[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 7l}~4dm2J  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of $i&\\QNn  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 70<K.T<b  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 4? {*(  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ,iOZ|  
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%fid=fopen('e21.dat','w'); pSrsp r  
N = 128;                       % Number of Fourier modes (Time domain sampling points) UQdyv(jXq  
M1 =3000;              % Total number of space steps B_@7IbB  
J =100;                % Steps between output of space YnxU
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T =10;                  % length of time windows:T*T0 7sN0`7  
T0=0.1;                 % input pulse width c+;S<g0  
MN1=0;                 % initial value for the space output location <W|1<=z(  
dt = T/N;                      % time step #f9qlM32  
n = [-N/2:1:N/2-1]';           % Index !>|`ly$6  
t = n.*dt;   2^bgC~2C1  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 F=5kF/}x-z  
u20=u10.*0.0;                  % input to waveguide 2 Z`"n:'&  
u1=u10; u2=u20;                 3dU#Ueu  
U1 = u1;   MVuP |&:n  
U2 = u2;                       % Compute initial condition; save it in U (6[Wr}SW5  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. SW-0h4  
w=2*pi*n./T; d:3= 1x  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T {9:
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L=4;                           % length of evoluation to compare with S. Trillo's paper A xR\ned  
dz=L/M1;                       % space step, make sure nonlinear<0.05 P59uALi  
for m1 = 1:1:M1                                    % Start space evolution M[vCpa  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS >!G5]?taa
 
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; /]l f>\x1  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform `NoCH[$!+  
   ca2 = fftshift(fft(u2)); x[a'(5PwY  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 'w`d$c/p  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   `~KAk  
   u2 = ifft(fftshift(c2));                        % Return to physical space tpz=}q  
   u1 = ifft(fftshift(c1)); ~:s!].H  
if rem(m1,J) == 0                                 % Save output every J steps. "#J}A0  
    U1 = [U1 u1];                                  % put solutions in U array gTyW#verh$  
    U2=[U2 u2]; }(rzH}X@  
    MN1=[MN1 m1]; h?3f5G*&H  
    z1=dz*MN1';                                    % output location ]N_140N~  
  end 95% :AQLV  
end ILIRI[7(  
hg=abs(U1').*abs(U1');                             % for data write to excel 2PI #ie4  
ha=[z1 hg];                                        % for data write to excel {8W |W2o$!  
t1=[0 t']; R3cG<MjmK  
hh=[t1' ha'];                                      % for data write to excel file cxk=| ?l  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Cb<~i  
figure(1) ?/^VOj4&  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn @nW'(x(  
figure(2) fVv$K&  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ar=hx+  
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非线性超快脉冲耦合的数值方法的Matlab程序 2voNg
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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。   (''$'5~  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 -1#e^9Ve\  
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%  This Matlab script file solves the nonlinear Schrodinger equations !/[AQ{**T!  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of R2'C s  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear oF`-cyj"  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 `~sf}S :  
%Ud.SJ3  
C=1;                           N n:m+ZDo^  
M1=120,                       % integer for amplitude 9n-RXVL+  
M3=5000;                      % integer for length of coupler chMt5L+5  
N = 512;                      % Number of Fourier modes (Time domain sampling points)  ; \Y-  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. )bF)RLZ  
T =40;                        % length of time:T*T0. vs*_;vx  
dt = T/N;                     % time step (d1V1t2r6  
n = [-N/2:1:N/2-1]';          % Index p3i qW,[@  
t = n.*dt;   (}~ 1{C@  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Ebmqq#SHjX  
w=2*pi*n./T; BZ8h*|uT"  
g1=-i*ww./2; \0xzBs1!  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 8'>.#vyMGv  
g3=-i*ww./2; i,\t]EJA
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P1=0; mOgx&ns;j  
P2=0; `1DU b7<  
P3=1; _AA`R`p;  
P=0; v#zfs'  
for m1=1:M1                 }d$vcEI$3  
p=0.032*m1;                %input amplitude Zm?G'06  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 uBV^nUjS"m  
s1=s10; Bx_8@+  
s20=0.*s10;                %input in waveguide 2 K.c6Rg  
s30=0.*s10;                %input in waveguide 3 9~*_(yjF  
s2=s20; jnx+wcd  
s3=s30; GN8`xR{J*  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   D<$j`r  
%energy in waveguide 1 E9 :|8#b  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   y$"~^8"z  
%energy in waveguide 2 9.]Cy8  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ?3e!A9x  
%energy in waveguide 3 cJ1{2R  
for m3 = 1:1:M3                                    % Start space evolution \ltErd-  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Qt)7m
f  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; X,Q6  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; (W{rv6cq  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform +$Ddd`J'  
   sca2 = fftshift(fft(s2)); GNj/jU<o!  
   sca3 = fftshift(fft(s3)); :$u{  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift    $Adp  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ahz@HX  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 8O}A/*1FJ  
   s3 = ifft(fftshift(sc3)); '3Y0D1`v  
   s2 = ifft(fftshift(sc2));                       % Return to physical space J/H#d')c  
   s1 = ifft(fftshift(sc1)); '8((;N|I^  
end 8M5!5Jzv  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ()rx>?x5  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); QvT-&|  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ({}O M=_  
   P1=[P1 p1/p10]; 9X*eE  
   P2=[P2 p2/p10]; x Jj8njuq4  
   P3=[P3 p3/p10]; 2Q;Y@%G  
   P=[P p*p]; EUYa =-  
end D[FfJcV'$  
figure(1) cnjj) c  
plot(P,P1, P,P2, P,P3); [M zc^I&  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~