[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 P gK> Z,  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of a2\r^fY/  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ed=]RR4R  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~k[q:$T  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ohj(1jt  
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%fid=fopen('e21.dat','w'); 5zR9N>!c  
N = 128;                       % Number of Fourier modes (Time domain sampling points) t (>}  
M1 =3000;              % Total number of space steps [W{WfJ-HwG  
J =100;                % Steps between output of space i%eq!q  
T =10;                  % length of time windows:T*T0 |#_`aT"  
T0=0.1;                 % input pulse width T.kQ] h2ZG  
MN1=0;                 % initial value for the space output location mhZ60RW  
dt = T/N;                      % time step J_ S]jE{  
n = [-N/2:1:N/2-1]';           % Index 5<?s86GHh'  
t = n.*dt;   >qhoGg  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 1hnw+T<<W  
u20=u10.*0.0;                  % input to waveguide 2 uy^vQ/  
u1=u10; u2=u20;                 HHU0Nku@ho  
U1 = u1;   (#`1[n+b`x  
U2 = u2;                       % Compute initial condition; save it in U <qpDAz4k  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Zn]njf1x  
w=2*pi*n./T; -p\uW0XA  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T [h^>Iq (Z  
L=4;                           % length of evoluation to compare with S. Trillo's paper ~KF>Jow?Y  
dz=L/M1;                       % space step, make sure nonlinear<0.05 .uGvmD<;x  
for m1 = 1:1:M1                                    % Start space evolution i1E~F  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS zPKx: I3  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 2IGoAt>V  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ohP
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   ca2 = fftshift(fft(u2)); Ug1n4X3FKn  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation _K5R?"H0  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   rbw5.NU  
   u2 = ifft(fftshift(c2));                        % Return to physical space #ovmX  
   u1 = ifft(fftshift(c1)); 9;*-y$@  
if rem(m1,J) == 0                                 % Save output every J steps. sa26u`?  
    U1 = [U1 u1];                                  % put solutions in U array ]gHi5]\NC
 
    U2=[U2 u2]; eVy>  
    MN1=[MN1 m1]; m5/d=k0l  
    z1=dz*MN1';                                    % output location eAPNF?0yh  
  end CMI V"-  
end {+V]saYP  
hg=abs(U1').*abs(U1');                             % for data write to excel bXw
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ha=[z1 hg];                                        % for data write to excel GV"HkE;  
t1=[0 t']; +4Uxq{.K  
hh=[t1' ha'];                                      % for data write to excel file $V0G[!4  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ZFNn
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figure(1) ^UEExjf  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2sryhS'(H  
figure(2) QxaW
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn d}2$J1`  
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非线性超快脉冲耦合的数值方法的Matlab程序 L~PBD?l  
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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。   f*ICZM  
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 i6@c@n  
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%  This Matlab script file solves the nonlinear Schrodinger equations E9"P~ nz  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of X*^^W_LH.  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g$N/pg2>cT  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N#Y|MfLc  
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C=1;                           dpPu&m+  
M1=120,                       % integer for amplitude Tt.#O~2:9  
M3=5000;                      % integer for length of coupler ;;#_[Zl  
N = 512;                      % Number of Fourier modes (Time domain sampling points) \[57Dmo  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ~Gz b^  
T =40;                        % length of time:T*T0. BM,]W
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dt = T/N;                     % time step aA|<W g  
n = [-N/2:1:N/2-1]';          % Index p!OCF]r  
t = n.*dt;   ]#fmih^  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. &P@dx=6d  
w=2*pi*n./T; (1pR=  
g1=-i*ww./2; B,_/'DneQK  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; m);0sb  
g3=-i*ww./2; {|E'  
P1=0; '[z529HN  
P2=0; t6+c"=P#  
P3=1; KS3>c7  
P=0; 9[5qN!P;y  
for m1=1:M1                 fK %${   
p=0.032*m1;                %input amplitude K|{IX^3)V  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 iiw\  
s1=s10; *:
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s20=0.*s10;                %input in waveguide 2 %tOGs80_{  
s30=0.*s10;                %input in waveguide 3 `Pcbc\"*y  
s2=s20; D["~G v  
s3=s30; RI[=N:C^  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   .T63:  
%energy in waveguide 1 'BiR ,M$mY  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   %wD
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%energy in waveguide 2 U{JD\G8m  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Ki,SFww8r  
%energy in waveguide 3 cR*5iqA   
for m3 = 1:1:M3                                    % Start space evolution vR)f'+_Nz  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3bd(.he2u  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; RnaxRnXVR  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; F+m%PVW:  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform j TyR+#Wn  
   sca2 = fftshift(fft(s2)); ev'` K=n8  
   sca3 = fftshift(fft(s3)); :]rb}1nLB  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   c;13V(Djy  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); wqnHaWd*  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); e2><
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   s3 = ifft(fftshift(sc3)); ;J>upI  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ms]r1x"  
   s1 = ifft(fftshift(sc1)); b4R;#rm  
end Mjon++>Z  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); a7fFp9l!  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Lhz*o6)  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); rsaN<6#_^Q  
   P1=[P1 p1/p10]; #hZ`r5GvTj  
   P2=[P2 p2/p10]; 9zL(PkC%\  
   P3=[P3 p3/p10]; @BmI1  
   P=[P p*p]; li37*  
end #aua6V!"  
figure(1) N8E  
plot(P,P1, P,P2, P,P3); Img$D*BM  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~