squarepixel_toeplitz_1d.m

通过计算晶体结构来确定其光谱分布

%SquarePixel_Toeplitz_1D.m
%Purpose: Construct the Toeplitz matrix of 1D ebxn with Square pixels
%Ref:Linfang Shen, Sailing He, and Sanshui Xiao, Large absolute band gaps
%in one-dimensional photonic crystals formed by large dielectric pixels,
%Physical Review B 66, 165315-1->-6 (2002)
function [tp,sig]=SquarePixel_Toeplitz_1D(ebxn,pw,M,flag)
%ebxn=The first quadrant of 2D permittivity with Square pixels
%pw=width of each pixel
%M=maximal half order number of Fourier coefficients
%flag=1:Laurent's rule; 
%flag=2:inverse rule for x;
t=size(ebxn);
if min(t)~=1
    sig=-1;
    tp='ebxn is not one dimension';
    return;
end
cw=2*t(1)*pw;
N=2*M+1;
tp=zeros(N);
Sr=zeros(1,N);
Sc=zeros(1,N);
if flag==1
    ebxn1=ebxn;
else
    ebxn1=1./ebxn;
end
for m=0:-1:-2*M
    Sr(1-m)=SquarePixel_ebxn_1D_FC(ebxn1,pw,m);
end
for m=0:2*M
    Sc(1+m)=SquarePixel_ebxn_1D_FC(ebxn1,pw,m);
end 
if flag==1
    tp=toeplitz(Sc,Sr);
else
    tp=inv(toeplitz(Sc,Sr));
end
sig=1;