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function TransferMatrix
%------------BEGIN USER INPUT PARAMETERS SPECITIFCATION---------------
%
lambda=350:800; % Wavelengths over which field patterns are calculated
stepsize = 1;   % The electric field is calculated at a latice of points (nm)
                % in the device cross section seperated by this distance

% plotWavelengths specifies which wavelengths to plot when plotting E-field
% intensity distributions (figure 1). Specify values by adding wavelength
% values to the array. Values must be within the range of calculated
% wavelenths (ie. must be an element of the lambda array). All wavelengths
% are in nanometers.
plotWavelengths = [400 500 600];

% Specify Layers in device (an arbitrary number of layers is permitted) and 
% thicknesses.
%
% Change these arrays to change the order or number of layers and/or
% thickness of layers. List the layers in the order that they appear in the
% device starting with the side the light is incident on.  THE NAMES OF THE
% LAYERS MUST CORRESPOND TO THE NAMES OF THE MATERIALS IN THE INDEX OF 
% REFRACTION LIBRARY FILE, 'Index_of_Refraction_library.xls'. The first
% layer must be the transparent substrate (glass) or 'Air' if the active
% layers are on the reflective electrode (rather than transparent electrode) side 
% of the device.  The layer thicknesses are in nanometers.

layers = { 'Ag' 'SiO2' 'SiO2' 'aSi'}; % Names of layers of materials starting from side light is incident from
thicknesses = [ 50  500 500 100 ];  % thickness of each corresponding layer in nm (thickness of the first layer is irrelivant)

% Set plotGeneration to 'true' if you want to plot generation rate as a
% function of position in the device and output the calculated short circuit current
% under AM1.5G illumination (assuming 100% internal quantum efficiency)
plotGeneration = true;
activeLayer = 4; % index of material layer where photocurrent is generated
%
%------------END USER INPUT PARAMETERS SPECIFICATION-------------------



% Load in index of refraction for each material
n = zeros(size(layers,2),size(lambda,2));
for index = 1:size(layers,2)
    n(index,:) = LoadRefrIndex(layers{index},lambda);
end
t = thicknesses;

% Constants
h = 6.62606957e-34; 	% Js Planck's constant
c = 2.99792458e8;	% m/s speed of light
q = 1.60217657e-19;	% C electric charge

% Calculate Incoherent power transmission through substrate
% See Griffiths "Intro to Electrodynamics 3rd Ed. Eq. 9.86 & 9.87
T_glass=abs(4*1*n(1,:)./(1+n(1,:)).^2); 
R_glass=abs((1-n(1,:))./(1+n(1,:))).^2;

% Calculate transfer matrices, and field at each wavelength and position
t(1)=0;
t_cumsum=cumsum(t);
x_pos=(stepsize/2):stepsize:sum(t); %positions to evaluate field
%x_mat specifies what layer number the corresponding point in x_pos is in:
x_mat= sum(repmat(x_pos,length(t),1)>repmat(t_cumsum',1,length(x_pos)),1)+1; 
R=lambda*0;
E=zeros(length(x_pos),length(lambda));
for l = 1:length(lambda)
    % Calculate transfer matrices for incoherent reflection and transmission at the first interface
    S=I_mat(n(1,l),n(2,l));
    for matindex=2:(length(t)-1)
        S=S*L_mat(n(matindex,l),t(matindex),lambda(l))*I_mat(n(matindex,l),n(matindex+1,l));
    end
    R(l)=abs(S(2,1)/S(1,1))^2; %JAP Vol 86 p.487 Eq 9 Power Reflection from layers other than substrate
    T(l)=abs(2/(1+n(1,l)))/sqrt(1-R_glass(l)*R(l)); %Transmission of field through glass substrate Griffiths 9.85 + multiple reflection geometric series

    % Calculate all other transfer matrices
    for material = 2:length(t) 
        xi=2*pi*n(material,l)/lambda(l);
        dj=t(material);
        x_indices=find(x_mat == material); %indices of points which are in the material layer considered
        x=x_pos(x_indices)-t_cumsum(material-1); %distance from interface with previous layer
        % Calculate S matrices (JAP Vol 86 p.487 Eq 12 and 13)
        S_prime=I_mat(n(1,l),n(2,l));
        for matindex=3:material
            S_prime=S_prime*L_mat(n(matindex-1,l),t(matindex-1),lambda(l))*I_mat(n(matindex-1,l),n(matindex,l));
        end
        S_doubleprime=eye(2);
        for matindex=material:(length(t)-1)
            S_doubleprime=S_doubleprime*I_mat(n(matindex,l),n(matindex+1,l))*L_mat(n(matindex+1,l),t(matindex+1),lambda(l));
        end
        % Normalized Field profile (JAP Vol 86 p.487 Eq 22)
        E(x_indices,l)=T(l)*(S_doubleprime(1,1)*exp(-1i*xi*(dj-x))+S_doubleprime(2,1)*exp(1i*xi*(dj-x))) ./(S_prime(1,1)*S_doubleprime(1,1)*exp(-1i*xi*dj)+S_prime(1,2)*S_doubleprime(2,1)*exp(1i*xi*dj));
    end 
end

% Overall Reflection from device with incoherent reflections at first
% interface (typically air-glass)
Reflection=R_glass+T_glass.^2.*R./(1-R_glass.*R);

% Plots electric field intensity |E|^2 vs position in device for
% wavelengths specified in the initial array, plotWavelengths. 
close all
figure(1)
plotString = '';
legendString = cell(1,size(plotWavelengths,2));
for index=1:size(plotWavelengths,2)
    plotString = strcat(plotString, ['x_pos,abs(E(:,', num2str(find(lambda == plotWavelengths(index))), ').^2),']);
    legendString{index} = [num2str(plotWavelengths(index)), ' nm'];
end
eval(['plot(', plotString, '''LineWidth'',2)'])
axislimit1=axis;

% Draws vertical lines at each material boundary in the stack and labels
% each layer
for matindex=2:length(t)
    line([sum(t(1:matindex)) sum(t(1:matindex))],[0 axislimit1(4)]);
    text((t_cumsum(matindex)+t_cumsum(matindex-1))/2,0,layers{matindex},'HorizontalAlignment','center','VerticalAlignment','bottom')
end

title('E-field instensity in device');
xlabel('Position in Device (nm)');
ylabel('Normalized Electric field intensity |E|^2');
legend(legendString);

% Absorption coefficient in cm^-1 (JAP Vol 86 p.487 Eq 23)
a=zeros(length(t),length(lambda));
for matindex=2:length(t)
     a(matindex,:)=4*pi*imag(n(matindex,:))./(lambda*1e-7);
end

% Plots normalized intensity absorbed /cm3-nm at each position and
% wavelength as well as the total reflection expected from the device
% (useful for comparing with experimentally measured reflection spectrum)
figure(2)
Absorption=zeros(length(t),length(lambda));
plotString = '';
for matindex=2:length(t)
    Pos=find(x_mat == matindex);
    AbsRate=repmat(a(matindex,:).*real(n(matindex,:)),length(Pos),1).*(abs(E(Pos,:)).^2);
    Absorption(matindex,:)=sum(AbsRate,1)*stepsize*1e-7;
    plotString = strcat(plotString, ['lambda,Absorption(', num2str(matindex), ',:),']);
end

eval(['plot(', plotString, 'lambda,Reflection,''LineWidth'',2)'])
title('Fraction of Light absorbed or reflected');
xlabel('Wavelength (nm)');
ylabel('Light Intensity Fraction');
legend(layers{2:size(layers,2)}, 'Reflectance');

% Plots generation rate as a function of position in the device and
% calculates Jsc
if plotGeneration == true
    
    % Load in 1sun AM 1.5 solar spectrum in mW/cm2nm
    AM15_data=xlsread('AM15.xls');
    AM15=interp1(AM15_data(:,1), AM15_data(:,2), lambda, 'linear', 'extrap');

    figure(3)
    % Energy dissipation mW/cm3-nm at each position and wavelength (JAP Vol
    % 86 p.487 Eq 22)
    ActivePos=find(x_mat == activeLayer);
    Q=repmat(a(activeLayer,:).*real(n(activeLayer,:)).*AM15,length(ActivePos),1).*(abs(E(ActivePos,:)).^2);

    % Exciton generation rate per second-cm3-nm at each position and wavelength
    Gxl=(Q*1e-3).*repmat(lambda*1e-9,length(ActivePos),1)/(h*c);

    if length(lambda)==1
        lambdastep= 1;
    else
        lambdastep=(max(lambda)-min(lambda))/(length(lambda)-1);
    end
    Gx=sum(Gxl,2)*lambdastep; % Exciton generation rate as a function of position/(sec-cm^3)
    plot(x_pos(ActivePos),Gx,'LineWidth',2)
    axislimit3=axis;
    axis([axislimit1(1:2) axislimit3(3:4)])
    % inserts vertical lines at material boundaries
    for matindex=2:length(t)
        line([sum(t(1:matindex)) sum(t(1:matindex))],[0 axislimit3(4)]);
        text((t_cumsum(matindex)+t_cumsum(matindex-1))/2,0,layers{matindex},'HorizontalAlignment','center','VerticalAlignment','bottom')
    end

    title('Generation Rate in Device') 
    xlabel('Position in Device (nm)');
    ylabel('Generation rate /(sec-cm^3)');

    % outputs predicted Jsc under AM1.5 illumination assuming 100% internal
    % quantum efficiency at all wavelengths
    Jsc=sum(Gx)*stepsize*1e-7*q*1e3 %in mA/cm^2

    % Calculate parasitic absorption
    parasitic_abs=(1-Reflection-Absorption(activeLayer,:))';
    
    % sends absorption, reflection, and wavelength data to the workspace
    assignin('base','absorption',Absorption');
    assignin('base','reflection',Reflection');
    assignin('base','parasitic_abs',parasitic_abs);
    assignin('base','lambda',lambda');
end

%------------------- Helper Functions ------------------------------------
% Function I_mat
% This function calculates the transfer matrix, I, for reflection and
% transmission at an interface between materials with complex dielectric 
% constant n1 and n2.
function I = I_mat(n1,n2)
r=(n1-n2)/(n1+n2);
t=2*n1/(n1+n2);
I=[1 r; r 1]/t;

% Function L_mat
% This function calculates the propagation matrix, L, through a material of
% complex dielectric constant n and thickness d for the wavelength lambda.
function L = L_mat(n,d,lambda)
xi=2*pi*n/lambda;
L=[exp(-1i*xi*d) 0; 0 exp(1i*xi*d)];

% Function LoadRefrIndex
% This function returns the complex index of refraction spectra, ntotal, for the
% material called 'name' for each wavelength value in the wavelength vector
% 'wavelengths'.  The material must be present in the index of refraction
% library 'Index_of_Refraction_library.xls'.  The program uses linear
% interpolation/extrapolation to determine the index of refraction for
% wavelengths not listed in the library.
function ntotal = LoadRefrIndex(name,wavelengths)

%Data in IndRefr, Column names in IndRefr_names
[IndRefr,IndRefr_names]=xlsread('Index_of_Refraction_library2.xls');

% Load index of refraction data in spread sheet, will crash if misspelled
file_wavelengths=IndRefr(:,strmatch('Wavelength',IndRefr_names));
n=IndRefr(:,strmatch(strcat(name,'_n'),IndRefr_names));
k=IndRefr(:,strmatch(strcat(name,'_k'),IndRefr_names));

% Interpolate/Extrapolate data linearly to desired wavelengths
n_interp=interp1(file_wavelengths, n, wavelengths, 'linear', 'extrap');
k_interp=interp1(file_wavelengths, k, wavelengths, 'linear', 'extrap');

%Return interpolated complex index of refraction data
ntotal = n_interp+1i*k_interp; 

Answer 1

[Cris LaPierre]

Your code is trying to load an xls file, but your file is 'xlsx'.

[IndRefr,IndRefr_names]=xlsread('Index_of_Refraction_library2.xls');

Update the extension to 'xlsx' and your code runs fine.

[zina shadidi]

thank you Cris LaPierre

[Simenew]

Error in TransferMatrix (line 36)

n(index,:) = LoadRefrIndex(layers{index},lambda);???