[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(.:9A*0  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Nz],IG.  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of CJJzCVj  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 'F$l{iR  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 :=/>Vbd: )  
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%fid=fopen('e21.dat','w'); Dm-zMCf}Q  
N = 128;                       % Number of Fourier modes (Time domain sampling points) @++.F
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M1 =3000;              % Total number of space steps iTAx
=SG  
J =100;                % Steps between output of space EodQ*{l  
T =10;                  % length of time windows:T*T0 2L} SJUk*  
T0=0.1;                 % input pulse width 1][S#H/?  
MN1=0;                 % initial value for the space output location Y!gCMLL  
dt = T/N;                      % time step  .5y+fL  
n = [-N/2:1:N/2-1]';           % Index _;UE9S%  
t = n.*dt;   h?8]C#6^  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 h9Y%{v  
u20=u10.*0.0;                  % input to waveguide 2 zN:K%AiGxe  
u1=u10; u2=u20;                 /|eA9 ]  
U1 = u1;   0QOBL'{7)  
U2 = u2;                       % Compute initial condition; save it in U =aoMii   
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. #EsNeBu  
w=2*pi*n./T; p~,]*y:XT  
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
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dz=L/M1;                       % space step, make sure nonlinear<0.05 Ou1JIxZ)|  
for m1 = 1:1:M1                                    % Start space evolution li 6%)  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; zOa_X~!@  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform x*nSHb  
   ca2 = fftshift(fft(u2)); OC<5E121>Y  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Hr]h Jc  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ktdW`R\+  
   u2 = ifft(fftshift(c2));                        % Return to physical space /S(zff[at  
   u1 = ifft(fftshift(c1)); HAJ7m!P  
if rem(m1,J) == 0                                 % Save output every J steps. pFHz"]  
    U1 = [U1 u1];                                  % put solutions in U array (m:Zk$  
    U2=[U2 u2]; q11>f  
    MN1=[MN1 m1]; _c
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    z1=dz*MN1';                                    % output location rjPL+T_  
  end FTQ%JTgT  
end GrAujc5|  
hg=abs(U1').*abs(U1');                             % for data write to excel frT]5?{  
ha=[z1 hg];                                        % for data write to excel 4W)B'+ZK8  
t1=[0 t']; x>*Drm 7  
hh=[t1' ha'];                                      % for data write to excel file tP2qK_\e=  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format $W9{P;  
figure(1) ^,;z|f'%*  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ?hWwj6i&  
figure(2) \&iP`v`K  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn [zlN!.Z  
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非线性超快脉冲耦合的数值方法的Matlab程序 [5MJwRM^!;  
ZOQTINf  
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。   z3K6%rb-  
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 Q'YH>oGh^  

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%  This Matlab script file solves the nonlinear Schrodinger equations pk3<|  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of N%"Y  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear YJ;j x0  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {jho&Ai  
(jFGa2{  
C=1;                           v%s`~~u%^  
M1=120,                       % integer for amplitude i]|Yg$  
M3=5000;                      % integer for length of coupler tdSfi<y5I  
N = 512;                      % Number of Fourier modes (Time domain sampling points) UF<uU-C"  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. {6c2{@  
T =40;                        % length of time:T*T0. pm\x~3jHs  
dt = T/N;                     % time step LK, bO|  
n = [-N/2:1:N/2-1]';          % Index 5KDGSo  
t = n.*dt;   HaYE9/xS  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 'C ~y5j  
w=2*pi*n./T; _',prZ*  
g1=-i*ww./2; ALNc'MW!  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; OV%Q3$15  
g3=-i*ww./2;
HN.3  
P1=0; &*7?)eI!i  
P2=0; MwR0@S}*
 
P3=1; 0LfU=X0#7  
P=0; H*Kj3NgY  
for m1=1:M1                 ae*Mf7  
p=0.032*m1;                %input amplitude LF~*^n>  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 f"9q^  
s1=s10; >9q&PEc  
s20=0.*s10;                %input in waveguide 2 KTn}w:+B\  
s30=0.*s10;                %input in waveguide 3 }*ZHgf]~#  
s2=s20; 1e>s{  
s3=s30; NDs!a  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   sp5eVAd  
%energy in waveguide 1 u)V#S:9]  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   72X0Tq
4  
%energy in waveguide 2 HE'2"t[a  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8 XICF  
%energy in waveguide 3 Xy@7y[s]  
for m3 = 1:1:M3                                    % Start space evolution n< ud> JIb  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS GF>'\@Th  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ( @3\`\X  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; L dm?JrU  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 0MkSf*  
   sca2 = fftshift(fft(s2)); CMCO}#  
   sca3 = fftshift(fft(s3)); z%e8K(  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   )E,\H@A  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); RheRe  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);  -Y H<  
   s3 = ifft(fftshift(sc3)); Pp|*J^U 4  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 7hi"6,  
   s1 = ifft(fftshift(sc1)); c{&*w")J  
end 8S<@"
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   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); KM!k$;my  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 2con[!U  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); nIoPC[%_  
   P1=[P1 p1/p10]; :J:,m  
   P2=[P2 p2/p10]; *0|IXGr  
   P3=[P3 p3/p10]; .>mr%#p  
   P=[P p*p]; 5e}A@GyC  
end CXO2N1~(J  
figure(1) x)JOClLr  
plot(P,P1, P,P2, P,P3); >A<bBK#  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~