# In this test, the LC long axis is rotated to be within the XY plane (theta=90 for in-plane anisotropy) # The LC is rotated within the XY plane, the different rotations should induce different phase difference between S and P # if the LC is at 45° between X and Y, the difference of phase between S and P should be 0 # The phase difference should be opposite (x -1) when the long axis is along X or Y # The purpose of this script is to show how to set up the different attribute to perform the same rotation # It also shows we get the same results with the different solvers. clear; ############################################################# ### Choose test case #### ############################################################# attribute_case=2; #1=LC attribute / 2=Matrix attribute / 3=Rotation attribute solver_case=3; #1=RCWA / 2=FDTD / 3=STACK # Note: STACK is run by setting the RI matrix directly so there is no effect of attribute type for this solver plot_result=true; phi_sweep=linspace(0,90,3); #Rotation around Z for 0°, 45°, and 90° switchtolayout; setmaterial("Anisotropic_LC","Refractive Index",[1.5,1.5,1.6]); # The long axis is defined initially along the Z axis theta=90; #theta=90 brings the long axis within the XY plane setnamed("LC","material","Anisotropic_LC"); if (attribute_case==1){attribute_type="LC attribute";} if (attribute_case==2){attribute_type="Matrix attribute";} if (attribute_case==3){attribute_type="Rotation attribute";} if (solver_case==1){solver_type="RCWA";} if (solver_case==2){solver_type="FDTD";} if (solver_case==3){solver_type="STACK";attribute_type="N/A";} ############################################################# ### support functions #### ############################################################# function apply_attribute(attribute_case,theta,phi){ #LC attribute if (attribute_case==1){ setnamed("LC attribute","theta",theta*pi/180); # Bring the long axis within the XY plane setnamed("LC attribute","phi",phi*pi/180); # Rotate around Z setnamed("LC","grid attribute name","LC attribute"); } #Matrix attribute if (attribute_case==2){ # Define the rotation matrix Uy=[cos(theta*pi/180),0,sin(theta*pi/180); 0,1,0; -sin(theta*pi/180),0,cos(theta*pi/180)]; Uz=[cos(phi*pi/180),-sin(phi*pi/180),0; sin(phi*pi/180),cos(phi*pi/180),0; 0,0,1]; U = mult(Uz,Uy); U = ctranspose(U); # Note the ctranspose operation here specific to the convention of this attribute pos=find(abs(U)<1e-5);U(pos)=0; ?'Rotation Matrix:'; ?num2str(U); # Apply the rotation matrix on the attribute setnamed("Matrix attribute","U",U); setnamed("LC","grid attribute name","Matrix attribute"); } # Rotation Atribute if (attribute_case==3){ # Apply the rotation matrix on the attribute setnamed("Rotation attribute","theta",theta*pi/180); setnamed("Rotation attribute","phi",phi*pi/180); setnamed("LC","grid attribute name","Rotation attribute"); } } function run_solver(solver_case,theta,phi){ # RCWA solver // Note that the index monitor is part of the results output by the solver if (solver_case==1){ run("RCWA"); # Check the results results=getresult("RCWA","grating_characterization"); n0=find(results.n==0); m0=find(results.m==0); Phase_P=angle(pinch(results.Tpp(1,1,n0,m0,1))); Phase_S=angle(pinch(results.Tss(1,1,n0,m0,1))); Phase_diff=Phase_P-Phase_S; ?Phase_diff; index_result=getresult('RCWA','index'); ?'index xx:'+num2str(index_result.index_xx(1,1,2,1)); ?'index yy:'+num2str(index_result.index_yy(1,1,2,1)); ?'index z:'+num2str(index_result.index_z(1,1,2,1)); } # FDTD solver // Note that you would need to add an index monitor to extract the index info if (solver_case==2){ #Run FDTD and check the field run("FDTD"); # Check the results E=getresult("monitor_FDTD","E");E=E.E; Phase_diff=angle(E(1,1,1,1,1))-angle(E(1,1,1,1,2)); } # STACK (independent from attribute, permittivity matrix is directly defined) if (solver_case==3){ N_layers = 3; Nfreqs = 1; d = [0; 2.5e-6; 0]; # air/ birefringent slab / air f = c/(0.55e-6); n = matrix(N_layers, Nfreqs, 9); n(1, :, 1) = 1; # Incidence Medium, must be isotropic and loss-less n(1, :, 5) = 1; # Incidence Medium, must be isotropic and loss-less n(1, :, 9) = 1; # Incidence Medium, must be isotropic and loss-less # Define the rotation to apply on the index matrix Uy=[cos(theta*pi/180),0,sin(theta*pi/180); 0,1,0; -sin(theta*pi/180),0,cos(theta*pi/180)]; Uz=[cos(phi*pi/180),-sin(phi*pi/180),0; sin(phi*pi/180),cos(phi*pi/180),0; 0,0,1]; U = mult(Uz,Uy); U=ctranspose(U); pos=find(abs(U)<1e-5);U(pos)=0; nxx=getindex('Anisotropic_LC',f,1); nyy=getindex('Anisotropic_LC',f,2); nzz=getindex('Anisotropic_LC',f,3); n0=[nxx,0,0;0,nyy,0;0,0,nzz]; n(2,:,:)=mult(mult(ctranspose(U),n0),U); #Same operation than what the Matrix attribute is doing n(3, :, 1) = 1; # Outgoing material can be lossy n(3, :, 5) = 1; # Outgoing material can be lossy n(3, :, 9) = 1; # Outgoing material can be lossy ?num2str(U); ?'index xx:'+num2str(n(2,1,1)); ?'index yy:'+num2str(n(2,1,5)); ?'index z:'+num2str(n(2,1,9)); RT= stackrt(n,d,f,0); Phase_diff=angle(RT.tpp)-angle(RT.tss); } return Phase_diff; } ############################################################# ### Run simulation in selected case #### ############################################################# ## Initialize the matrix data Phase_diff=matrix(length(phi_sweep)); Phase_P=matrix(length(phi_sweep)); Phase_S=matrix(length(phi_sweep)); ## Start the sweep over Phi ?'---------------------'; ?'Solver: ' + solver_type; ?'Attribute: ' + attribute_type; for (p=1:length(phi_sweep)){ switchtolayout; phi=phi_sweep(p); ?' '; ?'Phi = ' + num2str(phi) + '°'; apply_attribute(attribute_case,theta, phi); Phase_diff(p)=run_solver(solver_case,theta,phi); } if (plot_result==1){ title_plot="Solver " + solver_type +" / Attribute " + attribute_type; plot(phi_sweep,Phase_diff,"Phi [deg]","Phase Difference S/P", title_plot); }