Reply To: Regarding box of monitors and far field simulations

[pnair]

Hello Amrita,

Thank you for the reply and a detailed explanation of farfield analysis group and the corrected script.

I run the simulation with the script suggested here. But, It is generating an error:

Target wavelength = 1.54e-06

Wavelength used = 1.54e-06

Angular distribution i=1, 1.54um

Projecting in x-y plane

Projecting in y-z plane

Projecting in x-z plane

Error: Result XY_halfspace: variable not found.

And, I am not able to visualize the farfied data in the xy_half space and its showing"failed to calculate results"

Please find the attached script that you have suggested here and I have used the same script for the simulations:

##############################################

# Far field from closed box

# This script calculates scattering cross-section and far field projection in half space

#

# Note: The far field projection calculation assumes that all of the monitors

# are in a single homogeneous material (i.e. there is no substrate)

# If a substrate is present, results from this object will be invalid.

# If multiple frequency points are collected, the projection can be slow!! One could reduce the halfspace resolution for faster analysis.

# For more information, see http://docs.lumerical.com/en/layout_analysis_projections_from_monitor.html

#

# symm x,y,z: symmetry boundary conditions

# 0 for no symmetry, 1 for symmetric, -1 for antisymmetric

# Autodetection is managed by examining fields at the symmetry boundary

# For more information, see http://docs.lumerical.com/en/index.html?ref_sim_obj_symmetric_anti-symmetric.html

#

# do halfspace: Calculate the far field in the full half space for all frequencies. This takes longer than the 1D radar line cross sections. 1 for yes, 0 for no

# do polar plot: Calculate the far field scattering angular distribution for a specified target wavelength. 1 for yes, 0 for no

# target wavelength: Desired wavelength for polar plot. The closest wavelength recorded by the monitors will be found and used for the plot.

# halfspace res: Define the resolution of the half space projection. This will significantly affect the time to run the analysis.

# polar plot res: Define the resolution of the polat plots.

#

# Output properties

# XY, YZ, XZ: E, |E|^2, |H|^2 far field profile of scattered field in plane, as a function of frequency

# XY_halfspace: E, |E|^2, |H|^2 in full upper/lower half space,, as a function of frequency. Similar to standard projection from a single monitor

#

# Tags: far field projection closed box

#

# Copyright 2015 Lumerical Solutions Inc

##############################################

 

##############################################

# automatically unfold field data if symmetry BC is applied

if (havedata("x1", "f")) {

symm_x = 0;

} else {

xtemp = getdata("y2", "x");

ztemp = getdata("y2", "z");

Eztemp = pinch(getdata("y2", "Ez"));

 

Ez2mid = sum(Eztemp(round(length(xtemp)/2), 1:length(ztemp))^2);

if (Ez2mid != 0) {

symm_x = 1;

} else {

symm_x = -1;

}

}

 

if (havedata("y1", "f")) {

symm_y = 0;

} else {

ytemp = getdata("x2", "y");

ztemp = getdata("x2", "z");

Eztemp = pinch(getdata("x2", "Ez"));

 

Ez2mid = sum(Eztemp(round(length(ytemp)/2), 1:length(ztemp))^2);

if (Ez2mid != 0) {

symm_y = 1;

} else {

symm_y = -1;

}

}

 

if(include_sub){

if (havedata("z1", "f")) {

symm_z = 0;

} else {

xtemp = getdata("y2", "x");

ztemp = getdata("y2", "z");

Eytemp = pinch(getdata("y2", "Ey"));

 

Ey2mid = sum(Eytemp(1:length(xtemp), round(length(ztemp)/2))^2);

if (Ey2mid != 0) {

symm_z = 1;

} else {

symm_z = -1;

}

}

}

f = getdata("x2","f"); # get freqency data

 

if (havedata("index","index_x")) { # get refractive index. Required to calcualte H2 from E2

n_index = getdata("index","index_x");

} else {

n_index = getdata("index","index_z");

}

##############################################

 

 

# define the angular resolution

phi = linspace(0,360,%polar plot res%); # user-modifiable in the Variables tab

npts = length(phi);

 

# define the field data matrices for angular distribution

E_xy = matrix(npts, 3, length(f)); # 3 for x, y, z component

E_yz = matrix(npts, 3, length(f)); # 3 for x, y, z component

E_xz = matrix(npts, 3, length(f)); # 3 for x, y, z component

E2_xy = matrix(npts,length(f));

E2_yz = matrix(npts,length(f));

E2_xz = matrix(npts,length(f));

H2_xy = matrix(npts,length(f));

H2_yz = matrix(npts,length(f));

H2_xz = matrix(npts,length(f));

 

 

# Identify the closest wavelength to target:

target_wavelength = %target wavelength%;

i_target = find(f,c/target_wavelength);

?"Target wavelength = " + num2str(target_wavelength);

?"Wavelength used = " + num2str(c/f(i_target));

 

 

if (havedata("z2","Ex")) { # have z data, 3D simulation

 

##############################################

# Angular distribution calculation for a 3D simulation begins

 

for (i = 1:length(f)){ # loop for all frequencies

 

# print the frequency point number running in the loop

?"Angular distribution i="+num2str(i)+", "+num2str(c/f(i)*1e6)+"um";

 

n = n_index(i); # select the frequency point for the index

 

######## x-y plane (phi=0 corresponds to the direction (1,0,0))

?" Projecting in x-y plane";

x = cos(phi*pi/180); y = sin(phi*pi/180); z = 0;

 

# Calculate far field by summing contribution from each monitor

temp = farfieldexact("x2",x,y,z,i) + farfieldexact("y2",x,y,z,i) + farfieldexact("z2",x,y,z,i);

if(havedata("x1")){

temp = temp - farfieldexact("x1",x,y,z,i);

}else{

temp2 = farfieldexact("x2",-x,y,z,i);

s = symm_x*[1,-1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(havedata("y1")){

temp = temp - farfieldexact("y1",x,y,z,i);

}else{

temp2 = farfieldexact("y2",x,-y,z,i);

s = symm_y*[-1,1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(include_sub){

if(havedata("z1")){

temp = temp - farfieldexact("z1",x,y,z,i);

}else{

temp2 = farfieldexact("z2",x,y,-z,i);

s = symm_z*[-1,-1,1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

}

E_xy (1:length(phi), 1:3, i) = temp;

E2_xy (1:length(phi), i) = sum(abs(temp)^2,2); # E2 = |Ex|^2 + |Ey|^2 + |Ez|^2

H2_xy (1:length(phi), i) = E2_xy (1:length(phi), i) * n^2 * eps0/mu0; # for a plane wave, E^2 and H^2 only differ by a factor of n^2*eps0/mu0

 

 

 

######## y-z plane (phi=0 corresponds to the direction (0,1,0))

?" Projecting in y-z plane";

x = 0; y = cos(phi*pi/180); z = sin(phi*pi/180);

 

# Calculate far field by summing contribution from each monitor

temp = farfieldexact("x2",x,y,z,i) + farfieldexact("y2",x,y,z,i) + farfieldexact("z2",x,y,z,i);

if(havedata("x1")){

temp = temp - farfieldexact("x1",x,y,z,i);

}else{

temp2 = farfieldexact("x2",-x,y,z,i);

s = symm_x*[1,-1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(havedata("y1")){

temp = temp - farfieldexact("y1",x,y,z,i);

}else{

temp2 = farfieldexact("y2",x,-y,z,i);

s = symm_y*[-1,1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(include_sub){

if(havedata("z1")){

temp = temp - farfieldexact("z1",x,y,z,i);

}else{

temp2 = farfieldexact("z2",x,y,-z,i);

s = symm_z*[-1,-1,1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

}

E_yz (1:length(phi), 1:3, i) = temp;

E2_yz (1:length(phi), i) = sum(abs(temp)^2,2); # E2 = |Ex|^2 + |Ey|^2 + |Ez|^2

H2_yz (1:length(phi), i) = E2_yz (1:length(phi), i) * n^2 * eps0/mu0; # for a plane wave, E^2 and H^2 only differ by a factor of n^2*eps0/mu0

 

 

 

######### x-z plane (phi=0 corresponds to the direction (1,0,0))

?" Projecting in x-z plane";

x = cos(phi*pi/180); y = 0; z = sin(phi*pi/180);

 

# Calculate far field by summing contribution from each monitor

temp = farfieldexact("x2",x,y,z,i) + farfieldexact("y2",x,y,z,i) + farfieldexact("z2",x,y,z,i);

if(havedata("x1")){

temp = temp - farfieldexact("x1",x,y,z,i);

}else{

temp2 = farfieldexact("x2",-x,y,z,i);

s = symm_x*[1,-1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(havedata("y1")){

temp = temp - farfieldexact("y1",x,y,z,i);

}else{

temp2 = farfieldexact("y2",x,-y,z,i);

s = symm_y*[-1,1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(include_sub){

if(havedata("z1")){

temp = temp - farfieldexact("z1",x,y,z,i);

}else{

temp2 = farfieldexact("z2",x,y,-z,i);

s = symm_z*[-1,-1,1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

}

E_xz (1:length(phi), 1:3, i) = temp;

E2_xz (1:length(phi), i) = sum(abs(temp)^2,2); # E2 = |Ex|^2 + |Ey|^2 + |Ez|^2

H2_xz (1:length(phi), i) = E2_xz (1:length(phi), i) * n^2 * eps0/mu0; # for a plane wave, E^2 and H^2 only differ by a factor of n^2*eps0/mu0

 

} # end of the angular distribution for loop

 

if (%do polar plot%) { # polar plot for target wavelength

polar(phi*pi/180, E2_xy(1:length(phi), i_target), E2_yz(1:length(phi), i_target), E2_xz(1:length(phi), i_target),

"angle (degrees)", "|E|^2", "|E|^2 vs angle @ "+num2str(c/f(i_target)*1e6)+"um");

legend("xy plane","yz plane","xz plane");

} # end of if polar plot

 

# create datasets for XY, YZ, XZ for angular distribution

XY = matrixdataset("XY");

XY.addparameter("phi",phi*pi/180.); #phi angle in radians

XY.addparameter("lambda",c/f,"f",f);

XY.addattribute("E",pinch(E_xy,2,1),pinch(E_xy,2,2),pinch(E_xy,2,3)); # Ex, Ey, Ez

XY.addattribute("E2",E2_xy);

XY.addattribute("H2",H2_xy);

 

YZ = matrixdataset("YZ");

YZ.addparameter("phi",phi*pi/180.); #phi angle in radians

YZ.addparameter("lambda",c/f,"f",f);

YZ.addattribute("E",pinch(E_yz,2,1),pinch(E_yz,2,2),pinch(E_yz,2,3)); # Ex, Ey, Ez

YZ.addattribute("E2",E2_yz);

YZ.addattribute("H2",H2_yz);

 

XZ = matrixdataset("XZ");

XZ.addparameter("phi",phi*pi/180.); #phi angle in radians

XZ.addparameter("lambda",c/f,"f",f);

XZ.addattribute("E",pinch(E_xz,2,1),pinch(E_xz,2,2),pinch(E_xz,2,3)); # Ex, Ey, Ez

XZ.addattribute("E2",E2_xz);

XZ.addattribute("H2",H2_xz);

# end of the angular distribution for a 3D simulation

##############################################

 

##############################################

# Halfspace calculation for a 3D simulation begins

 

# calculate the far field in XY upper/lower half space

if (%do halfspace%) {

 

res = %halfspace res%; # projection resolution, user-modifiable in the Variables tab

u1 = linspace(-1,1,res);

u2 = u1;

X = meshgridx(u1,u2); # These three lines define the orientation of the hemisphere (ie. XY based halfspace)

Y = meshgridy(u1,u2);

Z = sqrt(1-X^2-Y^2);

filter = abs(imag(Z))<=0; # filter out any values outside of hemisphere

filter2=matrix(res,res,length(f)); # same as filter, just for all frequencies

filter3=matrix(res,res,3,length(f)); # same as filter2, just for all frequencies, Ex, Ey, Ez

for (j=1:length(f)){ # just for filter2 and fitler3 for all frequencies

filter2(1:res,1:res,j)=filter;

filter3(1:res,1:res,1,j)=filter; filter3(1:res,1:res,2,j)=filter; filter3(1:res,1:res,3,j)=filter;

}

x = reshape(X,[res^2,1]); # reshape coordinate matrix into a vector. This is the required form for farfieldexact.

y = reshape(Y,[res^2,1]);

z = reshape(Z,[res^2,1]);

x = [x,x]; # Concatenate a 2nd copy of the vector, for the lower half space

y = [y,y];

z = [z,-z];

npts = length(z); # size of position vector

 

# define halfspace dataset

E_XY_halfspace = matrix (2*res^2,3,length(f));

E2_XY_halfspace = matrix (2*res^2,length(f));

H2_XY_halfspace = matrix (2*res^2,length(f));

 

 

for (i = 1 : length(f)) { # loop for all frequency points

 

?"Projecting in XY upper half space, i=" + num2str(i)+", "+num2str(c/f(i)*1e6)+"um";

# Calculate far field by summing contribution from each monitor

temp = farfieldexact("x2",x,y,z,i) + farfieldexact("y2",x,y,z,i) + farfieldexact("z2",x,y,z,i);

if(havedata("x1")){

temp = temp - farfieldexact("x1",x,y,z,i);

}else{

temp2 = farfieldexact("x2",-x,y,z,i);

s = symm_x*[1,-1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(havedata("y1")){

temp = temp - farfieldexact("y1",x,y,z,i);

}else{

temp2 = farfieldexact("y2",x,-y,z,i);

s = symm_y*[-1,1,-1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

if(include_sub){

if(havedata("z1")){

temp = temp - farfieldexact("z1",x,y,z,i);

}else{

temp2 = farfieldexact("z2",x,y,-z,i);

s = symm_z*[-1,-1,1];

temp2(1:npts,1) = s(1)*temp2(1:npts,1);

temp2(1:npts,2) = s(2)*temp2(1:npts,2);

temp2(1:npts,3) = s(3)*temp2(1:npts,3);

temp = temp - temp2;

}

}

E_XY_halfspace (1:2*res^2,1:3,i) = temp;

E2_XY_halfspace (1:2*res^2,i)= sum(abs(temp)^2,2); # E2 = |Ex|^2 + |Ey|^2 + |Ez|^2

} # end of halfspace for loop

 

E_XY_upper_halfspace = E_XY_halfspace(1:res^2,1:3,1:length(f)); # separate the upper/lower data

E_XY_lower_halfspace = E_XY_halfspace((res^2+1):(2*res^2),1:3,1:length(f));

E_XY_upper_halfspace = reshape(E_XY_upper_halfspace,[res,res,3,length(f)]); # reshape the data back into a 2D matrix

E_XY_lower_halfspace = reshape(E_XY_lower_halfspace,[res,res,3,length(f)]);

E_XY_upper_halfspace = E_XY_upper_halfspace*filter3; # set all values outside of hemisphere (ie. the corners of the matrices) to zero

E_XY_lower_halfspace = E_XY_lower_halfspace*filter3;

 

E2_XY_upper_halfspace = E2_XY_halfspace(1:res^2,1:length(f)); # separate the upper/lower data

E2_XY_lower_halfspace = E2_XY_halfspace((res^2+1):(2*res^2),1:length(f));

E2_XY_upper_halfspace = reshape(E2_XY_upper_halfspace,[res,res,length(f)]); # reshape the data back into a 2D matrix

E2_XY_lower_halfspace = reshape(E2_XY_lower_halfspace,[res,res,length(f)]);

E2_XY_upper_halfspace = E2_XY_upper_halfspace*filter2; # set all values outside of hemisphere (ie. the corners of the matrices) to zero

E2_XY_lower_halfspace = E2_XY_lower_halfspace*filter2;

 

# create halfspace dataset

XY_halfspace = matrixdataset("XY_halfspace");

XY_halfspace.addparameter("ux",u1);

XY_halfspace.addparameter("uy",u2);

XY_halfspace.addparameter("lambda",c/f,"f",f);

XY_halfspace.addattribute("E_upper",pinch(E_XY_upper_halfspace,3,1),pinch(E_XY_upper_halfspace,3,2),pinch(E_XY_upper_halfspace,3,3));

XY_halfspace.addattribute("E_lower",pinch(E_XY_lower_halfspace,3,1),pinch(E_XY_lower_halfspace,3,2),pinch(E_XY_lower_halfspace,3,3));

XY_halfspace.addattribute("E2_upper",E2_XY_upper_halfspace);

XY_halfspace.addattribute("E2_lower",E2_XY_lower_halfspace);

XY_halfspace.addattribute("H2_upper",E2_XY_upper_halfspace * n^2*eps0/mu0);

XY_halfspace.addattribute("H2_lower",E2_XY_lower_halfspace * n^2*eps0/mu0);

}

# end of the halfspace calculation for a 3D simulation

##############################################

 

# end of 3D

 

} else {

##############################################

# Angular distribution for a 2D simulation, only for the XY plane

 

for (i = 1 : length(f)) { # for all frequency points

 

n = n_index(i); # select the frequency point for the index

 

# x-y plane (phi=0 corresponds to the direction (0,1,0))

?" Projecting in x-y plane. 2D simulation.";

x = -sin(phi*pi/180);

y = cos(phi*pi/180);

z = 0;

 

temp = farfieldexact("x2",x,y,i) + farfieldexact("y2",x,y,i);

if(havedata("x1")){

temp = temp - farfieldexact("x1",x,y,i);

}else{

temp2 = farfieldexact("x2",-x,y,i);

s = symm_x*[1,-1,-1];

temp2(1:length(phi),1) = s(1)*temp2(1:length(phi),1);

temp2(1:length(phi),2) = s(2)*temp2(1:length(phi),2);

temp2(1:length(phi),3) = s(3)*temp2(1:length(phi),3);

temp = temp - temp2;

}

if(havedata("y1")){

temp = temp - farfieldexact("y1",x,y,i);

}else{

temp2 = farfieldexact("y2",x,-y,i);

s = symm_y*[-1,1,-1];

temp2(1:length(phi),1) = s(1)*temp2(1:length(phi),1);

temp2(1:length(phi),2) = s(2)*temp2(1:length(phi),2);

temp2(1:length(phi),3) = s(3)*temp2(1:length(phi),3);

temp = temp - temp2;

}

 

E_xy (1:length(phi), 1:3, i) = temp;

E2_xy (1:length(phi), i) = sum(abs(temp)^2,2); # E2 = |Ex|^2 + |Ey|^2 + |Ez|^2

H2_xy (1:length(phi), i) = E2_xy (1:length(phi), i) * n^2 * eps0/mu0; # for a plane wave, E^2 and H^2 only differ by a factor of n^2*eps0/mu0

 

} # end of for loop 2D

 

if (%do polar plot%) { # polar plot for target wavelength

polar(phi*pi/180, E2_xy(1:length(phi), i_target), "angle (degrees)", "|E|^2", "|E|^2 vs angle @ "+num2str(c/f(i_target)*1e6)+"um");

legend("xy plane");

} # end of if polar plot

 

# create dataset for XY

XY = matrixdataset("XY");

XY.addparameter("phi",phi*pi/180.); #phi angle in radians

XY.addparameter("lambda",c/f,"f",f);

XY.addattribute("E",pinch(E_xy,2,1),pinch(E_xy,2,2),pinch(E_xy,2,3)); # Ex, Ey, Ez

XY.addattribute("E2",E2_xy);

XY.addattribute("H2",H2_xy);

 

} # end of angular distribution for 2D simulation