ScriptSolveForFixed

An example script showing how to obtain the field expansion coefficients and far-field cross-sections for a spheroid at a single wavelength, and fixed orientation. Outputs the far-field cross-sections with accuracy estimates.

Contents

Instructions

Note that you need to run InitPath in the root folder first to add required folders to the Matlab path so that functions can be called Alternatively, uncomment the following line

run('..\InitPath');

The following parameters should be defined:

clear all
close all

Parameters of the scattering problem

We define parameters for a gold nanorod in water, modeled as a prolate spheroid

a = 10; % short semi-axis in nm
c = 50; % long semi-axis in nm
lambda = 650; % wavelength in nm
epsilon2 = epsAu(lambda); % dielectric function of particle
epsilon1 = 1.33^2; % dielectric constant of embedding medium (water)
% Incident excitation polarised along main axis
sIncType = 'KxEz';

Convergence parameters

% Maximum multipole order for T-matrix and series expansions of fields
N = 40;
% Number of points for Gaussian quadratures to compute integrals in P and Q matrices
nNbTheta = 120;

Collect simulation parameters in a structure

k1 = 2*pi/lambda * sqrt(epsilon1);
s = sqrt(epsilon2)/sqrt(epsilon1);

stParams.a=a; stParams.c=c;
stParams.k1=k1; stParams.s=s;
stParams.N=N; stParams.nNbTheta=nNbTheta;
stParams.sIncType = sIncType;

Optional control parameters

stOptions.bGetR = false;
stOptions.Delta = 0;
stOptions.NB = 0; % NB will be estimated automatically
stOptions.bGetSymmetricT = false;

T-matrix calculation

tic; % timer
% Solve for T-matrix
stC = slvForFixed(stParams, stOptions);
% use this call instead to keep the expansion coefficients for further
% processing
% [stC, stAbcdnm] = slvForT(stParams,stOptions);

fprintf('T-matrix (N = %d) ... done in %.f seconds.\n', N, toc);

% To test for convergence and accuracy for a given set of parameters, one
% can for example repeat the calculation with N=N+5 and nNbTheta=nNbTheta+5
% as illustrated below
fprintf('Convergence testing...\n');
tic;
stParams2=stParams;
stParams2.N=stParams2.N+5;
stParams2.nNbTheta=stParams2.nNbTheta+5;
[stC2, ~] = slvForFixed(stParams2, stOptions);

fprintf('\nT-matrix (N = %d) ... done in %.f seconds.\n\n', N, toc);
fprintf('Results for a=%g, c=%g, k1=%g, s=%g+%gi, N=%d, Nt=%d\n',...
        a, c, k1, real(s),imag(s), N, nNbTheta);

fprintf('\nCross sections for fixed excitation (and estimated accuracy):\n');
fprintf('Cext = %.20g,   relative error: %.5g\n', stC.Cext, abs(stC.Cext./stC2.Cext-1));
fprintf('Csca = %.20g,   relative error: %.5g\n', stC.Csca, abs(stC.Csca./stC2.Csca-1));
fprintf('Cabs = %.20g,   relative error: %.5g\n', stC.Cabs, abs(stC.Cabs./stC2.Cabs-1));
fprintf('\nCross sections for orientation-averaged excitation (and estimated accuracy):\n');
fprintf('<Cext> = %.20g,   relative error: %.5g\n', stC.Cextoa, abs(stC.Cextoa./stC2.Cextoa-1));
fprintf('<Csca> = %.20g,   relative error: %.5g\n', stC.Cscaoa, abs(stC.Cscaoa./stC2.Cscaoa-1));
fprintf('<Cabs> = %.20g,   relative error: %.5g\n', stC.Cabsoa, abs(stC.Cabsoa./stC2.Cabsoa-1));

sphCalculatePQ: Calculating P,Q for 41 m-values with N_Q = 40, N_B = 41, N_Theta = 120
T-matrix (N = 40) ... done in 2 seconds.
Convergence testing...
sphCalculatePQ: Calculating P,Q for 46 m-values with N_Q = 45, N_B = 45, N_Theta = 125

T-matrix (N = 40) ... done in 2 seconds.

Results for a=10, c=50, k1=0.0128564, s=0.119065+2.67664i, N=40, Nt=120

Cross sections for fixed excitation (and estimated accuracy):
Cext = 509.7977525837234225,   relative error: 3.6637e-15
Csca = 99.483485613090834931,   relative error: 1.6653e-15
Cabs = 410.31426697063261599,   relative error: 4.1078e-15

Cross sections for orientation-averaged excitation (and estimated accuracy):
<Cext> = 249.93383391529411597,   relative error: 1.7208e-14
<Csca> = 36.305224719494638919,   relative error: 2.8866e-15
<Cabs> = 213.62860919579946994,   relative error: 1.9651e-14

Published with MATLAB® R2015a