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WC2D_TE_Exy_FEM_f.m
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WC2D_TE_Exy_FEM_f.m
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function[Ex,Ey,f0_xy]=WC2D_TE_Exy_FEM_f(x,y,eps,nmodes,f0_guess,f0_min,f0_max)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
c=2.99792458e8;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nx=length(x);
Ny=length(y);
Nxy=Nx*Ny;
dx=x(2)-x(1);
dy=y(2)-y(1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% Building of the operators %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% First derivative X %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DX1(Ny=5,Nx=4); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% 0 0 0 0 0 |1/2 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 1/2 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 1/2 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 1/2 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 1/2| 0 0 0 0 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% -1/2 0 0 0 0 | 0 0 0 0 0 |1/2 0 0 0 0 | 0 0 0 0 0 %
% 0 -1/2 0 0 0 | 0 0 0 0 0 | 0 1/2 0 0 0 | 0 0 0 0 0 %
% 0 0 -1/2 0 0 | 0 0 0 0 0 | 0 0 1/2 0 0 | 0 0 0 0 0 %
% 0 0 0 -1/2 0 | 0 0 0 0 0 | 0 0 0 1/2 0 | 0 0 0 0 0 %
% 0 0 0 0 -1/2| 0 0 0 0 0 | 0 0 0 0 1/2| 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 -1/2 0 0 0 0 | 0 0 0 0 0 |1/2 0 0 0 0 %
% 0 0 0 0 0 | 0 -1/2 0 0 0 | 0 0 0 0 0 | 0 1/2 0 0 0 %
% 0 0 0 0 0 | 0 0 -1/2 0 0 | 0 0 0 0 0 | 0 0 1/2 0 0 %
% 0 0 0 0 0 | 0 0 0 -1/2 0 | 0 0 0 0 0 | 0 0 0 1/2 0 %
% 0 0 0 0 0 | 0 0 0 0 -1/2| 0 0 0 0 0 | 0 0 0 0 1/2 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 0 0 0 0 -1/2 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 -1/2 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 -1/2 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 -1/2 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 -1/2| 0 0 0 0 0 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Second derivative X %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DX2(Ny=5,Nx=4); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% -2 0 0 0 0 | 1 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 -2 0 0 0 | 0 1 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 -2 0 0 | 0 0 1 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 -2 0 | 0 0 0 1 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 -2 | 0 0 0 0 1 | 0 0 0 0 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 1 0 0 0 0 |-2 0 0 0 0 | 1 0 0 0 0 | 0 0 0 0 0 %
% 0 1 0 0 0 | 0 -2 0 0 0 | 0 1 0 0 0 | 0 0 0 0 0 %
% 0 0 1 0 0 | 0 0 -2 0 0 | 0 0 1 0 0 | 0 0 0 0 0 %
% 0 0 0 1 0 | 0 0 0 -2 0 | 0 0 0 1 0 | 0 0 0 0 0 %
% 0 0 0 0 1 | 0 0 0 0 -2 | 0 0 0 0 1 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 1 0 0 0 0 |-2 0 0 0 0 | 1 0 0 0 0 %
% 0 0 0 0 0 | 0 1 0 0 0 | 0 -2 0 0 0 | 0 1 0 0 0 %
% 0 0 0 0 0 | 0 0 1 0 0 | 0 0 -2 0 0 | 0 0 1 0 0 %
% 0 0 0 0 0 | 0 0 0 1 0 | 0 0 0 -2 0 | 0 0 0 1 0 %
% 0 0 0 0 0 | 0 0 0 0 1 | 0 0 0 0 -2 | 0 0 0 0 1 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 0 0 0 0 | 1 0 0 0 0 |-2 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 1 0 0 0 | 0 -2 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 1 0 0 | 0 0 -2 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 1 0 | 0 0 0 -2 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 1 | 0 0 0 0 -2 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Axy=ones(1,(Nx-1)*Ny);
DX1 = (-0.5)*diag(Axy,-Ny) + (+0.5)*diag(Axy,Ny);
DX2 = (-2)*diag(ones(1,Ny*Nx)) + (1)*diag(Axy,-Ny) + (1)*diag(Axy,Ny);
%%%%%%%%%%%%%%%%%%%%%%%%%%%% First derivative Y %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DY1(Ny=5,Nx=4); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% 0 1/2 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% -1/2 0 1/2 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 -1/2 0 1/2 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 -1/2 0 1/2| 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 -1/2 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 1/2 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 -1/2 0 1/2 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 -1/2 0 1/2 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 -1/2 0 1/2| 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 -1/2 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 1/2 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 -1/2 0 1/2 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 -1/2 0 1/2 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 -1/2 0 1/2| 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 -1/2 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 1/2 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 -1/2 0 1/2 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 -1/2 0 1/2 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 -1/2 0 1/2 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 -1/2 0 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Second derivative Y %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DY2(Ny=5,Nx=4); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% -2 1 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 1 -2 1 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 1 -2 1 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 1 -2 1 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 1 -2 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 |-2 1 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 1 -2 1 0 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 1 -2 1 0 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 1 -2 1 | 0 0 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 1 -2 | 0 0 0 0 0 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 0 0 0 0 |-2 1 0 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 1 -2 1 0 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 1 -2 1 0 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 1 -2 1 | 0 0 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 1 -2 | 0 0 0 0 0 %
% ----------------------------------------------------------------------------- %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 |-2 1 0 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 1 -2 1 0 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 1 -2 1 0 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 1 -2 1 %
% 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 0 0 | 0 0 0 1 -2 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
AA=ones(1,Nx*Ny);
BB=ones(1,Nx*Ny-1);
BB(Ny:Ny:end)=0;
DY1=diag(BB,-1)*(-0.5) + diag(BB,1)*(0.5);
DY2=(-2)*diag(AA) + (1)*diag(BB,-1) + (1)*diag(BB,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Building of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H0 = DX2/dx^2 + DY2/dy^2 ;
H11 = H0 + DX1/dx * diag(1./eps(:)) * diag( DX1/dx * eps(:) ) ;
H11 = -diag(1./eps(:)) * H11;
H22 = H0 + DY1/dy * diag(1./eps(:)) * diag( DY1/dy * eps(:) ) ;
H22 = -diag(1./eps(:)) * H22;
H12 = DX1/dx * diag(1./eps(:)) * diag( DY1/dy * eps(:) ) ;
H12 = -diag(1./eps(:)) * H12;
H21 = DY1/dy * diag(1./eps(:)) * diag( DX1/dx * eps(:) ) ;
H21 = -diag(1./eps(:)) * H21;
Hxy = [ H11 H12 ; H21 H22 ] ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%% Diagonalisation of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Guess = (2*pi*f0_guess/c)^2;
Hxy=sparse(Hxy);
[psi_xy,k0_xy] = eigs(Hxy,nmodes,'SM'); %% eigen values are ordered
%[psi_xy,k0_xy] = eigs(Hxy,nmodes,Guess);
f0_xy=sqrt(diag(k0_xy)) * c /2/pi;
lambda_xy= 2*pi ./ sqrt(diag(k0_xy)) * 1e6;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% Filtering and reshaping the Wavefunction %%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
idx1=real(f0_xy)>f0_min;
idx2=real(f0_xy)<f0_max;
%idx3=imag(f0_xy)==0;
%idx=logical( idx1.*idx2.*idx3);
idx=logical( idx1.*idx2);
f0_xy=f0_xy(idx);
psi_xy=psi_xy(:,idx);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% here is a small patch due to differences between Octave and Matlab
% Matlab order the eigen values while Octave reverse it
if real(f0_xy(end))<real(f0_xy(1))
psi_xy=psi_xy(:,end:-1:1);
f0_xy=f0_xy(end:-1:1);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Ex = psi_xy( 1:Nxy , : ) ;
Ey = psi_xy( Nxy+1:end , : ) ;
nmodes=length(f0_xy);
Ex = reshape(Ex,[Ny,Nx,nmodes]);
Ey = reshape(Ey,[Ny,Nx,nmodes]);
end