[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 XK4idC  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of pn6!QpV5  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of yp:_W@  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear TGe{NUO  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 )Vb_0n=^  
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%fid=fopen('e21.dat','w'); vS|uN(a.P  
N = 128;                       % Number of Fourier modes (Time domain sampling points) x0!5z1KQh  
M1 =3000;              % Total number of space steps KW.QVBuVO#  
J =100;                % Steps between output of space DIurFDQSS  
T =10;                  % length of time windows:T*T0 uM
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T0=0.1;                 % input pulse width vQpR0IEf]e  
MN1=0;                 % initial value for the space output location v"
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dt = T/N;                      % time step :LwNOuavN  
n = [-N/2:1:N/2-1]';           % Index 51k^?5cO  
t = n.*dt;   BI,j/SRK  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $Z;?d@6yI  
u20=u10.*0.0;                  % input to waveguide 2 //}[(9b'\  
u1=u10; u2=u20;                 s]
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U1 = u1;   1>SCY_Cv  
U2 = u2;                       % Compute initial condition; save it in U 3./4] _p  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. YkKq}DXj  
w=2*pi*n./T; j&.MT@  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T |NcfR"[c  
L=4;                           % length of evoluation to compare with S. Trillo's paper `
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dz=L/M1;                       % space step, make sure nonlinear<0.05 =-c"~
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for m1 = 1:1:M1                                    % Start space evolution 4S]`S\w  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS P#g"c.?;  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; D+.h*{gD  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform U>z8gdzu  
   ca2 = fftshift(fft(u2)); "s]c79t  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation rI5)w_E?  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   \O
m< FH}  
   u2 = ifft(fftshift(c2));                        % Return to physical space 0vs9# <&V  
   u1 = ifft(fftshift(c1)); xrK%3nA4s"  
if rem(m1,J) == 0                                 % Save output every J steps. tndtwM*B'  
    U1 = [U1 u1];                                  % put solutions in U array I T)rhi:  
    U2=[U2 u2]; KbY5 qou  
    MN1=[MN1 m1]; 1|VnPQqA  
    z1=dz*MN1';                                    % output location `V@{#+X  
  end *FkG32k  
end F(8>"(C  
hg=abs(U1').*abs(U1');                             % for data write to excel p*r
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ha=[z1 hg];                                        % for data write to excel CqUK[#kW(  
t1=[0 t']; l("Dw8H  
hh=[t1' ha'];                                      % for data write to excel file s fxQ  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format  ?6!7fs,  
figure(1) N4%q-fi  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 4425,AR  
figure(2) g(\FG
  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn  ? {Lp  
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非线性超快脉冲耦合的数值方法的Matlab程序 GQTMQXn(  
zQ$*!1FmN  
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。   oXgKuR  
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 Zi=Nr3b  
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%  This Matlab script file solves the nonlinear Schrodinger equations J'O</o@e  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of AlNiqnZ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear zxtx~XO  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004  =uZ[  
m<wng2`NTv  
C=1;                           31LXzQvFG  
M1=120,                       % integer for amplitude qWf7k+7G  
M3=5000;                      % integer for length of coupler [0D( PV(n  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Lo
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dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ?9_<LE q  
T =40;                        % length of time:T*T0. Z;bzp3v  
dt = T/N;                     % time step AHP_B&s,Qe  
n = [-N/2:1:N/2-1]';          % Index maLKUSgo  
t = n.*dt;   ZD] ^Y}  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.  KAmv7  
w=2*pi*n./T; iK6L\'k  
g1=-i*ww./2; V+X>t7.Q  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; D;
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g3=-i*ww./2; 'H2TwSbIXI  
P1=0; mxhO:.l  
P2=0; 2/qP:3)  
P3=1; I|JMkP  
P=0; M-u:8dPu  
for m1=1:M1                 ,V!s w5_5m  
p=0.032*m1;                %input amplitude \~1M\gZP  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ci>+Zi6  
s1=s10; xR2E? 0T  
s20=0.*s10;                %input in waveguide 2 imAsE;:  
s30=0.*s10;                %input in waveguide 3 QF(.fq8, U  
s2=s20; $ +;`[b   
s3=s30; 7=t4;8|j;  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ]:JoGGE a0  
%energy in waveguide 1 m]BxGwT=m  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   V2cLwQ'0  
%energy in waveguide 2 L5E.`^?  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   .oYUA}  
%energy in waveguide 3 0.C y4sH'  
for m3 = 1:1:M3                                    % Start space evolution S,m)yh.  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS v'7,(.E  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; (,`ypD+3q  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;  2&O!<C j  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform " 4#V$V  
   sca2 = fftshift(fft(s2)); 1q<BYc+z  
   sca3 = fftshift(fft(s3)); m5SJB]a/  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   quHq?oXV,  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); D\]gIXg  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); {,tEe'H7  
   s3 = ifft(fftshift(sc3)); .`&($W  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ~h6aw  
   s1 = ifft(fftshift(sc1)); X>j% y7v  
end i ~fkjn  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); s@K)RhTY  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); +M!f}=H  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); T>s~bIzL*e  
   P1=[P1 p1/p10]; Io*`hA]  
   P2=[P2 p2/p10]; BB5(=n+  
   P3=[P3 p3/p10]; 0&2(1  
   P=[P p*p]; I.TdYSB  
end oCdWf63D  
figure(1) ~YKe:K+&z  
plot(P,P1, P,P2, P,P3); BpZE  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~