[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 ?@_dx=su  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ' vwBG=9C  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ze-iDd_y  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear U^xFqJY6  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 t.cplJF&Ue  
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%fid=fopen('e21.dat','w'); :O7J9K|  
N = 128;                       % Number of Fourier modes (Time domain sampling points) )Ii=8etdv  
M1 =3000;              % Total number of space steps pPE4~g 05h  
J =100;                % Steps between output of space D)Zv  
T =10;                  % length of time windows:T*T0 DsoF4&>g[B  
T0=0.1;                 % input pulse width mS0W@#|K  
MN1=0;                 % initial value for the space output location `JRdOe  
dt = T/N;                      % time step $Ix^Rm9c  
n = [-N/2:1:N/2-1]';           % Index gisZmu0  
t = n.*dt;   n#*cVB81  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ?g'l/xuRe  
u20=u10.*0.0;                  % input to waveguide 2 yZ`\.GgC^&  
u1=u10; u2=u20;                 r* U6govky  
U1 = u1;   jzQgDed ]  
U2 = u2;                       % Compute initial condition; save it in U V|7 cdX#H  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ZM"t.  
w=2*pi*n./T; Vh&uSi1V  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T s[hD9$VB>  
L=4;                           % length of evoluation to compare with S. Trillo's paper ;/v^@  
dz=L/M1;                       % space step, make sure nonlinear<0.05 r<U }lK  
for m1 = 1:1:M1                                    % Start space evolution
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS x-[l`k.V  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ,D8Tca\v  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform COa
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   ca2 = fftshift(fft(u2)); '>Z Ou3>  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation %EuSP0  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   di|l?l^l  
   u2 = ifft(fftshift(c2));                        % Return to physical space u7S7lR"lxW  
   u1 = ifft(fftshift(c1)); =_5-z|<  
if rem(m1,J) == 0                                 % Save output every J steps. -{dwLl_  
    U1 = [U1 u1];                                  % put solutions in U array $3So`8Bm[$  
    U2=[U2 u2]; [8ih-k  
    MN1=[MN1 m1]; HxjhP(  
    z1=dz*MN1';                                    % output location zQ6otDZx  
  end =vR>KE  
end k{; 2*6b0  
hg=abs(U1').*abs(U1');                             % for data write to excel % 74}H8q_z  
ha=[z1 hg];                                        % for data write to excel dP82bk/e  
t1=[0 t']; B{44|aq1|  
hh=[t1' ha'];                                      % for data write to excel file gD-<^Q-  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ZPXxrmq%  
figure(1) Hg]r5Fe/c  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn cG.4%Va@s_  
figure(2) 'Ag?#vB  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn `,J\E<4J  
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非线性超快脉冲耦合的数值方法的Matlab程序 O%OeYO69  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   7a2uNt,X  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 % _N-:.S  
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%  This Matlab script file solves the nonlinear Schrodinger equations \]zHM.E1  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of $. Ih-  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear V V<Zl  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'Je;3"@  
rAgb<D@,H  
C=1;                           Wh,p$|vL  
M1=120,                       % integer for amplitude H?PaN)_6-+  
M3=5000;                      % integer for length of coupler @,
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N = 512;                      % Number of Fourier modes (Time domain sampling points) opd^|xx0  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ->d3FR  
T =40;                        % length of time:T*T0. Mp}U>+
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dt = T/N;                     % time step o
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n = [-N/2:1:N/2-1]';          % Index _qr?v=,-A  
t = n.*dt;   'bTtdFvJ  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. [&51m^  
w=2*pi*n./T; n}EH{k9#  
g1=-i*ww./2; *4]}_ .rG#  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; nPE{Gp) }  
g3=-i*ww./2; .^eajb`:  
P1=0; #V@[<S2  
P2=0; A|7%j0T  
P3=1; L\aG.\  
P=0; EjrK.|I0  
for m1=1:M1                 R10R,*6>  
p=0.032*m1;                %input amplitude 0 *2^joUv  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 !#3v<_]#d  
s1=s10; ',P$m&
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s20=0.*s10;                %input in waveguide 2 G .NGS%v  
s30=0.*s10;                %input in waveguide 3 Cs))9'cD]  
s2=s20; UyENzK<%u  
s3=s30; Zcjh  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ,N93H3(  
%energy in waveguide 1 ;?4EVZ#o  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   "Doz~R\\  
%energy in waveguide 2 -%,=%FBi~4  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]jjHIFX  
%energy in waveguide 3 QWcQtM  
for m3 = 1:1:M3                                    % Start space evolution 3?5JY;}h>"  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS DHQS7%)f`  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; fN&@y$  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; JVydTvc  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform )Vd^#p  
   sca2 = fftshift(fft(s2)); a`I \19p]  
   sca3 = fftshift(fft(s3)); e>0gE`8A  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   - ({h @  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); cDS\=Bf  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); m~04I~8vk  
   s3 = ifft(fftshift(sc3)); xu\s2x$  
   s2 = ifft(fftshift(sc2));                       % Return to physical space R"W5R-  
   s1 = ifft(fftshift(sc1)); Q<0X80w>  
end OYSq)!:  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 7cB/G:{  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); s@zO`uBc  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); agt/;>q\~  
   P1=[P1 p1/p10]; gu|=uW K  
   P2=[P2 p2/p10]; :CLWmMC_  
   P3=[P3 p3/p10]; iYD5~pK8  
   P=[P p*p]; uP G\1  
end `R;i1/  
figure(1) -U*J5Q  
plot(P,P1, P,P2, P,P3); oz:"w nX  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~