ScriptSolveForTSpectrum

An example script showing how to obtain the orientation-averaged optical properties for a spheroid as a function of wavelength. Plots the wavelength-dependent spectra for orientation-averaged extinction, scattering, and absorption cross-sections.

Contents

Initialization

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:

lambda, k1, and s can here be wavelength-dependent vectors [L x 1]

clear all
close all

Parameters of the scattering problem

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

a = 15; % in nm
c = 45; % in nm, i.e. 30 x 90nm full-axes
lambda = (400:5:900).'; % in nm
epsilon2 = epsAu(lambda);
epsilon1 = 1.33^2; % for water

Convergence parameters

% Maximum multipole order for T-matrix and series expansions of fields
N = 20;
% Number of points for Gaussian quadratures to compute integrals in P and Q matrices
nNbTheta = 50;

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.lambda=lambda;
stParams.epsilon2=epsilon2;
stParams.epsilon1=epsilon1;

% Optional parameters may also be defined as follows:
stOptions.bGetR = false;
stOptions.Delta = 0;
stOptions.NB = 0; % NB will be estimated automatically
stOptions.bGetSymmetricT = false;
stOptions.bOutput = false; % false to suppress messages in lambda-loop

T-matrix calculation

Solve for T (all wavelengths)

tic;
stCoa = slvForTSpectrum(stParams,stOptions);

fprintf('\nT-matrices (N = %d) ... done in %.2f seconds.\n', N, toc);

% To test for convergence and accuracy, we choose the wavelength with the largest
% k1|s| and repeat the calculation with N=N+5 and nNbTheta=nNbTheta+5
[~,indWorst]=max(abs(stParams.k1 .* stParams.s));
stParams2 = pstGetParamsStructOneLambda(stParams,lambda(indWorst));
stParams2.N=stParams2.N+5;
stParams2.nNbTheta=stParams2.nNbTheta+5;
fprintf('\nConvergence testing for lambda = %.2f.\n', lambda(indWorst));
tic;
[stCoa2, ~] = slvForT(stParams2,stOptions);
relerrExt = (abs(stCoa.Cext(indWorst)./stCoa2.Cext-1));
relerrSca = (abs(stCoa.Csca(indWorst)./stCoa2.Csca-1));
relerrAbs = (abs(stCoa.Cabs(indWorst)./stCoa2.Cabs-1));
fprintf('\nT-matrix (N = %d) ... done in %.2f seconds.\n', N, toc);
 
Loop over 101 lambdas...

T-matrices (N = 20) ... done in 15.22 seconds.

Convergence testing for lambda = 900.00.

T-matrix (N = 20) ... done in 0.33 seconds.

Plotting orientation-averaged cross-sections

figure('Name','ScriptSolveForTSpectrum');
plot(lambda,[stCoa.Cext,stCoa.Csca,stCoa.Cabs]);
legend({['<Cext> (err. ', num2str(relerrExt,3),')'], ...
    ['<Csca> (err. ', num2str(relerrSca,3),')'], ...
    ['<Cabs> (err. ', num2str(relerrAbs,3),')']}, ...
    'Location','Best');
title(['a=', num2str(a), ', c=',num2str(c),', N=', int2str(N), ', Nt=', int2str(nNbTheta)]);
xlabel('Wavelength [nm]')
ylabel('Cross-section [nm^2]')