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WC3D_FEM_f.m
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WC3D_FEM_f.m
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function[Ex,Ey,Ez,f0]=WC3D_FEM_f(x,y,z,eps,nmodes,f0_guess,f0_min,f0_max)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
c=2.99792458e8;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nx=length(x);
Ny=length(y);
Nz=length(z);
Nxyz=Nx*Ny*Nz;
dx=x(2)-x(1);
dy=y(2)-y(1);
dz=z(2)-z(1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% Building of the operators %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Second derivative X %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DX2(Ny=3,Nx=3,Nz=3); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% -2 0 0 | 1 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 -2 0 | 0 1 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 -2 | 0 0 1 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 1 0 0 |-2 0 0 | 1 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 1 0 | 0 -2 0 | 0 1 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 1 | 0 0 -2 | 0 0 1 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 1 0 0 |-2 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 1 0 | 0 -2 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 1 | 0 0 -2 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% =========================================================================================================== %
% 0 0 0 | 0 0 0 | 0 0 0 ||-2 0 0 | 1 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 -2 0 | 0 1 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 -2 | 0 0 1 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 0 0 0 || 1 0 0 |-2 0 0 | 1 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 1 0 | 0 -2 0 | 0 1 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 1 | 0 0 -2 | 0 0 1 || 0 0 0 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 1 0 0 |-2 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 1 0 | 0 -2 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 1 | 0 0 -2 || 0 0 0 | 0 0 0 | 0 0 0 %
% =========================================================================================================== %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 ||-2 0 0 | 1 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 -2 0 | 0 1 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 -2 | 0 0 1 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 1 0 0 |-2 0 0 | 1 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 1 0 | 0 -2 0 | 0 1 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 1 | 0 0 -2 | 0 0 1 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 1 0 0 |-2 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 1 0 | 0 -2 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 1 | 0 0 -2 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Axy = [ ones(1,(Nx-1)*Ny) zeros(1,Ny) ];
Axyz = [ repmat(Axy,1,Nz-1) ones(1,(Nx-1)*Ny) ];
DX1 = (-0.5)*diag(Axyz,-Ny) + (+0.5)*diag(Axyz,Ny);
DX2 = (-2)*diag(ones(1,Nx*Ny*Nz)) + (1)*diag(Axyz,-Ny) + (1)*diag(Axyz,Ny);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Second derivative Y %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DY2(Ny=3,Nx=3,Nz=3); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% -2 1 0 | 0 0 0 | 0 0 0 || 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 | 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 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 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 | 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 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 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 %
% 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 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 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 | 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 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 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 | 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 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 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 || 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 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 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 | 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 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 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 | 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 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 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 || 0 0 0 | 0 0 0 | 0 1 -2 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
BB=ones(1,Nx*Ny*Nz-1);
BB(Ny:Ny:end)=0;
DY1 = (-0.5)*diag(BB,-1) + (+0.5)*diag(BB,1);
DY2 = (-2)*diag(ones(1,Nx*Ny*Nz)) + (1)*diag(BB,-1) + (1)*diag(BB,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Second derivative Z %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DZ2(Ny=3,Nx=3,Nz=3); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% -2 0 0 | 0 0 0 | 0 0 0 || 1 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 -2 0 | 0 0 0 | 0 0 0 || 0 1 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 -2 | 0 0 0 | 0 0 0 || 0 0 1 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 |-2 0 0 | 0 0 0 || 0 0 0 | 1 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 -2 0 | 0 0 0 || 0 0 0 | 0 1 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 -2 | 0 0 0 || 0 0 0 | 0 0 1 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 |-2 0 0 || 0 0 0 | 0 0 0 | 1 0 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 -2 0 || 0 0 0 | 0 0 0 | 0 1 0 || 0 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 -2 || 0 0 0 | 0 0 0 | 0 0 1 || 0 0 0 | 0 0 0 | 0 0 0 %
% =========================================================================================================== %
% 1 0 0 | 0 0 0 | 0 0 0 ||-2 0 0 | 0 0 0 | 0 0 0 || 1 0 0 | 0 0 0 | 0 0 0 %
% 0 1 0 | 0 0 0 | 0 0 0 || 0 -2 0 | 0 0 0 | 0 0 0 || 0 1 0 | 0 0 0 | 0 0 0 %
% 0 0 1 | 0 0 0 | 0 0 0 || 0 0 -2 | 0 0 0 | 0 0 0 || 0 0 1 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 1 0 0 | 0 0 0 || 0 0 0 |-2 0 0 | 0 0 0 || 0 0 0 | 1 0 0 | 0 0 0 %
% 0 0 0 | 0 1 0 | 0 0 0 || 0 0 0 | 0 -2 0 | 0 0 0 || 0 0 0 | 0 1 0 | 0 0 0 %
% 0 0 0 | 0 0 1 | 0 0 0 || 0 0 0 | 0 0 -2 | 0 0 0 || 0 0 0 | 0 0 1 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 1 0 0 || 0 0 0 | 0 0 0 |-2 0 0 || 0 0 0 | 0 0 0 | 1 0 0 %
% 0 0 0 | 0 0 0 | 0 1 0 || 0 0 0 | 0 0 0 | 0 -2 0 || 0 0 0 | 0 0 0 | 0 1 0 %
% 0 0 0 | 0 0 0 | 0 0 1 || 0 0 0 | 0 0 0 | 0 0 -2 || 0 0 0 | 0 0 0 | 0 0 1 %
% =========================================================================================================== %
% 0 0 0 | 0 0 0 | 0 0 0 || 1 0 0 | 0 0 0 | 0 0 0 ||-2 0 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 1 0 | 0 0 0 | 0 0 0 || 0 -2 0 | 0 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 1 | 0 0 0 | 0 0 0 || 0 0 -2 | 0 0 0 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 1 0 0 | 0 0 0 || 0 0 0 |-2 0 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 1 0 | 0 0 0 || 0 0 0 | 0 -2 0 | 0 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 1 | 0 0 0 || 0 0 0 | 0 0 -2 | 0 0 0 %
% ----------------------------------------------------------------------------------------------------------- %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 1 0 0 || 0 0 0 | 0 0 0 |-2 0 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 1 0 || 0 0 0 | 0 0 0 | 0 -2 0 %
% 0 0 0 | 0 0 0 | 0 0 0 || 0 0 0 | 0 0 0 | 0 0 1 || 0 0 0 | 0 0 0 | 0 0 -2 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Axyz=ones(1,Nx*Ny*(Nz-1));
DZ1 = (-0.5)*diag(Axyz,-Nx*Ny) + (+0.5)*diag(Axyz,Nx*Ny);
DZ2 = (-2)*diag(ones(1,Nx*Ny*Nz)) + (1)*diag(Axyz,-Nx*Ny) + (1)*diag(Axyz,Nx*Ny);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Building of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H0 = DX2/dx^2 + DY2/dy^2 + DZ2/dz^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;
H33 = H0 + DZ1/dz * diag(1./eps(:)) * diag( DZ1/dz * eps(:) ) ;
H33 = -diag(1./eps(:)) * H33;
H12 = DX1/dx * diag(1./eps(:)) * diag( DY1/dy * eps(:) ) ;
H12 = -diag(1./eps(:)) * H12;
H13 = DX1/dx * diag(1./eps(:)) * diag( DZ1/dz * eps(:) ) ;
H13 = -diag(1./eps(:)) * H13;
H21 = DY1/dy * diag(1./eps(:)) * diag( DX1/dx * eps(:) ) ;
H21 = -diag(1./eps(:)) * H21;
H23 = DY1/dy * diag(1./eps(:)) * diag( DZ1/dz * eps(:) ) ;
H23 = -diag(1./eps(:)) * H23;
H31 = DZ1/dz * diag(1./eps(:)) * diag( DX1/dx * eps(:) ) ;
H31 = -diag(1./eps(:)) * H31;
H32 = DZ1/dz * diag(1./eps(:)) * diag( DY1/dy * eps(:) ) ;
H32 = -diag(1./eps(:)) * H32;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H = [
H11 H12 H13
H21 H22 H23
H31 H32 H33 ] ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%% Diagonalisation of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Guess = (2*pi*f0_guess/c)^2;
H=sparse(H);
[psi,k0] = eigs(H,nmodes,'SM'); %% eigen values are ordered
%[psi,k0] = eigs(H,nmodes,Guess);
f0=sqrt(diag(k0)) * c /2/pi;
lambda= 2*pi ./ sqrt(diag(k0)) * 1e6;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% Filtering and reshaping the Wavefunction %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
idx1=real(f0)>f0_min;
idx2=real(f0)<f0_max;
idx3=imag(f0)==0;
idx=logical( idx1.*idx2.*idx3);
f0=f0(idx);
psi=psi(:,idx);
%f0=f0(end:-1:1,:); % in Octave, the eigen solution are reversed
%psi=psi(:,end:-1:1); % in Octave, the eigen solution are reversed
nmodes=length(f0);
Ex = psi( 1:Nxyz , : );
Ey = psi( Nxyz+1:2*Nxyz , : );
Ez = psi( 2*Nxyz+1:end , : );
Ex = reshape(Ex,[Ny,Nx,Nz,nmodes]);
Ey = reshape(Ey,[Ny,Nx,Nz,nmodes]);
Ez = reshape(Ez,[Ny,Nx,Nz,nmodes]);
end