[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 q'%!qa+  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of w} r mYQ  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7Kti&T  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #_zj5B38E  
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%fid=fopen('e21.dat','w'); 9 $zx<O  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Rj-4K@a8#N  
M1 =3000;              % Total number of space steps bs)Ro/7}  
J =100;                % Steps between output of space Kp6%
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T =10;                  % length of time windows:T*T0 %/R[cj8  
T0=0.1;                 % input pulse width 8cj}9}k  
MN1=0;                 % initial value for the space output location 8*eVP*g  
dt = T/N;                      % time step
T )bMHk  
n = [-N/2:1:N/2-1]';           % Index U \jFB*U  
t = n.*dt;   Srrzj-9^)K  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 )~#3A@  
u20=u10.*0.0;                  % input to waveguide 2 }1NNXxQ  
u1=u10; u2=u20;                 * K0aR!  
U1 = u1;   _w7yfZLv+  
U2 = u2;                       % Compute initial condition; save it in U N^jr  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. +<WNAmh   
w=2*pi*n./T; 9dp1NjOtAc  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
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L=4;                           % length of evoluation to compare with S. Trillo's paper b>nwX9Y/U  
dz=L/M1;                       % space step, make sure nonlinear<0.05 @y,>cDg  
for m1 = 1:1:M1                                    % Start space evolution "}:SXAZ5`  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS v5*JBW+c*  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; AdRK)L  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform B8zc#0!1  
   ca2 = fftshift(fft(u2)); }q:4Zh'l!  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation "f-HOd\=  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   'NDr$Qc3  
   u2 = ifft(fftshift(c2));                        % Return to physical space nsu RG  
   u1 = ifft(fftshift(c1));
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if rem(m1,J) == 0                                 % Save output every J steps. Lo}zT-F  
    U1 = [U1 u1];                                  % put solutions in U array C%"aj^u  
    U2=[U2 u2]; !~Kg_*IT  
    MN1=[MN1 m1]; ~P"o
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    z1=dz*MN1';                                    % output location ;V84Dy#b  
  end 9M@,BXOt  
end "
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hg=abs(U1').*abs(U1');                             % for data write to excel H1$n6J  
ha=[z1 hg];                                        % for data write to excel w+hpi
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t1=[0 t']; P5v;o9B&  
hh=[t1' ha'];                                      % for data write to excel file *4c5b'u  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format BxesoB  
figure(1) ra^"Vr  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn xU |8.,@  
figure(2) E*QLw*H  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn *Z3b6X'e  
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非线性超快脉冲耦合的数值方法的Matlab程序 Sea6xGdq  
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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。   `{Fz  
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 rg
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%  This Matlab script file solves the nonlinear Schrodinger equations Xl E0oN~{  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of '|G8yojz  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 5X:3'
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |?ZNGPt  
Xi!e=5&Pa  
C=1;                           kT:?1w'  
M1=120,                       % integer for amplitude a?*pO`<J{  
M3=5000;                      % integer for length of coupler e /L([  
N = 512;                      % Number of Fourier modes (Time domain sampling points) U"a7myB+jX  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. jwheJG  
T =40;                        % length of time:T*T0. $5>m\wrl  
dt = T/N;                     % time step CaV)F3   
n = [-N/2:1:N/2-1]';          % Index xxOhGA)  
t = n.*dt;   ]N:Wt2   
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Pxgul7  
w=2*pi*n./T; 3Qu-X\  
g1=-i*ww./2; `k(m2k?  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9rT"_d#  
g3=-i*ww./2; 4K,S5^`Gx  
P1=0; yh.WTgcW  
P2=0; vILgM\or  
P3=1; 'a"Uw"/p[  
P=0; \xmDkWzE  
for m1=1:M1                 qf{HGn_9~1  
p=0.032*m1;                %input amplitude '30JJ0  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 SME]C')7  
s1=s10; lLI%J>b@  
s20=0.*s10;                %input in waveguide 2 gOy{ RE  
s30=0.*s10;                %input in waveguide 3 +R"n_6N  
s2=s20; OXbC\^qo@  
s3=s30; t;_1/mt  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   l
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%energy in waveguide 1 EBpg  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   w{GEWD{&  
%energy in waveguide 2 VOT9cP^6  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ZHCrKp  
%energy in waveguide 3 7?\r9bD  
for m3 = 1:1:M3                                    % Start space evolution x!u6LDq0  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS i*mI-l
 
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; L+0:'p=  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;

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   sca1 = fftshift(fft(s1));                       % Take Fourier transform Uh'W d_?  
   sca2 = fftshift(fft(s2)); m3XT8F*&  
   sca3 = fftshift(fft(s3)); XnRm9%  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   xM/WS':V  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 7mL1$i6=  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); $SfY<j,R  
   s3 = ifft(fftshift(sc3)); U@:l~xJ  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ](`:<>c  
   s1 = ifft(fftshift(sc1)); bG+Gg*0p  
end {ea*dX872:  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); BL%3[JQ  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); zR?1iV.]  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));  _w FK+>  
   P1=[P1 p1/p10]; >E WK cocM  
   P2=[P2 p2/p10]; ${`q
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   P3=[P3 p3/p10]; o%K1!'  
   P=[P p*p]; -o57"r^x  
end (A-Uo   
figure(1) SRrp=>w?  
plot(P,P1, P,P2, P,P3); jJ?G7Q5l  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~