1.1 Overview

x_simulation_nodes is a number specifying the number of simulation nodes in the x-dimension of the simulation domain. x_simulation_nodes must be a positive number greater than or equal to 2. See below for restrictions.

y_simulation_nodes is a number specifying the number of simulation nodes in the y-direction of the simulation domain. y_simulation_node must be a positive number greater than or equal to 1. See below for restrictions.

z_simulation_nodes is a number specifying the number of simulation nodes in the z-direction of the simulation domain. z_simulation_nodes must be a

positive number greater than or equal to 2. See below for restrictions.

x_length is the x-dimension of the simulation domain in micrometers. See below for restrictions.

y_length is the y-dimension of the simulation domain in micrometers. See below for restrictions.

z_length is the z-dimension of the simulation domain in micrometers. See below for restrictions.

Restrictions exist on the values x_length, x_simulation_nodes, y_length, y_simulation_nodes, z_length and z_simulation_nodes: TEMPEST 5.0 uses a cubic discrization grid placing the restriction that Dx=Dy=Dz which means that x_length/x_simulation_nodes = y_length/y_simulation_nodes=z_length/z_simulation_nodes. Consequently it is not necessary to specify all six parameters but rather only enough to completely define all three dimensions of the domain and the discretization Dx. Any unspecified parameters will be deduced by TEMPEST. If more than the minimum number of parameters are specified then they must satisfy the above restriction (to within numerical error) otherwise TEMPEST will give an error. Also, for 2D simulations the dimension in which there exists only one node must be chosen as the y-dimension.

keyword x_symmetry specifies that the simulated topography has mirror symmetry in the x direction. Nodes with coordinates (0,y,z) will use nodes with coordinates (1,y,z) as their west neighbors and nodes with coordinates (x_simulation_nodes-1,y,z) will use nodes with corrdinates (x_simulation_nodes-2,y,z) as their east neighbors. If x_symmetry is not specified then periodic boundary conditions apply in the x-dimension where nodes with coordinates (0,y,z) use nodes with with coordinates (x_simulation_nodes-1,y,z) as their west neighbors and nodes with coordinates (x_simulation_nodes-1,y,z) use nodes with coordinates (0,y,z) as thier east neighbors.

keyword y_symmetry specifies that the simulated topography has mirror symmetry in the y direction. Nodes with coordinates (x,0,z) will use nodes with coordinates (x,1,z) as their south neighbors and nodes with coordinates (x,y_simulation_nodes-1,z) will use nodes with corrdinates (x,y_simulation_nodes-2,z) as their north neighbors. If y_symmetry is not specified then periodic boundary conditions apply in the y-dimension where nodes with coordinates (x,0,z) use nodes with with coordinates (x,y_simulation_nodes-1,z) as their south neighbors and nodes with coordinates (x,y_simulation_nodes-1,z) use nodes with coordinates (x,0,z) as thier north neighbors. If y_simulation_nodes is 1, for example in a 2D simulation, y_symmetry will have no effect and all nodes will use themselves as their both their north and south neighbors.

keyword z_symmetry specifies that the simulated topography has mirror symmetry in the z direction. Nodes with coordinates (x,y,0) will use nodes with coordinates (x,y,1) as their down neighbors and nodes with coordinates (x,y,z_simulation_nodes-1) will use nodes with corrdinates (x,y,z_simulation_nodes-2) as their up neighbors. If z_symmetry is not specified then periodic boundary conditions apply in the z-dimension where nodes with coordinates (x,y,0) use nodes with with coordinates (x,y,z_simulation_nodes-1) as their down neighbors and nodes with coordinates (x,y,z_simulation_nodes-1) use nodes with coordinates (x,y,0) as thier up neighbors.

4.1.2 Illumination

lambda is the free space wavelength of the incident illumination in micrometers. TEMPEST assumes monochromatic illumination.

sets the total amount of exposure time (used when dynamic resist material is present). If not specified, the default exposure time is 30 seconds.

set the number of exposure steps (used when dynamic resist material is present). The time step will be exposure_time/exposure_steps. When not specified, the default number of exposure steps is 5.

unit can be either position or node. If position is specified then x_pos, y_pos and z_pos are the x, y and z coordinates in micrometers of a point source excitation. If node is specified then x_pos, y_pos and z_pos are the x, y and z nodal coordinates of the point source. The amplitude, phase and polarization of the point source are determined by the remaining parameters with the following formula:

where and are magnitude and phase functions determined by the remaining arguments. type can be uniform or file meaning that the distribution of intensity accross the plane is uniform or nonuniform and read in from a file on disk.

If uniform is selected then the distribution is uniform and represents a plane wave travelling in the direction specified by arg1 and arg2. arg1 is the measured from the positive normal to the plane. arg2 is the azimuthal angle measured from the axis in the counterclockwise direction. See diagram below:

If file is selected then the distribution is loaded in from disk. arg1 and arg2 are the filenames of the magnitude and phase files respectively.

4.1.3 Topography

primitive unit [pos1 pos2 pos3 . . .] material [arg1 arg2 arg3 arg4 . . .]

The number of positioning arguments (pos1, pos2 etc.) depends on the primitive chosen and the number of material arguments (arg1, arg2 etc) depends on the material chosen. In all cases unit can be either position or node specifing whether the positioning arguments are in micrometers or nodes (nodes are always numbered starting from zero) and primitive can be selected from any of the following primitives:

specifies the existence of a sphere with radius radius centered at (xcenter, ycenter, zcenter).

specifies the existence of a circular cylinder oriented along the x-direction from xl to xh with radius radius. The circular cross-section on the yz-plane is centered at (ycenter, zcenter).

specifies the existence a circular cylinder oriented along the y-direction from yl to yh with radius radius. The circular cross-section on the zx-plane is centered at (zcenter, xcenter).

specifies the existence of a circular cylinder oriented along the z-direction from zl to zh with radius radius. The circular cross-section on the xy-plane is centered at (xcenter, ycenter).

xwedge specifies the existence of a wedge with a triangular interface with the yz-plane defined by the coordinates (y1, z1), (y2, z2), and (y3, z3). The wedge is oriented along the x-direction from xl to xh.

specifies the existence of a wedge with a triangular interface with the zx-plane defined by the coordinates (z1, x1), (z2, x2), and (z3, x3). The wedge is oriented along the y-direction from yl to yh.

specifies the existence of a wedge with a triangular interface with the xy-plane defined by the coordinates (x1, y1), (x2, y2), and (x3, y3). The wedge is oriented along the y-direction from zl to zh.

index n k

The block represents an isotropic, linear, non-dispersive, non-magnetic material (such air, glass, resist, silicon are at optical wavelengths). n is the refractive index of the material and k represents the lossiness of the material (k=0 implies lossless material). give formula involving n-jk)^2=epsilon complex = . For this material, mu = m0=1.whatever

same as index except used when k>n. yadda yadaa yada

perfect conductor approximation ....

gindex exx exy exz eyx eyy eyz ezx ezy ezz

sexx sexy sexz seyx seyy seyz sezx sezy sezz

mxx mxy mxz myx myy myz mzx mzy mzz

smxx smxy smxz smyx smyy smyz smzx smzy smzz

-not working yet

black_matter

The fields inside a block with this material specification are zero. This can be used as a perfect electric/magnetic conductor boundary condition. The can also be used in regions of the domain which in which the fields are know to be zero (such as deep inside a metal object) to save computation time.

resist specifies that the current block has dynamic change with respect to exposure. init_conc is the initial PAC value of the photoresist block. a is Dill's bleachable absorption coefficient of the photoresist in per micro-meter. b is Dill's unbleachable absorption coefficient of the photoresist in per micro-meter. c is the bleach rate of the photoresist model proposed by Dill in centi-meter squared per milli-Joule.

4.1.4 Analysis

This sets the minimum number of cycles TEMPEST will run to min_wave_cycles regardless of the convergence status. If unspecified, the default value is zero.

Simulation continues until steady-state is reached or until the domain has been excited with max_wave_cycles wave cycles, whichever comes first. If unspecified, the program will run until convergence occurs.

specify the time step to be used in seconds. If unspecified, TEMPEST automatically calculates the time step to be used based on .....

Steady-state is determined by comparing the field values at evenly distributed set of test points at the same instant in successive wave cycles. If the relative variation of the electric field intensity at each node in the test grid is less than fraction for three consecutive wave cycles, steady-state is reached. A typical value for fraction is 0.1 and the relative variation is defined:

unless the denominator is deemed extremeley small in which case the point is not included in the comparison.

4.1.5 Data

plot_var must be one of the keywords: refractive, block, ex, ey, ez, hx, hy, hz or pac.

4.2 TEMPEST command

prompt: tempest input_file output_file

See Appendix A for suggested file naming convention.

4.3 Post-TEMPEST Commands

>>plotbin(`filename');

This command calls the plotbin.m script file. It is used to plot refractive index plots, block number plots and field plots at a particular instant of time.

This command calls the plotbinsten.m script file. It is similar to the plotbin command above but it stencils in the topography borders. filename is a field file (such as the x component of the electric field at steady state) and top_filename is a plot file which either contains the refractive index or block number of region corresponding that of filename.

This command calls the plotam.m script file. It is used to view the time averaged (as opposed to instantaneous) field amplitude constructed from two plot files differing by one-quarter cycle (the in-phase and quadrature field plots). filename.i and filename.q are instantaneous field plots taken at two different times one-quarter cycle apart.

This command calls the plotamsten.m script file. It is similar to the plotam command above except that the topography information taken from top_filename is stenciled in.

This command calls the plotam6.m script file. It is used to assemble all three components of a field at two different times (in-phase and quadrature) (six files in total) to yield the time averaged total field intensity. It is very similar to plotam but includes three field components (the x,y and z) instead of just one. filename should be the name of the files without the .x.i, .x.q etc. extensions. The script file automatically adds them. See examples in Chapter 3 for a better understanding of how this command works.

This command calls the plotam6sten.m script file. It is used similar to the plotam6 command above except that the topography information taken from top_filename is stenciled in.

5.0 Useful Hints

5.1 Material Interface at the Boundaries

5.2 Verification of Loaded Topography

5.3 Real and Imaginary Parts of the Refractive Index

5.4 Number of Simulation Nodes

x_simulation_nodes > (15*largest_index*x_length)/wavelength

and the number of simulation nodes in the y- and z-directions can be determined from x_simulation_nodes by the ratios of x_length, y_length and z_length.

5.5 Periodic Structures

5.6 Isolated Structures

5.7 PML Thickness

5.8 2D simulations

5.9 Symmetry - using it properly

5.10 Proximity to Sources and Boundary Conditions

5.11 Convergence Problems

A.0 Appendix A: Suggested File Naming Convention

All files should have a prefex the same as the input file prefix.

The output file should have a .out extention. (ex. hole.out)

All plot output files should indicate which region of the domain is plotted and what data is being plotted. If only a plane of nodes is output then the following convention should be applied:

prefix.{xy or yz or zx}.position.{e or h or ref or pac or blk}[.{x or y or z}.{i or q or time}]

example: hole.yz.0.e.x.i means the in-phase component of the x component of the electric field at steady state for an yz plane of the domain located at x = 0.

example: hole.zx.3.blk means the block number for a zx plane of the domain located at y = 3.

example: hole.yz.35.e.x.2.25 means the x component of the electric field after 2.25 cycles of simulation (non-steady-state plot).

It is important to follow the naming conventions for some of the MATLAB scripts to work correctly.

B.0 Appendix B: MATLAB scripts

function a=plotbin(file1)

% comment

fp1=fopen(file1);

size1=fread(fp1,3,'long')

if size1(1)==1

nx=size1(2);

ny=size1(3);

xlab='y axis (nodes)';

ylab='z axis (nodes)';

end

if size1(2)==1

nx=size1(1);

ny=size1(3);

xlab='x axis (nodes)';

ylab='z axis (nodes)';

end

if size1(3)==1

nx=size1(1);

ny=size1(2);

xlab='x axis (nodes)';

ylab='y axis (nodes)';

end

a=fread(fp1,[nx ny],'float');

pcolor(a');

axis('equal');

colormap('hot');

shading('flat');

colorbar;

xlabel(xlab);

ylabel(ylab);

title('Electric Field');

fclose(fp1);

plotbinsten.m

function a=plotbinsten(file1,file2)

% comment

fp1=fopen(file1);

fp2=fopen(file2);

size1=fread(fp1,3,'long')

size2=fread(fp2,3,'long')

if size1(1)==1

nx=size1(2);

ny=size1(3);

xlab='y axis (nodes)';

ylab='z axis (nodes)';

end

if size1(2)==1

nx=size1(1);

ny=size1(3);

xlab='x axis (nodes)';

ylab='z axis (nodes)';

end

if size1(3)==1

nx=size1(1);

ny=size1(2);

xlab='x axis (nodes)';

ylab='y axis (nodes)';

end

a=fread(fp1,[nx ny],'float');

dsten=fread(fp2,[nx ny],'float');

d1sten=dsten;

d1sten(2:nx+1,2:ny+1)=dsten;

dsten=abs(sign(dsten-d1sten(1:nx,1:ny)));

for x = 1:nx,

for y = 1:ny,

dsten(x,y)=dsten(x,y)*(rem(x+y,2)-.5);

end

end

pcolor((a+2*max(max(a))*dsten)');

axis('equal');

colormap('hot');

shading('flat');

colorbar;

xlabel(xlab);

ylabel(ylab);

title('Electric Field');

fclose(fp1);

fclose(fp2);

plotam.m

function [a,b,c] = plotam(file1,file2)

% comment

fp1=fopen(file1);

fp2=fopen(file2);

size1=fread(fp1,3,'long');

size2=fread(fp2,3,'long');

if size1(1)==1

nx=size1(2);

ny=size1(3);

xlab='y axis (nodes)';

ylab='z axis (nodes)';

end

if size1(2)==1

nx=size1(1);

ny=size1(3);

xlab='x axis (nodes)';

ylab='z axis (nodes)';

end

if size1(3)==1

nx=size1(1);

ny=size1(2);

xlab='x axis (nodes)';

ylab='y axis (nodes)';

end

a=fread(fp1,[nx ny],'float');

b=fread(fp2,[nx ny],'float');

c=a.*a+b.*b;

pcolor(c');

shading('flat');

caxis([0 2*average(c)]);

axis('equal');

colormap('hot');

colorbar;

xlabel(xlab);

ylabel(ylab);

title('<|E|^2>');

fclose(fp1);

fclose(fp2);

plotamsten.m

function [a,b,c] = plotamsten(file1,file2,file3)

% comment

fp1=fopen(file1);

fp2=fopen(file2);

fp3=fopen(file3);

size1=fread(fp1,3,'long');

size2=fread(fp2,3,'long');

size3=fread(fp3,3,'long');

if size1(1)==1

nx=size1(2);

ny=size1(3);

xlab='y axis (nodes)';

ylab='z axis (nodes)';

end

if size1(2)==1

nx=size1(1);

ny=size1(3);

xlab='x axis (nodes)';

ylab='z axis (nodes)';

end

if size1(3)==1

nx=size1(1);

ny=size1(2);

xlab='x axis (nodes)';

ylab='y axis (nodes)';

end

a=fread(fp1,[nx ny],'float');

b=fread(fp2,[nx ny],'float');

d=fread(fp3,[nx ny],'float');

c=a.*a+b.*b;

d1=d;

d1(2:nx+1,2:ny+1)=d;

d=abs(sign(d-d1(1:nx,1:ny)));

for x = 1:nx,

for y = 1:ny,

d(x,y)=d(x,y)*(rem(x+y,2)-.5);

end

end

pcolor((c+2*max(max(c))*d)');

shading('flat');

caxis([0 2*average(c)]);

c=c+2*max(max(c))*d;

axis('equal');

colormap('hot');

colorbar;

xlabel(xlab);

ylabel(ylab);

title('<|E|^2>');

fclose(fp1);

fclose(fp2);

fclose(fp3);

plotam6.m

function g = plotam6(file);

% comment

fp1=fopen([file '.x.i']);

fp2=fopen([file '.x.q']);

fp3=fopen([file '.y.i']);

fp4=fopen([file '.y.q']);

fp5=fopen([file '.z.i']);

fp6=fopen([file '.z.q']);

size1=fread(fp1,3,'long')

size2=fread(fp2,3,'long')

size3=fread(fp3,3,'long')

size4=fread(fp4,3,'long')

size5=fread(fp5,3,'long')

size6=fread(fp6,3,'long')

if size1(1)==1

nx=size1(2);

ny=size1(3);

xlab='y axis (nodes)';

ylab='z axis (nodes)';

end

if size1(2)==1

nx=size1(1);

ny=size1(3);

xlab='x axis (nodes)';

ylab='z axis (nodes)';

end

if size1(3)==1

nx=size1(1);

ny=size1(2);

xlab='x axis (nodes)';

ylab='y axis (nodes)';

end

a=fread(fp1,[nx ny],'float');

b=fread(fp2,[nx ny],'float');

c=fread(fp3,[nx ny],'float');

d=fread(fp4,[nx ny],'float');

e=fread(fp5,[nx ny],'float');

f=fread(fp6,[nx ny],'float');

g=a.*a+b.*b+c.*c+d.*d+e.*e+f.*f;

g=0.5*g;

pcolor(g');

shading('flat');

caxis([0 3000]);

%caxis([0 2*average(g)]);

axis('equal');

colormap('hot');

colorbar;

xlabel(xlab);

ylabel(ylab);

title('<|E|^2>');

fclose(fp1);

fclose(fp2);

fclose(fp3);

fclose(fp4);

fclose(fp5);

fclose(fp6);

plotam6sten.m

function g = plotam6sten(file,stenfile);

% comment

fp1=fopen([file '.x.i']);

fp2=fopen([file '.x.q']);

fp3=fopen([file '.y.i']);

fp4=fopen([file '.y.q']);

fp5=fopen([file '.z.i']);

fp6=fopen([file '.z.q']);

fp7=fopen([stenfile]);

size1=fread(fp1,3,'long')

size2=fread(fp2,3,'long')

size3=fread(fp3,3,'long')

size4=fread(fp4,3,'long')

size5=fread(fp5,3,'long')

size6=fread(fp6,3,'long')

size7=fread(fp7,3,'long')

if size1(1)==1

nx=size1(2);

ny=size1(3);

xlab='y axis (nodes)';

ylab='z axis (nodes)';

end

if size1(2)==1

nx=size1(1);

ny=size1(3);

xlab='x axis (nodes)';

ylab='z axis (nodes)';

end

if size1(3)==1

nx=size1(1);

ny=size1(2);

xlab='x axis (nodes)';

ylab='y axis (nodes)';

end

a=fread(fp1,[nx ny],'float');

b=fread(fp2,[nx ny],'float');

c=fread(fp3,[nx ny],'float');

d=fread(fp4,[nx ny],'float');

e=fread(fp5,[nx ny],'float');

f=fread(fp6,[nx ny],'float');

dsten=fread(fp7,[nx ny],'float');

g=a.*a+b.*b+c.*c+d.*d+e.*e+f.*f;

g=0.5*g;

d1sten=dsten;

d1sten(2:nx+1,2:ny+1)=dsten;

dsten=abs(sign(dsten-d1sten(1:nx,1:ny)));

for x = 1:nx,

for y = 1:ny,

dsten(x,y)=dsten(x,y)*(rem(x+y,2)-.5);

end

end

pcolor((g+2*max(max(g))*dsten)');

shading('flat');

caxis([0 3000]);

%caxis([0 2*average(g)]);

g=g+2*max(max(g))*dsten;

axis('equal');

colormap('hot');

colorbar;

xlabel(xlab);

ylabel(ylab);

title('<|E|^2>');

fclose(fp1);

fclose(fp2);

fclose(fp3);

fclose(fp4);

fclose(fp5);

fclose(fp6);

fclose(fp7);

Last Modified: 04:09pm , July 23, 1998