[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 }QL 2#R  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of VY5/C;0^h  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 1c} %_Z/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear F#w=z/  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |h; _r&  
IE-c^'W=}m  
%fid=fopen('e21.dat','w'); Sb&[V>!2^  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ?m?DAd~ZY  
M1 =3000;              % Total number of space steps Uva b*9vX  
J =100;                % Steps between output of space Ty21-0F  
T =10;                  % length of time windows:T*T0 [BpIzhy&}  
T0=0.1;                 % input pulse width &K_"5.7-56  
MN1=0;                 % initial value for the space output location i0%S6vmaS  
dt = T/N;                      % time step s3*h=5bX=  
n = [-N/2:1:N/2-1]';           % Index XJ|CC.]1u  
t = n.*dt;   q.l"Y#d  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 jcWv&u|  
u20=u10.*0.0;                  % input to waveguide 2 JEK6Ms;)A  
u1=u10; u2=u20;                 w34&m  
U1 = u1;   %C!u/:.Kv  
U2 = u2;                       % Compute initial condition; save it in U oc>ne]_'  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. H\\0V.}!  
w=2*pi*n./T; i 5"g?Wa2N  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 5m`@ 4%)zp  
L=4;                           % length of evoluation to compare with S. Trillo's paper .&AS-">Z  
dz=L/M1;                       % space step, make sure nonlinear<0.05 <303PPX^6  
for m1 = 1:1:M1                                    % Start space evolution J3oj}M*  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ztNm,1pnQ  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; LP8Stj JP  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform Z)6gh{B08  
   ca2 = fftshift(fft(u2)); G H
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation OA\2ja~+  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   SEn-8ZF  
   u2 = ifft(fftshift(c2));                        % Return to physical space CF`tNA3fxm  
   u1 = ifft(fftshift(c1)); /Ot=GhN]  
if rem(m1,J) == 0                                 % Save output every J steps. MOuI;EF  
    U1 = [U1 u1];                                  % put solutions in U array L {6y]t7^  
    U2=[U2 u2]; _yq"F#,*  
    MN1=[MN1 m1]; V=pg9KR!T  
    z1=dz*MN1';                                    % output location jJc?/1jv  
  end HB+\2jEE  
end tK3.HvD  
hg=abs(U1').*abs(U1');                             % for data write to excel VuDS
jh  
ha=[z1 hg];                                        % for data write to excel ?8g[0/  
t1=[0 t']; `c^ _5:euX  
hh=[t1' ha'];                                      % for data write to excel file c]`}DH,TJ  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format uUUj?%  
figure(1) N:j"W,8  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn S{7*uK3$  
figure(2) }+KSZ,  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^mLZT*
  
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非线性超快脉冲耦合的数值方法的Matlab程序 bE-{ U/;  
iV!o)WvG,F  
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。   _L mDF8Q(  
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 / c1=`OJ  
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%  This Matlab script file solves the nonlinear Schrodinger equations seh1(q?Va4  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of eeX^zaKl]  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear DGl_SMJb  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ozZW7dveU  
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C=1;                           TFbMrIF  
M1=120,                       % integer for amplitude 5CZii=@  
M3=5000;                      % integer for length of coupler }Yt/e-Yg%r  
N = 512;                      % Number of Fourier modes (Time domain sampling points) *ip2|2G$  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. &?m|PK)I
 
T =40;                        % length of time:T*T0. p2N;-  
dt = T/N;                     % time step
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n = [-N/2:1:N/2-1]';          % Index ^2L\Y2  
t = n.*dt;   d'~ kf#  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. v\>!J?  
w=2*pi*n./T; {VBx;A3*I  
g1=-i*ww./2; [A?Dx-R;(  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 1b:3'E.#w  
g3=-i*ww./2; MA\"JAP/  
P1=0; ~y.{WuUD  
P2=0; 5mwtlC':l?  
P3=1; p\]Mf#B  
P=0; JivkY"= F  
for m1=1:M1                 z1t YD  
p=0.032*m1;                %input amplitude TfaL5evio  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 uGIA4CUm  
s1=s10; ZUJ!  
s20=0.*s10;                %input in waveguide 2 gs)wQgJ[  
s30=0.*s10;                %input in waveguide 3 {&,9Zy]"S  
s2=s20; iR;Sd >)  
s3=s30; &kKopJH  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   X{A|{u=  
%energy in waveguide 1 P;o6rQf  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   SoZ$1$o2  
%energy in waveguide 2 |Q
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Z?k4Kb  
%energy in waveguide 3 $]IX11.m  
for m3 = 1:1:M3                                    % Start space evolution Kh<xQ:eMy  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS %n-:mSus  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; s`W
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =e'b*KTL,  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform n82N@z<8]  
   sca2 = fftshift(fft(s2)); *-~B{2b<  
   sca3 = fftshift(fft(s3)); Pt~mpRlH
 
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   >S4klW=*I  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); M)td%<_  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); &WN#HI."]  
   s3 = ifft(fftshift(sc3)); [MfKBlA  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Q2sX7 cE  
   s1 = ifft(fftshift(sc1)); N*6Y5[g!\  
end ea-NqdGs;m  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <rd7<@>5D  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); \
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); VT1Nd  
   P1=[P1 p1/p10]; t2Dx$vT*&  
   P2=[P2 p2/p10]; `2X~3im  
   P3=[P3 p3/p10]; rYUhGm
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   P=[P p*p]; `6:;*#jO,  
end K7 >Z)21  
figure(1) <Z%iP{  
plot(P,P1, P,P2, P,P3); ZS51QB  
C2RR(n=N^  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~