[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 % rBzA<  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of x*7@b8J  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 2u{~35  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear bR\7j+*&  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Hv,|XE@Y  
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%fid=fopen('e21.dat','w'); Psb !Z(  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ggso9ZlLu+  
M1 =3000;              % Total number of space steps uvys>]+  
J =100;                % Steps between output of space s%[F,hQRk  
T =10;                  % length of time windows:T*T0 %6K7uvTq  
T0=0.1;                 % input pulse width ,'L>:pF3  
MN1=0;                 % initial value for the space output location q0sf\|'<}  
dt = T/N;                      % time step 2y[Q  
n = [-N/2:1:N/2-1]';           % Index *TOdIq&z  
t = n.*dt;   #w$Y
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ;(Yb9Mr)z  
u20=u10.*0.0;                  % input to waveguide 2 A40DbD\^ad  
u1=u10; u2=u20;                 qGk+4 yC  
U1 = u1;   ^2+Ex+  
U2 = u2;                       % Compute initial condition; save it in U ,H7X_KbFD4  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 2.qPMqH  
w=2*pi*n./T; C6+ 5G-Z  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T P^Hgm  
L=4;                           % length of evoluation to compare with S. Trillo's paper Q*M#e  
dz=L/M1;                       % space step, make sure nonlinear<0.05 T,38Pu@r  
for m1 = 1:1:M1                                    % Start space evolution ,EqQU|  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS VQ
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 5Cf!NNV  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform sz7*x{E  
   ca2 = fftshift(fft(u2)); CEfqFn3^  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation UmKE]1Yw4r  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   r&=ulg  
   u2 = ifft(fftshift(c2));                        % Return to physical space g)Z8WH$;H3  
   u1 = ifft(fftshift(c1)); 2=cx`"a$  
if rem(m1,J) == 0                                 % Save output every J steps. W'G|sk  
    U1 = [U1 u1];                                  % put solutions in U array j?T'N:Qd  
    U2=[U2 u2]; PgtLyzc  
    MN1=[MN1 m1]; c~|(j \FI  
    z1=dz*MN1';                                    % output location [@$ SLl^Y  
  end 79DNNj~  
end VZ]iep  
hg=abs(U1').*abs(U1');                             % for data write to excel 2mY!gVi  
ha=[z1 hg];                                        % for data write to excel |3$Ew.  
t1=[0 t']; 4KPnV+h"b  
hh=[t1' ha'];                                      % for data write to excel file uYW4$6S3  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format oZ{,IZ45  
figure(1) Jb,54uN  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn W]4Z4&  
figure(2) EKc<|e,F  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +.cpZqWn3  
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非线性超快脉冲耦合的数值方法的Matlab程序 :>-zT[Lcn  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   vNi;)"&*  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 q@.>eB'92P  
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%  This Matlab script file solves the nonlinear Schrodinger equations Q0A4}  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Y7GsL7I  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear txEN7!  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <ZT C^=3  
082}=Tsx   
C=1;                           \g0vzo"u  
M1=120,                       % integer for amplitude h!tpi`8\z  
M3=5000;                      % integer for length of coupler P"c@V,.  
N = 512;                      % Number of Fourier modes (Time domain sampling points) kBP?_ O  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. lpT&v;$`  
T =40;                        % length of time:T*T0. bH+NRNI]  
dt = T/N;                     % time step ]9!y3"..W{  
n = [-N/2:1:N/2-1]';          % Index AKk=XAGW  
t = n.*dt;   @Y0
ZW't  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Q#MB=:0{  
w=2*pi*n./T; qrMED_(D  
g1=-i*ww./2; @9^OHRZX  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ~[=<Os  
g3=-i*ww./2; tSy 9v  
P1=0; %oBP6|e  
P2=0; [kg^S`gc#  
P3=1; u|KjoO   
P=0; 8Z!%rS  
for m1=1:M1                 08\w!!a:  
p=0.032*m1;                %input amplitude ,
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 (]w6q&,  
s1=s10; eA N{BPN[  
s20=0.*s10;                %input in waveguide 2 1zRYd`IPoq  
s30=0.*s10;                %input in waveguide 3 $yU 5WEX  
s2=s20; 7U7!'xU  
s3=s30; 5V 2ZAYV  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   zk<V0NJIL*  
%energy in waveguide 1 #91^1jyMf  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Tm^kZuT{  
%energy in waveguide 2 l/3=o}8q  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   bo<P%$(D  
%energy in waveguide 3 *VsGa<V  
for m3 = 1:1:M3                                    % Start space evolution KHx2$*E_  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS AL":j6!OQ  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; y`9#zYgqA  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 2hV -h  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform gWgp:;Me  
   sca2 = fftshift(fft(s2)); ZH~bY2^;  
   sca3 = fftshift(fft(s3)); +cfcr*  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   "{8j!+]4i  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); {.Qv1oOa  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); D%+yp  
   s3 = ifft(fftshift(sc3)); @QTw9,pS  
   s2 = ifft(fftshift(sc2));                       % Return to physical space !4Aj#`)  
   s1 = ifft(fftshift(sc1)); _1[Wv?  
end I^EZ
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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)))); kqX=3Zo  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); *=i&n>  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); N3$1f$`  
   P1=[P1 p1/p10]; mr7Oi `dE  
   P2=[P2 p2/p10]; # fqrZ9:@  
   P3=[P3 p3/p10]; (:8a6=xQ  
   P=[P p*p]; _-BP?'lN  
end kNK0KL  
figure(1) uZ8-?  
plot(P,P1, P,P2, P,P3); 3IRur,|'  
1\}XL=BE  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~