[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 M
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Y<lJj"G  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of +{ Q]$b  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear EHByo[  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1-`Il]@?8  
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%fid=fopen('e21.dat','w'); E/MD]ox  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ?kfLOJQ:I  
M1 =3000;              % Total number of space steps
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J =100;                % Steps between output of space V=%j]`Os  
T =10;                  % length of time windows:T*T0 _tJp@\rOz=  
T0=0.1;                 % input pulse width .!yXto:  
MN1=0;                 % initial value for the space output location K.k%Tg[ ~  
dt = T/N;                      % time step @J"Gn-f~  
n = [-N/2:1:N/2-1]';           % Index $j?zEz  
t = n.*dt;   SJ(<u2J]  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 +AGI)uQQ  
u20=u10.*0.0;                  % input to waveguide 2 N#(p_7M  
u1=u10; u2=u20;                 V/C":!;  
U1 = u1;   )erI3?k  
U2 = u2;                       % Compute initial condition; save it in U b4o`eR  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. M`6rI  
w=2*pi*n./T; B(+J?0Dj  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T .wj?}Fr?97  
L=4;                           % length of evoluation to compare with S. Trillo's paper ^Ec);Z  
dz=L/M1;                       % space step, make sure nonlinear<0.05 +6dq+8msF  
for m1 = 1:1:M1                                    % Start space evolution 0s>ozAJ  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS HE>6A|rgDr  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; UVND1XV^f  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Uy$1X  
   ca2 = fftshift(fft(u2)); -:mT8'.F-  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation WvV!F?uqZ  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   -\ {.]KL  
   u2 = ifft(fftshift(c2));                        % Return to physical space A
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   u1 = ifft(fftshift(c1)); AUZ^XiK  
if rem(m1,J) == 0                                 % Save output every J steps. #9Src\V  
    U1 = [U1 u1];                                  % put solutions in U array WX@a2c.'  
    U2=[U2 u2]; vU
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    MN1=[MN1 m1]; h+,Eu7\88  
    z1=dz*MN1';                                    % output location *^|.bBG  
  end KmUH([#  
end {ek axSR  
hg=abs(U1').*abs(U1');                             % for data write to excel IIrp-EMXJ  
ha=[z1 hg];                                        % for data write to excel A.`) 0dV  
t1=[0 t']; -M{.KqyW  
hh=[t1' ha'];                                      % for data write to excel file QfHJZ7K.4  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format y2nwDw(xF  
figure(1) <d&9`e1Hc  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn fpESuVKr  
figure(2) CF|4, K)  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn V4~`yT?*"  
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非线性超快脉冲耦合的数值方法的Matlab程序 ?4G/f<ou  
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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。   ((Jiv=%  
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 CFo>D\*J  
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%  This Matlab script file solves the nonlinear Schrodinger equations 1?!z<<  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 5 5$J%;&  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Dht,!LVb;  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $G $147z  
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C=1;                           y5oC|v7  
M1=120,                       % integer for amplitude 57nSyd]PR  
M3=5000;                      % integer for length of coupler 3W<_J_[  
N = 512;                      % Number of Fourier modes (Time domain sampling points) I=vGS  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 7Pb:z4j  
T =40;                        % length of time:T*T0. yu^n;gWH  
dt = T/N;                     % time step i.~*G8!DM  
n = [-N/2:1:N/2-1]';          % Index 2.6F5&:($  
t = n.*dt;   3Gr:.V9=  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. kimqm  
w=2*pi*n./T; [pAW':  
g1=-i*ww./2; .|Ee,Un  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; PPj_
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g3=-i*ww./2; "q<}#]u  
P1=0; :h(r2?=7  
P2=0; U/p|X)  
P3=1; x JXPtm  
P=0; Oo-%;l`&  
for m1=1:M1                 zJxO\  
p=0.032*m1;                %input amplitude E;*JD x  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 06r-@iY.]  
s1=s10; ZvSWIQ6  
s20=0.*s10;                %input in waveguide 2 DrY5Q&S  
s30=0.*s10;                %input in waveguide 3 Zo12F**{  
s2=s20; q>n0'`q   
s3=s30; s]lIDp}  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   K1*oYHB  
%energy in waveguide 1 q-k~L\Ys  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Ok/U"N-  
%energy in waveguide 2 cVR#\OM  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   JsDugn ,B  
%energy in waveguide 3 \NgBF  
for m3 = 1:1:M3                                    % Start space evolution i wFI lJ@  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS "3\C;B6I  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; S8S<>W  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 76'vsg  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 7K.in3M(  
   sca2 = fftshift(fft(s2)); C=y[WsT  
   sca3 = fftshift(fft(s3)); +CQ$-3  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   8Ev,9  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); udjahI<{  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 0r|mg::'  
   s3 = ifft(fftshift(sc3)); eG F{.]  
   s2 = ifft(fftshift(sc2));                       % Return to physical space #JLxM/5^1~  
   s1 = ifft(fftshift(sc1)); Wwf],Ya  
end sy s6 V?  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); l7p*::(9  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); @y+Hb@ >.  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); `H#G/zOr  
   P1=[P1 p1/p10]; 4!3mSWNV  
   P2=[P2 p2/p10]; Z:e|~#  
   P3=[P3 p3/p10]; 3P&K<M#\  
   P=[P p*p]; ;DG&HO  
end ~"t33U6  
figure(1) 5PCMxjon  
plot(P,P1, P,P2, P,P3); CnvM>]  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~