML browser will open the file, or you can use your default Internet browser to open files with the XML extension.

During the calculations you can see the status information on the solving process in the Command Prompt window (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.1 Solver application is on – see more in Computation Process). You can see an example of resulting data in the XML format. You can see an example of resulting graph in Figure #40.

Introduction to v. 6.2

This sub-section presents ten step-by-step examples of brief calculations of frequently used grating efficiency problems with scanning in varied parameters. PCGrate-S(X) v.6.2 series software enables high-speed calculation of both multilayer resonance and small wavelength-to-period ratio cases using one of the two independent solvers, i.e. Penetrating and Separating. The last is primarily intended for efficiency calculations for any uncoated, including rough and high-conductive, gratings and mirrors, specific types of coated gratings, and photonic crystals. A few examples of such efficiency calculations of large-period grisms, randomly rough ruled gratings, and 2-D photonic crystals are added for using with all types of PCGrate-S(X) v. 6.2 software including Demo. The input “grt”-type data files, which can be run by the PCGrate Demo v. 6.2 Complete type software are stored in the …/PCGrate-S*/Examples directory as well as in the separate archive file that can be downloaded at http://www.iigrate.com/loadpurc/download . The information on preparing and saving the input data and on plotting output graphs for the selected samples is also included.

On our website at http://www.iigrate.com/etestlab/ or http://www.iigrate.com/etestlab/ you can find more computation examples using the PCGrate-S(X) v. 6.2 programs with data files, plots, and tables.

Also, keep in mind !

IMPORTANT NOTE

If you change one Solver type for another, all parameters of the grating except the scanning parameters will be set to their default values. Therefore, during the change of Solver type you will see a confirmation window.

Example 1: Ruled Spherical Al/Al2O3 Grating for the TM Polarization in the VUV

Input specification:

General tab

Solver optimizing:

Solver type: Penetrating

Type of low border conductivity: Finite

Accuracy optimization: Accelerating convergence: On

Equal S-interval: On

Number of collocation points: 100

Maximal number of accountable +/- terms: 50

Solver options: Enable cache: On

Enable paralleling: On

Save near field parameters: Off

Grating shape:

Type of grating shape: Spherical

Grating shape parameters: Grooved width: 50 mm

Groove height: 50 mm

Meridional radius: 200 mm

Number of plane sections: Meridional: 3

Sagittal: 3

Beam and mounting geometry:

Wavelength: 140 nm

Wave front type: Spherical

Wave radius: 97 mm

Type of diffraction: Classical (in-plane)

Type of polarization: TM(S)

Frequency: 3600 /mm

Optical mount configuration: Littrow

Littrow order number: -1

Deviation angle: 0 deg.

Scanning options:

Scanning parameter: Wavelength

Scan range number: 1

Scan range start value: 90 nm

Scan range step value: 5 nm

Scan range end value: 190 nm

Scan range number of collocation points: 100

Layers tab

Layer 0:

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Trapezoidal/Sawtooth

Left angle: 9 deg.

Classical ruled profile changing: On

Layer 1:

Vertical shift between borders (layer thickness): 2 nm

Upper profile horizontal offset: 0 nm

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: From library: Al2O3_Palik_handbook.ri

Type of inter/extrapolation: Linear

Layer 2:

Upper profile horizontal offset: 0 nm

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: From library: Al_Palik_handbook.ri

Type of inter/extrapolation: Linear

Output specifications:

· Save the “Input parameters” and “Far field parameters” reports for a point of scan, 140 nm, as text files.

· Plot the Absorption (TM), and Efficiency (TM) of reflected order # -2, # -1, and # 0 functions vs. the Wavelength parameter.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application in a new window by clicking on its icon.

· Press the General tab in the lower left corner.

· Choose the Solver optimizing item in the upper left corner.

· Press the Penetrating button in the Solver type group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Press the Accelerating convergence button in the Accuracy optimization group.

· Press the Equal S-interval button in the group.

· Enter “100” in the Number of collocation points field.

· Enter “50” in the Number of accountable +/- terms or orders field.

· Check the Enable cache check box in the Solver options group.

· Check the Enable paralleling check box in the group.

· Uncheck the Save near field parameters check box.

· Choose the Grating shape item in the upper left corner.

· Choose the Spherical radio button in the Type of grating shape group in the upper right corner.

· Enter “50” and use the default unit in the Groove height field in the group..

· Enter “200” and use the default unit in the Meridional radius field.

· Enter “3” in the Meridional field in the Number of plane sections group.

· Enter “3” in the Sagittal field in the group.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “140” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Spherical button in the Wave front type group.

· Enter “97” and use the default unit in the Wave radius field in the group (to change a unit, right-click the unit and, then, check the mm unit on the context menu).

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the TM (S) button in the Type of polarization group.

· Press the Frequency button in the group.

· Enter “3600” in the Frequency field.

· Press the Littrow button in the Optical mount configuration group.

· Enter “–1” in the Littrow order number field in the group.

· Enter “0” in the Deviation angle field.

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Wavelength item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button.

· Use the default unit and choose the Scan range 1 item in the Scanning parameters tree in the middle (to change a unit, choose the Wavelength item and, then, the nm item in the Measurement unit combo-box on the right).

· Enter “90” in the Scan range start value field on the right.

· Enter “5” in the Scan range step value field.

· Enter “190” in the Scan range end value field on the right.

· Enter “100” in the Scan range number of collocation points field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Enter “1.0” in the Re field in the Magnetic permeability group on the right.

· Enter “0” in the Im field in the group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Trapezoidal button.

· Press the Sawtooth button.

· Enter “9” and use the default unit in the Left angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Check the Classical ruled profile changing check box.

· Choose the Layer 1 item in the tree on the left.

· Repeat the previous step for all layer items having numbers greater than 2 and choose the Layer 1 item.

· Enter “0” in the Upper profile horizontal offset field in the group.

· Enter “1.0” in the Re field in the Magnetic permeability group.

· Enter “0” in the Im field in the group.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “Al2O3_Palik_handbook.ri” file in the …/PCGrate* 6.2/RefractiveIndices directory using the Open dialog window.

· Click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Choose the Layer 2 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field in the Geometry of layer group.

· Enter “1.0” in the Re field in the Magnetic permeability group.

· Enter “0” in the Im field in the group.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “Al_Palik_handbook.ri” file in the …/PCGrate* 6.2/RefractiveIndices directory using the Open dialog window.

· Click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 1” as the name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

During the calculations you can see the status information on the solving process in the status pane of the PCGrate* 6.2 Main application (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.2 Solver application is on – see more in Computation Process).

The step-by-step instruction for saving output data files and preparing a graph containing the above listed functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the Text reports item in the tree.

· Choose the Input parameters in the Report type combo box in the right upper corner.

· Choose the 140.(0) nm item in the tree on the right.

· Press the Save button.

· Choose the Far field parameters in the Report type combo box.

· Press the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Length item.

· Type a name in the Graph name field (or use the default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. length (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button in the upper right corner.

· Choose the Absorption (TM) item in the Plot of combo box and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order –2, reflected) item (type “–2” in the field and choose “reflected” in the combo box) and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order –1, reflected) item (type “–1” in the field) and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency (TM) (for order 0, reflected) item and, then, click the OK button.

· Use buttons located to the left of the graph to change display modes of the graph.

Your output text-type files “Grating Example 1 Input Parameters (Wavelength, Range 1, Step 11).txt” and “Grating Example 1 Far Field Parameters (Wavelength, Range 1, Step 11).txt” for the wavelength of 140 nm are stored in the …/PCGrate* 6.2/Results directory. The main output data file “Grating Example 1.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 1 Graphs.dat” and “Grating Example 1 Orders.dat” files are also stored by default in this directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting graph in Figure #33.

Example 2: Blazed Transmission Grating for the NP Polarization in the Visible

Input specification:

General tab

Solver optimizing:

Solver type: Penetrating

Type of low border conductivity: Finite

Accuracy optimization: Accelerating convergence: On

Equal S-interval: On

Number of collocation points: 100

Maximal number of accountable +/- terms: 50

Solver options: Enable cache: On

Enable paralleling: On

Save near field parameters: On

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 100 mm

Groove height: 50 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Beam and mounting geometry:

Wavelength: 500 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: NP ((P+S)/2)

Frequency: 100 /mm

Optical mount configuration: Blazed

Scanning options:

Scanning parameter: Trapezoid left angle

Scan range number: 1

Scan range start value: 5 deg.

Scan range step value: 0.5 deg.

Scan range end value: 19.5 deg.

Scan range number of collocation points: 100

Layers tab

Layer 0:

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Trapezoidal/Triangular

Left angle: 18 deg.

Right angle: 40 deg.

Layer 1:

Upper profile horizontal offset: 0 nm

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: From library: SiO2_Palik_handbook.ri

Type of inter/extrapolation: Linear

Output specifications:

· Export the “Input parameters”, “Far field parameters”, and “Near field parameters” reports for a point of scan, 18 deg., to MS Excel™.

· Plot the Efficiency of transmitted order function vs. the Order number parameter for scanning steps: 6 deg., 9 deg., 12 deg., 15 deg., and 18 deg.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application in a new window by clicking on its icon.

· Press the General tab in the lower left corner.

· Choose the Solver optimizing item in the upper left corner.

· Press the Penetrating button in the Solver type group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Press the Accelerating convergence button in the Accuracy optimization group.

· Press the Equal S-interval button in the group.

· Enter “100” in the Number of collocation points field.

· Enter “50” in the Number of accountable +/- terms or orders field.

· Check the Enable cache check box in the Solver options group.

· Check the Enable paralleling check box in the group.

· Check the Save near field parameters check box.

· Choose the Grating shape item in the upper left corner.

· Choose the Plane radio button in the Type of grating shape group in the upper right corner.

· Enter “50” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Enter “1.0” in the Re field in the Magnetic permeability group on the right.

· Enter “0” in the Im field in the group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab on the right.

· Press the Trapezoidal button.

· Press the Triangular button.

· Enter “18” and use the default unit in the Left angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Enter “40” and use the default unit in the Right angle field.

· Repeat the previous step for all border items having numbers greater than 1.

· Repeat the previous step for all layer items having numbers greater than 1.

· Choose the Layer 1 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field in the Geometry of layer group in the middle.

· Enter “1.0” in the Re field in the Magnetic permeability group on the right.

· Enter “0” in the Im field in the group.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “SiO2_Palik_handbook.ri” file in the …/PCGrate* 6.2/RefractiveIndices directory using the Open dialog window.

· Click the Open button.

· Press the Linear button in the Type of inter/extrapolation group.

· Press the General tab in the lower left corner.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “500” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the NP ((P+S)/2) button in the Type of polarization group.

· Press the Frequency button in the group.

· Enter “100” in the Frequency field.

· Press the Blazed button in the Optical mount configuration group.

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Trapezoid left angle item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button on the right.

· Use the default unit and choose the Scan range 1 item in the Scanning parameters tree in the middle (to change a unit, choose the Border 1 item and, then, the deg item in the Measurement unit combo-box on the right).

· Enter “5” in the Scan range start value field.

· Enter “0.5” in the Scan range step value field.

· Enter “19.5” in the Scan range end value field on the right.

· Enter “100” in the Scan range number of collocation points field.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 2” as the name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

During the calculations you can see the status information on the solving process in the status pane of the PCGrate* 6.2 Main application (if the Enable Status Sending flag on The Tools Menu of the PCGrate* 6.2 Solver application is on – see more in Computation Process).

The step-by-step instruction for saving output data files and preparing a graph containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Choose the Text reports item in the tree.

· Choose the Input parameters in the Report type combo box in the upper right corner.

· Choose the 18.(0) deg item in the tree on the right.

· Press the Export to XLS button in the upper right corner, type a name in the field (or use the default name instead), and, then, click the Save button.

· Choose the Far field parameters in the Report type combo box.

· Press the Export to XLS button in the upper right corner, type a name in the field (or use the default name instead), and, then, click the Save button.

· Choose the Near field parameters in the Report type combo box.

· Press the Export to XLS button in the upper right corner, type a name in the field (or use the default name instead), and, then, click the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Discrete item.

· Type a name in the Graph name field (or use the default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. discrete (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button in the upper right corner.

· Choose the Efficiency vs. T. order number item in the Plot of combo box in the Add function to graph dialog window.

· Choose the 6.(0) deg item in the Scanning steps list in the Add function to graph dialog window and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item in the Plot of combo box.

· Choose the 9.(0) deg item in the Scanning steps list and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item.

· Choose the 12.(0) deg item and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item.

· Choose the 15.(0) deg item and, then, click the OK button.

· Click the Add function button.

· Choose the Efficiency vs. T. order number item.

· Choose the 18.(0) deg item and, then, click the OK button.

· Use the buttons located to the left of a graph to change display modes of the graph.

Your output Excel-type files “Grating Example 2 Input Parameters (Trapezoidal left angle, Item 1, Range 1, Step 27).xls”, “Grating Example 2 Far Field Parameters (Trapezoidal left angle, Item 1, Range 1, Step 27).xls”, and “Grating Example 2 Near Field Parameters (Trapezoidal left angle, Item 1, Range 1, Step 27).xls” for the triangular left angle of 18 deg. are stored in the …/PCGrate* 6.2/Exports directory. The main output data file “Grating Example 2.pcg” that contains all the necessary information on the problem as well as the additional “Grating Example 2 Graphs.dat” and “Grating Example 2 Orders.dat” files are stored by default in the …/PCGrate* 6.2/Results directory, but you can copy (obtain) these files to (from) any directory using the program’s Main menu “Calculations & Results/Results file/Copy to (Obtain from)” item or right-clicking the context menu and choosing the same item (see The Results Tab). You can see an example of resulting graph in Figure #34.

Example 3: Nonconformal Au/Dielectric Grating for the NP Polarization in the Visible-NIR

Input specification:

General tab

Solver optimizing:

Solver type: Penetrating

Type of low border conductivity: Finite

Accuracy optimization: Accelerating convergence: On

Equal X-interval: On

Number of collocation points: 50

Maximal number of accountable +/- terms: 33

Solver options: Enable cache: On

Enable paralleling: On

Save near field parameters: On

Grating shape:

Type of grating shape: Plane

Grating shape parameters: Grooved width: 100 mm

Groove height: 50 mm

Number of plane sections: Meridional: 1

Sagittal: 1

Beam and mounting geometry:

Wavelength: 1000 nm

Wave front type: Plane

Type of diffraction: Classical (in-plane)

Type of polarization: NP ((P+S)/2)

Frequency: 1000 /mm

Optical mount configuration: Littrow

Littrow order number: -1

Deviation angle: 10 deg.

Scanning options:

Scanning parameter: Wavelength

Scan range number: 1

Scan range start value: 700 nm

Scan range step value: 1 nm

Scan range end value: 850 nm

Scan range number of collocation points: 66

Scan range number: 2

Scan range start value: 850 nm

Scan range step value: 10 nm

Scan range end value: 1150 nm

Scan range number of collocation points: 50

Layers tab

Layer 0:

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 1

Im: 0

Border 1:

Function of border profile tab

Type of profiles: Sine trapezoidal/Sinusoidal

Depth: 125 nm

Layer 1:

Vertical shift between borders (layer thickness): 125 nm

Upper profile horizontal offset: 0 nm

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: Custom

Refractive index: Re: 2

Im: 0

Border 2:

Function of border profile tab

Type of profiles: Sine trapezoidal/Sinusoidal

Depth: 175 nm

Layer 2:

Upper profile horizontal offset: 0

Magnetic permeability: Re: 1

Im: 0

Refractive index/Electric permittivity origin: From library: Au_Palik_handbook.ri

Type of inter/extrapolation: Cubic spline

Output specifications:

· Use the program’s caching in calculations.

· Save the “Input parameters”, “Far field parameters”, and “Near field parameters” reports for the whole scan range as text files.

The step-by-step instruction for entering the above listed grating and light parameters (in accordance with the input specification), running calculations, and saving results follows further.

· Run (open) the Main application in a new window by clicking on its icon.

· Press the General tab in the lower left corner.

· Choose the Solver optimizing item in the upper left corner.

· Press the Penetrating button in the Solver type group and, if necessary, click the OK button in the dialog window.

· Press the Finite button in the Type of low border conductivity group.

· Press the Accelerating convergence button in the Accuracy optimization group.

· Press the Equal S-interval button in the group.

· Enter “50” in the Number of collocation points field.

· Enter “33” in the Number of accountable +/- terms or orders field.

· Check the Enable cache check box in the Solver options group.

· Check the Enable paralleling check box in the group.

· Check the Save near field parameters check box.

· Choose the Grating shape item in the upper left corner.

· Choose the Plane radio button in the Type of grating shape group in the upper right corner.

· Enter “50” and use the default unit in the Groove height field in the group.

· Enter “1” in the Meridional field in the Number of plane sections group.

· Enter “1” in the Sagittal field in the group.

· Choose the Beam and mounting geometry item in the upper left corner.

· Enter “1000” and use the default unit in the Wavelength field in the upper right corner (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Press the Plane button in the Wave front type group.

· Press the Classical (in-plaine) button in the Type of diffraction group.

· Press the NP ((P+S)/2) button in the Type of polarization group.

· Press the Frequency button in the group.

· Enter “1000” in the Frequency field.

· Press the Littrow button in the Optical mount configuration group.

· Enter “–1” in the Littrow order number field in the group..

· Enter “10” and use the default unit in the Deviation angle field (to change a unit, right-click the unit and, then, check the deg unit on the context menu).

· Choose the Scanning options item in the upper left corner.

· Choose the ±-item in the Scanning parameters tree in the middle.

· Click the “>” button on the right.

· Repeat the previous two steps until nothing is left in the Scanning parameters field.

· Choose the Wavelength item in the list of parameters in the Parameters available for scanning item on the right.

· Click the “<” button.

· Click the Add button on the right

· Enter “700” in the Scan range start value field in the upper right corner.

· Enter “1” in the Scan range step value field.

· Enter “850” in the Scan range end value field.

· Enter “66” in the Scan range number of collocation points field.

· Choose the Scan range 2 item in the Scanning parameters tree. Use the default unit.

· Enter “1150” in the Scan range end value field.

· Enter “10” in the Scan range step value field.

· Enter “850” in the Scan range start value field.

· Enter “50” in the Scan range number of collocation points field.

· Press the Layers tab in the lower left corner.

· Choose the Layer 0 item in the tree on the left.

· Enter “1.0” in the Re field in the Magnetic permeability group on the right.

· Enter “0” in the Im field in the group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group in the middle.

· Enter “1.0” in the Re field in the group.

· Enter “0” in the Im field.

· Choose the Border 1 item in the tree on the left.

· Press the Function of border profile tab in the middle.

· Press the Sine trapezoidal button.

· Press the Sinusoidal button.

· Enter “125” and use the default unit in the Depth field (to change a unit, right-click the unit and, then, check the nm unit on the context menu).

· Delete a border item having a number greater than 2, if any exists, by choosing it and clicking the Delete selected item button on the Main toolbar, or choosing Edit/Layers & borders/Delete item on the Main menu, or right-clicking the Border # item and, then, clicking the Delete selected item command on the context menu.

· Repeat the previous step for all border items having numbers greater than 2.

· Repeat the previous step for all layer items having numbers greater than 2.

· Choose the Layer 1 item in the tree on the left.

· Enter “125” and use the default unit in the Vertical shift between borders field in the Geometry of layer group in the middle.

· Enter “0” in the Upper profile horizontal offset field in the group.

· Enter “1.0” in the Re field in the Magnetic permeability group.

· Enter “0” in the Im field in the group.

· Choose the Custom item in the lower combo-box in the Refractive index/Electric permittivity group.

· Choose the Refractive index item in the upper combo-box in the group.

· Enter “2.0” in the Re field.

· Enter “0” in the Im field.

· Choose the Border 2 item in the tree on the left.

· Press the Function of border profile tab.

· Enter “175” and use the default unit in the Depth field.

· Choose the Layer 2 item in the tree on the left.

· Enter “0” in the Upper profile horizontal offset field.

· Enter “1.0” in the Re field in the Magnetic permeability group.

· Enter “0” in the Im field in the group.

· Choose the Refractive index item in the upper combo-box in the Refractive index/Electric permittivity group.

· Choose the From library item in the lower combo-box in the group.

· Choose (or press the Browse button before) the “Au_Palik_handbook.ri” file in the …/PCGrate* 6.2/RefractiveIndices directory using the Open dialog window.

· Click the Open button.

· Press the Cubic spline button in the Type of inter/extrapolation group.

· Click the Start calculations button on the Main toolbar or choose the Calculations & Results/Start item on the Main menu.

· Type “Grating Example 3” as a name of the solved problem in the field (instead of default name) and click the Save button when the PCGrate problem solved dialog window appears.

The step-by-step instruction for saving output data files and preparing and printing a graph containing the above-described functions (in accordance with the output specification) follows further.

· Run (open) the Main application.

· Press the Results tab in the lower left corner.

· Type a name in the field (or use default name instead) in the Save As dialog window and click the Save button.

· Type a name in the field (or use default name instead) in the dialog window and click the Save button.

· Type a name in the field (or use default name instead) and click the Save button.

· Choose the Graphs item in the tree on the left.

· Click the Type of Y axis combo box in the Add graph dialog window and, then, choose the Real item.

· Click the Type of X axis combo box, choose the Length item.

· Type a name in the Graph name field (or use default name instead) and, then, click the OK button.

· Choose the saved Graph name (the default name is Real vs. length (#)) item in the tree on the left (the sub-graph of the Graphs item).

· Click the Add function button in the upper right corner.

· Choose the Scan range 1 item in the Against group in the Add function to graph dialog window.

· Choose the Efficiency (for order -1, reflected) item (type “-1” in the field and choose “reflected” in the combo box) in the Plot of combo box in the dialog window and click the OK button.