%This is a simple demo for Photonic Crystals simulation
%10 points is considered.
%by Gao Haikuo
%date:20170411clear; clc;
global NG G f  Nkpoints eigenValue modeset kCorner
global epsa epsb epssys a b1 b2
epssys=1.0e-6; %设定一个最小量，避免系统截断误差或除0错误%this is the lattice vector and the reciprocal lattice vector
a=1; a1=a*[1 0]; a2=a*[0 1];
b1=2*pi/a*[1 0];b2=2*pi/a*[0 1];
Nkpoints=10; %每个方向上取的点数，
modeset=2;% 1:'TE' 2 'TM'
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%定义晶格的参数
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
epsa = 8.9; %inner
epsb = 1; %outer
Pf = 0.1257; %Pf = Ac/Au 填充率，可根据需要自行设定Au =a^2; %二维格子原胞面积Rc = (Pf *Au/pi)^(1/2); %介质柱截面半径Ac = pi*(Rc)^2; %介质柱横截面积kCorner=(2*pi/a)*[epssys 0;1/2 0;1/2 1/2]; %T X M %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%get gap[G,f]=getGAndf(Pf,Rc);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%get gapeigenValue=getFrequency(kCorner);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%get gapgap=getGap();%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%绘draw banddrawBand(gap);

function [G,f]=getGAndf(Pf,Rc)
global NG G f  Nkpoints eigenValue kCorner modeset a
global epsa epsb epssys b1 b2
NrSquare = 10;
NG =(2*NrSquare+1)^2;  % NG is the number of the G value
G = zeros(NG,2);
i = 1;
for l = -NrSquare:NrSquarefor m = -NrSquare:NrSquareG(i,:)=l*b1+m*b2;i = i+1;end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%生成k空间中的f(Gi-Gj)的值，i,j 从1到NG。
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f=zeros(NG,NG);
for i=1:NG for j=1:NG Gij=norm(G(i,:)-G(j,:)); if (Gij < epssys) f(i,j)=(1/epsa)*Pf+(1/epsb)*(1-Pf); else f(i,j)=(1/epsa-1/epsb)*Pf*2*besselj(1,Gij*Rc)/(Gij*Rc); end; end;
end; 

function eigenValue=getFrequency(kCorner)
global  NG Nkpoints modeset
n_kCorner=size(kCorner,1);
kCorner_ex=[kCorner;kCorner(1,:)];
eigenValue=zeros(Nkpoints,NG,n_kCorner,2);
for i_mode=modesetfor i_kCorner=1:n_kCornereigenValue(:,:,i_kCorner,i_mode)=...getEigValue(kCorner_ex(i_kCorner,:),...kCorner_ex(i_kCorner+1,:),i_mode);end
end

function [eigValue]=getEigValue(k_begin,k_end,mode)
%mode :1 for TE 2 for TM
global NG G f Nkpoints
THETA=zeros(NG,NG); %待解的TE波矩阵
stepsize=0:1/(Nkpoints-1):1; %每个方向上的步长
TX_TE_eig = zeros(Nkpoints,NG);
for n=1:Nkpoints %scan the 10 points along the directionfprintf(['\n k-point:',int2str(n),'of',int2str(Nkpoints),'.\n']);step = stepsize(n)*(k_end-k_begin)+k_begin;  % get the kfor i=1:(NG-1)   % Gfor j=(i+1):NG % G'
            kGi = step+G(i,:); %k+GkGj = step+G(j,:); %K+G'
            switch modecase 1  %TE modeTHETA(i,j)=f(i,j)*dot(kGi,kGj); %(K+G)(K+G')f(G-G')case 2 %TH modeTHETA(i,j)=f(i,j)*norm(kGi)*norm(kGj);endTHETA(j,i)=conj(THETA(i,j)); endend    for i=1:NGkGi = step+G(i,:);THETA(i,i)=f(i,i)*norm(kGi)*norm(kGi); endeigValue(n,:)=sort(sqrt(eig(THETA))).';
end

function gap=getGap()
global  eigenValue kCorner modeset NG a
gap=[];
band=[];
n_kCorner=size(kCorner,1);
kCorner_ex=[kCorner;kCorner(1,:)];
for mode=modeset    for i_kCorner=1:n_kCornerfor k=1:NGsubLine=eigenValue(:,k,i_kCorner,mode)*a/(2*pi);L=min(subLine);H=max(subLine);band=mergeBand(band,L,H);endend
end
if size(band,1)>=2gap=[band(1:end-1,2),band(2:end,1)];
end

function band=mergeBand(band,L,H)
flag=1;
i_L=0;%最小值所在行数
flag_L_in=0;%是否在之间
i_H=0;
flag_H_in=0;
i=1;
flag_H_scan=1;
if isempty(band)band=[L,H];return;
end
while flagif L<band(i,1)i_L=i;flag=0;flag_L_in=0;elseif L<=band(i,2)i_L=i;flag=0;flag_L_in=1;elsei=i+1;if i>length(band(:,1))flag=0;flag_H_scan=0;band=[band;L,H];endend
end
flag=1;
if flag_H_scanwhile flagif H<band(i,1)i_H=i;flag=0;flag_H_in=0;elseif H<=band(i,2)i_H=i;flag=0;flag_H_in=1;elsei=i+1;if i>length(band(:,1))flag=0;i_H=i;endendend%mergeif i_L==i_H if L<band(i_L,1) && H>=band(i_H,1)band(i_L,1)=L;elseif H<band(i_L,1) band=[band(1:i_L-1,:);[L,H];band(i_L:end,:)];end elseif  i_H>length(band(:,1))band(i_L,1)=min([band(i_L,1),L]);band(i_L,2)=H;if i_L+1<=length(band(:,1))band(i_L+1:end,:)=[];endelseif  H>=band(i_H,1)  band(i_L,1)=min([band(i_L,1),L]);band(i_L,2)=max([band(i_H,2),H]);band(i_L+1:i_H,:)=[];elseband(i_L,1)=min([band(i_L,1),L]);band(i_L,2)=H; if i_L+1<=i_H-1band(i_L+1:i_H-1,:)=[];endend        end
end

function drawBand(gap)
global NG G f  Nkpoints eigenValue kCorner modeset a
n_kCorner=size(kCorner,1);
figure (1)
hold on;
colorSet=['r','b'];
for mode=modesetfor i_kCorner=1:n_kCornerfor k=1:NGh=plot((i_kCorner-1)*(Nkpoints-1) : i_kCorner*(Nkpoints-1),...eigenValue(:,k,i_kCorner,mode)*a/(2*pi),colorSet(mode));set(h, 'linesmoothing', 'on');endend
end
grid on;
xlabel('K-Space');
yLabel('Frequency(\omegaa/2\piC)');
xmax=n_kCorner*(Nkpoints-1);
axis([0 xmax 0 0.8]);
set(gca,'XTick',0:(Nkpoints-1):xmax);
xtixlabel = strvcat('T','X','M','T');
set(gca,'XTickLabel',xtixlabel);
%draw gap
for i=1:size(gap,1)fill([0, xmax,xmax,0],[gap(i,1),gap(i,1),gap(i,2),gap(i,2)],'r');
end
hold off;