[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 8xv\Zj+  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of K@,VR3y /  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of gJ7$G3&oZg  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear evR=Z\ _  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 2X]\:<[4  
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%fid=fopen('e21.dat','w'); lt4UNJ3w  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 5a~1RL  
M1 =3000;              % Total number of space steps Xo5L:(
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J =100;                % Steps between output of space w '"7~uN  
T =10;                  % length of time windows:T*T0 P}I*SV0  
T0=0.1;                 % input pulse width 5jLDe~  
MN1=0;                 % initial value for the space output location pZjFpd|  
dt = T/N;                      % time step CP'-CQ\Q  
n = [-N/2:1:N/2-1]';           % Index hJ@nW5CI  
t = n.*dt;   <>Im$N ai  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Uoe?5Of(*  
u20=u10.*0.0;                  % input to waveguide 2 Z4!3I@yZ  
u1=u10; u2=u20;                 zW _'sC  
U1 = u1;   AK!G#ug  
U2 = u2;                       % Compute initial condition; save it in U pi{ahuI#_o  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 3IkG*enI  
w=2*pi*n./T; 8HOmWQS  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ;1 fML,8  
L=4;                           % length of evoluation to compare with S. Trillo's paper )'g vaT  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ^n]s}t}csV  
for m1 = 1:1:M1                                    % Start space evolution 3:(`#YY  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 6>Cubb>  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }VGiT~2$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ]VME`]t`  
   ca2 = fftshift(fft(u2)); Bz{ g4!ku  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation D4|_?O3|m  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   'zb7:[[7%  
   u2 = ifft(fftshift(c2));                        % Return to physical space k y98/6  
   u1 = ifft(fftshift(c1)); uE$o4X  
if rem(m1,J) == 0                                 % Save output every J steps. 5ZVTI,4K  
    U1 = [U1 u1];                                  % put solutions in U array 1
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    U2=[U2 u2]; M@\'Y$)Y{  
    MN1=[MN1 m1]; Fk(5y)  
    z1=dz*MN1';                                    % output location cOQy|v`KD,  
  end t/Fe"T[,V  
end "ir*;|  
hg=abs(U1').*abs(U1');                             % for data write to excel n3N"Ax  
ha=[z1 hg];                                        % for data write to excel qHCs{ u  
t1=[0 t']; x_K%  
hh=[t1' ha'];                                      % for data write to excel file bv/b<N@4?$  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format u_BSWhiW  
figure(1) Q
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn n1Jz49[r  
figure(2) w%;'
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn MQ44uHJ  
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非线性超快脉冲耦合的数值方法的Matlab程序 Sg-xm+iSDt  
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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。   MlFvDy  
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 7;NV 1RV  
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%  This Matlab script file solves the nonlinear Schrodinger equations +0Gep}&z.  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Pc'?p  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Bv8C_-lV/  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ''uI+>Y  
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C=1;                           sd53 _sV  
M1=120,                       % integer for amplitude BvF_9  
M3=5000;                      % integer for length of coupler Q8?D}h  
N = 512;                      % Number of Fourier modes (Time domain sampling points) W#j,{&KVn  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. +`8)U3u0  
T =40;                        % length of time:T*T0. >nQyF  
dt = T/N;                     % time step mx~sxYa  
n = [-N/2:1:N/2-1]';          % Index k5D'RD  
t = n.*dt;   ]'(7T#  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. I?>T"nV +'  
w=2*pi*n./T; Tm\[q  
g1=-i*ww./2; BA,6f?ktXS  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 8n5nHne  
g3=-i*ww./2; C`wI6!  
P1=0; D}sGBsOW  
P2=0; _eV n#!|  
P3=1; )1Nnn  
P=0; cg00t+  
for m1=1:M1                 OL5HofgNm  
p=0.032*m1;                %input amplitude 4/?}xD|?  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Hs=N0Sk]j  
s1=s10; 4Z9wzQ>  
s20=0.*s10;                %input in waveguide 2 <C;>$kX  
s30=0.*s10;                %input in waveguide 3 "R@N|Qx'  
s2=s20; a +yI2s4Z  
s3=s30; UUu-(H-J  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   x9l0UD*+g  
%energy in waveguide 1 vN:[  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   <0)ud)~u  
%energy in waveguide 2 ?K {1S  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Wxau]uix  
%energy in waveguide 3 ?7)(qnbe"  
for m3 = 1:1:M3                                    % Start space evolution ^!o}>ls['  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 8zDH<Gb  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; BK9x`Oo2  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $'YKB8C  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ir:~*|  
   sca2 = fftshift(fft(s2)); y*h1W4:^-  
   sca3 = fftshift(fft(s3)); l/zC##1+.  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   bDBO+qA  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); W#I:j: p  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); qlITQKGG  
   s3 = ifft(fftshift(sc3)); 6h6?BQSE  
   s2 = ifft(fftshift(sc2));                       % Return to physical space rw[{@|)'z  
   s1 = ifft(fftshift(sc1)); V<ApHb  
end OP`Jc$|6  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); nVn|$ "r  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); l@rwf$-  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); r>~d[,^$m4  
   P1=[P1 p1/p10]; jS3(>  
   P2=[P2 p2/p10]; ttFY _F~S  
   P3=[P3 p3/p10]; RB7AI!'a?  
   P=[P p*p]; `k]!6osZ
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end |
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figure(1) |F@xwfgb  
plot(P,P1, P,P2, P,P3); PuZs5J3  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~