squarepixel_toeplitz.asv

通过计算晶体结构来确定其光谱分布

%RectPixel_Toeplitz.m
%Purpose: Construct the Toeplitz matrix of 2D ebxn with rectangular pixels
%Ref:Linfang Shen, Sailing He, and Sanshui Xiao, Large absolute band gaps
%in two-dimensional photonic crystals formed by large dielectric pixels,
%Physical Review B 66, 165315-1->-6 (2002)
function [tp,sig]=RectPixel_Toeplitz(ebxn,pw,M,flag)
%ebxn=The first quadrant of 2D permittivity with rectangular 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;
%flag=3:inverse rule for y.
t=size(ebxn);
if t(1)~=t(2)
    sig=-1;
    tp='ebxn is not a square matrix';
    return;
end
cw=2*t(1)*pw;
N=2*M+1;
tp=zeros(N^2);
Srr=zeros(1,N);
Src=zeros(1,N);
Scr=zeros(1,N);
Scc=zeros(1,N);
Sr=zeros(N,N^2);
Sc=zeros(N,N^2);
tl=zeros(N,2*N^2-N);
if flag==1
    ebxn1=ebxn;
else
    ebxn1=1./ebxn;
end
for n=0:-1:-2*M
    %row vector of a given n(y) in long row 
    for m=0:-1:-2*M
        Srr(1-m)=RectPixel_ebxn_2D_FC(ebxn1,pw,cw,m,n,flag);
    end
    
    %column vector of a given n(y)in long row
    for m=0:2*M
        Src(1+m)=RectPixel_ebxn_2D_FC(ebxn1,pw,cw,m,n,flag);
    end 
    
    %structure Toeplitz matrix of a given n(y), add it into a long row
    %matrix Sr
    st=-n*N+1;
    ed=st+N-1;
    if flag==1
        Sr(:,st:ed)=toeplitz(Src,Srr);
    else
        Sr(:,st:ed)=inv(toeplitz(Src,Srr));
    end
end
for n=0:2*M
    %row vector of a given n(y) in long column
    for m=0:-1:-2*M
        Scr(1-m)=RectPixel_ebxn_2D_FC(ebxn1,pw,cw,m,n);
    end
    
    %column vector of a given n(y)in long column
    for m=0:2*M
        Scc(1+m)=RectPixel_ebxn_2D_FC(ebxn1,pw,cw,m,n);
    end 
    
    %structure Toeplitz matrix of a given n(y), add it into a long column
    %matrix Sc    
    st=(2*M-n)*N+1;
    ed=st+N-1;
    if flag==1
        Sc(:,st:ed)=toeplitz(Scc,Scr);
    else
        Sc(:,st:ed)=inv(toeplitz(Scc,Scr));
    end
end

%catenate the row and column matrix, all elemental matrix of final result
%contained in it
tl=cat(2,Sc(:,1:2*M*N),Sr);

%structure the final large (double) Toeplitz matrix 
st2=N^2-N+1;
ed2=st2+N^2-1;
tp(1:N,:)=tl(:,st2:ed2);
for m=2:N
    st1=(m-1)*N+1;
    ed1=st1+N-1;
    st2=st2-N;
    ed2=st2+N^2-1;
    tp(st1:ed1,:)=tl(:,st2:ed2);
end
sig=1;