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Mie_LPR_Multilayer.m
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Mie_LPR_Multilayer.m
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% Mie theory for scattering, extinction, and absorption cross section
% core-shell structure can be calculated
% Wei E. I. Sha update Jan. 2019
% email:weisha@zju.edu.cn
function Mie_LPR_Multilayer
clc;clear
% load metal data
Au_data=load('./data/Au_epr.txt');
Au_epr=Au_data(:,1)+j*Au_data(:,2);
% load active material
active_data=load('./data/P3HT_PCBM_epr.txt');
P3HT_PCBM_epr=active_data(:,1)+j*active_data(:,2);
% parameter
epsc=1/(4*pi*9*10.^9); % permittivity in free space
murc=4*pi*10.^(-7); % permeability in free space
x=400:10:800; % wavelength in nm
% relative permittivity
Air=ones(1,length(x))*1; % air
Si_epr=3.4^2*ones(1,length(x))*1; % silicon
% wavelenth and frequency
wavelength=x*10^(-9);
omega=2*pi*3*10^8./wavelength;
MAX=4; % the number of Mie series (need increase for large sphere)
L=2; % how many layer (including for the outmost layer)
for fre=1:length(wavelength)
fre
eps_array=[Au_epr(fre),Air(fre)]; % relative permittivity (inner to outer)
mu_array=[1,1]; % relative permeability
r_array=[30]; % radius (inner to outer)
k_array=sqrt(mu_array.*eps_array)*2*pi/(wavelength(fre));
eps_array=eps_array*epsc;
mu_array=mu_array*murc;
r_array=r_array*10^(-9);
% inverse the order
inv_k_arr=k_array(end:-1:1);
inv_eps_arr=eps_array(end:-1:1);
inv_mu_arr=mu_array(end:-1:1);
inv_r_arr=r_array(end:-1:1);
% Outgoing wave reflection coef for TM wave (inner to outer)
for m=1:L-1;
for n=1:MAX
R_TM_Out(m,n)=...
(sqrt(eps_array(m+1)*mu_array(m))*ssb_der2(n,k_array(m),r_array(m))*ssb2(n,k_array(m+1),r_array(m))-...
sqrt(eps_array(m)*mu_array(m+1))*ssb_der2(n,k_array(m+1),r_array(m))*ssb2(n,k_array(m),r_array(m)))/...
(sqrt(eps_array(m)*mu_array(m+1))*ssb_der2(n,k_array(m+1),r_array(m))*ssb1(n,k_array(m),r_array(m))-...
sqrt(eps_array(m+1)*mu_array(m))*ssb_der1(n,k_array(m),r_array(m))*ssb2(n,k_array(m+1),r_array(m)));
T_TM_Out(m,n)=...
-i*eps_array(m+1)*sqrt(mu_array(m+1)/eps_array(m))/...
(sqrt(eps_array(m)*mu_array(m+1))*ssb_der2(n,k_array(m+1),r_array(m))*ssb1(n,k_array(m),r_array(m))-...
sqrt(eps_array(m+1)*mu_array(m))*ssb_der1(n,k_array(m),r_array(m))*ssb2(n,k_array(m+1),r_array(m)));
end
end
% Standing wave reflection coef for TM wave (outer to inner)
for m=1:L-1;
for n=1:MAX
R_TM_In(m,n)=...
(sqrt(inv_eps_arr(m)*inv_mu_arr(m+1))*ssb_der1(n,inv_k_arr(m+1),inv_r_arr(m))*ssb1(n,inv_k_arr(m),inv_r_arr(m))-...
sqrt(inv_eps_arr(m+1)*inv_mu_arr(m))*ssb_der1(n,inv_k_arr(m),inv_r_arr(m))*ssb1(n,inv_k_arr(m+1),inv_r_arr(m)))/...
(sqrt(inv_eps_arr(m+1)*inv_mu_arr(m))*ssb_der2(n,inv_k_arr(m),inv_r_arr(m))*ssb1(n,inv_k_arr(m+1),inv_r_arr(m))-...
sqrt(inv_eps_arr(m)*inv_mu_arr(m+1))*ssb_der1(n,inv_k_arr(m+1),inv_r_arr(m))*ssb2(n,inv_k_arr(m),inv_r_arr(m)));
T_TM_In(m,n)=...
-i*inv_eps_arr(m+1)*sqrt(inv_mu_arr(m+1)/inv_eps_arr(m))/...
(sqrt(inv_eps_arr(m+1)*inv_mu_arr(m))*ssb_der2(n,inv_k_arr(m),inv_r_arr(m))*ssb1(n,inv_k_arr(m+1),inv_r_arr(m))-...
sqrt(inv_eps_arr(m)*inv_mu_arr(m+1))*ssb_der1(n,inv_k_arr(m+1),inv_r_arr(m))*ssb2(n,inv_k_arr(m),inv_r_arr(m)));
end
end
% Standing wave reflection coef for TM wave£¨inner to outer£©
R_TM_In=R_TM_In(end:-1:1,:);
T_TM_In=T_TM_In(end:-1:1,:);
% Generalized reflection coef for TM wave
TM_Ref(1,:)=R_TM_In(1,:);
for m=2:L-1
for n=1:MAX
TM_Ref(m,n)=R_TM_In(m,n)+(T_TM_Out(m,n)*TM_Ref(m-1,n)*T_TM_In(m,n))/...
(1-R_TM_Out(m,n)*TM_Ref(m-1,n));
end
end
% Outgoing wave reflection coef for TE wave (inner to outer)
for m=1:L-1;
for n=1:MAX
R_TE_Out(m,n)=...
(sqrt(eps_array(m)*mu_array(m+1))*ssb_der2(n,k_array(m),r_array(m))*ssb2(n,k_array(m+1),r_array(m))-...
sqrt(eps_array(m+1)*mu_array(m))*ssb_der2(n,k_array(m+1),r_array(m))*ssb2(n,k_array(m),r_array(m)))/...
(sqrt(eps_array(m+1)*mu_array(m))*ssb_der2(n,k_array(m+1),r_array(m))*ssb1(n,k_array(m),r_array(m))-...
sqrt(eps_array(m)*mu_array(m+1))*ssb_der1(n,k_array(m),r_array(m))*ssb2(n,k_array(m+1),r_array(m)));
T_TE_Out(m,n)=...
-i*mu_array(m+1)*sqrt(eps_array(m+1)/mu_array(m))/...
(sqrt(eps_array(m+1)*mu_array(m))*ssb_der2(n,k_array(m+1),r_array(m))*ssb1(n,k_array(m),r_array(m))-...
sqrt(eps_array(m)*mu_array(m+1))*ssb_der1(n,k_array(m),r_array(m))*ssb2(n,k_array(m+1),r_array(m)));
end
end
% Standing wave reflection coef for TE wave (outer to inner)
for m=1:L-1;
for n=1:MAX
R_TE_In(m,n)=...
(sqrt(inv_eps_arr(m+1)*inv_mu_arr(m))*ssb_der1(n,inv_k_arr(m+1),inv_r_arr(m))*ssb1(n,inv_k_arr(m),inv_r_arr(m))-...
sqrt(inv_eps_arr(m)*inv_mu_arr(m+1))*ssb_der1(n,inv_k_arr(m),inv_r_arr(m))*ssb1(n,inv_k_arr(m+1),inv_r_arr(m)))/...
(sqrt(inv_eps_arr(m)*inv_mu_arr(m+1))*ssb_der2(n,inv_k_arr(m),inv_r_arr(m))*ssb1(n,inv_k_arr(m+1),inv_r_arr(m))-...
sqrt(inv_eps_arr(m+1)*inv_mu_arr(m))*ssb_der1(n,inv_k_arr(m+1),inv_r_arr(m))*ssb2(n,inv_k_arr(m),inv_r_arr(m)));
T_TE_In(m,n)=...
-i*inv_mu_arr(m+1)*sqrt(inv_eps_arr(m+1)/inv_mu_arr(m))/...
(sqrt(inv_eps_arr(m)*inv_mu_arr(m+1))*ssb_der2(n,inv_k_arr(m),inv_r_arr(m))*ssb1(n,inv_k_arr(m+1),inv_r_arr(m))-...
sqrt(inv_eps_arr(m+1)*inv_mu_arr(m))*ssb_der1(n,inv_k_arr(m+1),inv_r_arr(m))*ssb2(n,inv_k_arr(m),inv_r_arr(m)));
end
end
% Standing wave reflection coef for TE wave (inner to outer)
R_TE_In=R_TE_In(end:-1:1,:);
T_TE_In=T_TE_In(end:-1:1,:);
% Generalized reflection coef for TE wave
TE_Ref(1,:)=R_TE_In(1,:);
for m=2:L-1
for n=1:MAX
TE_Ref(m,n)=R_TE_In(m,n)+(T_TE_Out(m,n)*TE_Ref(m-1,n)*T_TE_In(m,n))/...
(1-R_TE_Out(m,n)*TE_Ref(m-1,n));
end
end
% total contribution
sum1=0;
sum2=0;
for n=1:MAX
sum1=sum1+(2*n+1)*(abs(TM_Ref(end,n))^2+abs(TE_Ref(end,n))^2);
sum2=sum2-(2*n+1)*real(TM_Ref(end,n)+TE_Ref(end,n));
end
% tm contribution
sum1_tm=0;
sum2_tm=0;
for n=1:MAX
sum1_tm=sum1_tm+(2*n+1)*(abs(TM_Ref(end,n))^2);
sum2_tm=sum2_tm-(2*n+1)*real(TM_Ref(end,n));
end
% te contribution
sum1_te=0;
sum2_te=0;
for n=1:MAX
sum1_te=sum1_te+(2*n+1)*(abs(TE_Ref(end,n))^2);
sum2_te=sum2_te-(2*n+1)*real(TE_Ref(end,n));
end
% scattering, extinction, and absorption cross section
sca=sum1*2*pi/abs(k_array(end))^2;
ext=sum2*2*pi/abs(k_array(end))^2;
absc=ext-sca;
sca_tm=sum1_tm*2*pi/abs(k_array(end))^2;
ext_tm=sum2_tm*2*pi/abs(k_array(end))^2;
absc_tm=ext_tm-sca_tm;
sca_te=sum1_te*2*pi/abs(k_array(end))^2;
ext_te=sum2_te*2*pi/abs(k_array(end))^2;
absc_te=ext_te-sca_te;
% normalized to geometric size
Absc(fre)=absc/pi/r_array(end)^2;
Sca(fre)=sca/pi/r_array(end)^2;
Ext(fre)=ext/pi/r_array(end)^2;
Absc_tm(fre)=absc_tm/pi/r_array(end)^2;
Sca_tm(fre)=sca_tm/pi/r_array(end)^2;
Ext_tm(fre)=ext_tm/pi/r_array(end)^2;
Absc_te(fre)=absc_te/pi/r_array(end)^2;
Sca_te(fre)=sca_te/pi/r_array(end)^2;
Ext_te(fre)=ext_te/pi/r_array(end)^2;
end
figure(1)
hold on;
plot(x,(Ext),'bo')
plot(x,(Absc),'kd')
%plot(x,Ext_tm,'r.-')
%plot(x,Ext_te,'g--')
xlabel('Wavelength (nm)')
ylabel('ECS and ACS')
% Spherical bessel 1
function output=sb1(degree,k,r)
output=sqrt(pi/(2*k*r))*besselj(degree+0.5,k*r);
% Modified spherical bessel 1
function output=ssb1(degree,k,r)
output=k*r*sb1(degree,k,r);
% Derivative of modified spherical bessel 1
function output=ssb_der1(degree,k,r)
output=sb1(degree,k,r)+k*r*(degree*sb1(degree-1,k,r)-(degree+1)*sb1(degree+1,k,r))/(2*degree+1);
% Spherical bessel 2
function output=sb2(degree,k,r)
output=sqrt(pi/(2*k*r))*besselh(degree+0.5,2,k*r);
% Modified spherical bessel 2
function output=ssb2(degree,k,r)
output=k*r*sb2(degree,k,r);
% Derivative of modified spherical bessel 2
function output=ssb_der2(degree,k,r)
output=sb2(degree,k,r)+k*r*(degree*sb2(degree-1,k,r)-(degree+1)*sb2(degree+1,k,r))/(2*degree+1);
% Associated legendre
function output=legen(degree,order,input)
var=legendre(degree,input);
output=var(order+1);
% Derivative of associated legendre
function output=legen_der(degree,order,input)
output=((degree+1)*input*legen(degree,order,input)-(degree-order+1)*legen(degree+1,order,input))/(1-input*input);