[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 Pl=]Srw  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ?jQ](i&  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of X.F^$  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear p{)
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /.Nov  
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%fid=fopen('e21.dat','w'); G.'+-v=\]  
N = 128;                       % Number of Fourier modes (Time domain sampling points) RF!a//  
M1 =3000;              % Total number of space steps  ,B<l  
J =100;                % Steps between output of space Qcjc,  
T =10;                  % length of time windows:T*T0 yqXH:757~  
T0=0.1;                 % input pulse width cV{%^0?D  
MN1=0;                 % initial value for the space output location J/!cGr(B~  
dt = T/N;                      % time step h4pTq[4*  
n = [-N/2:1:N/2-1]';           % Index }U w&Ny  
t = n.*dt;   l&YKD,H};  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 I:V0Xxz5t  
u20=u10.*0.0;                  % input to waveguide 2 y7i%W4  
u1=u10; u2=u20;                 F(#rQ_z]  
U1 = u1;   x_
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U2 = u2;                       % Compute initial condition; save it in U g$:Xuw1  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. JPM))4YDR  
w=2*pi*n./T; 6C4'BCYW(  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T [[~w0G~1  
L=4;                           % length of evoluation to compare with S. Trillo's paper Hy"x  
dz=L/M1;                       % space step, make sure nonlinear<0.05 XNMa0  
for m1 = 1:1:M1                                    % Start space evolution Do%-B1{ri  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS IL/Yc1  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7`IpBm<  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform FOwDp0
 
   ca2 = fftshift(fft(u2)); )Rat0$6  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Z}A%=Z\/3  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   7?gFy-  
   u2 = ifft(fftshift(c2));                        % Return to physical space |wEN
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   u1 = ifft(fftshift(c1)); @4(k(  
if rem(m1,J) == 0                                 % Save output every J steps. U'UQ|%5f  
    U1 = [U1 u1];                                  % put solutions in U array I2$T"K:eo  
    U2=[U2 u2]; d
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    MN1=[MN1 m1]; 1T_QX9  
    z1=dz*MN1';                                    % output location I|-p3g8\  
  end aq+Y7IR_  
end AB Xl  
hg=abs(U1').*abs(U1');                             % for data write to excel !|q<E0@w\  
ha=[z1 hg];                                        % for data write to excel zOEY6lAwI  
t1=[0 t']; SjjI
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hh=[t1' ha'];                                      % for data write to excel file 1pv}]&X  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format H
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figure(1) 0,s$T2  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn '/Bidb?  
figure(2) m]_FQWfet  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn _ ~RpGX  
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非线性超快脉冲耦合的数值方法的Matlab程序 @\oz4^  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   H_!4>G@  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 to8X=80-3  
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%  This Matlab script file solves the nonlinear Schrodinger equations O9'x-A%  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 6~#Ih)K  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear PN~@  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]Mj/&b>"e  
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C=1;                            %dErnc$  
M1=120,                       % integer for amplitude GEjd7s]C  
M3=5000;                      % integer for length of coupler Sx*oo{Kk%  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Gc.P,K/hr  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. .t&R>9cZ^  
T =40;                        % length of time:T*T0. 5!C_X5M  
dt = T/N;                     % time step B,z<%DAE  
n = [-N/2:1:N/2-1]';          % Index P3 c\S[F  
t = n.*dt;   wpA`(+J  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. mD:IO  
w=2*pi*n./T; &2-L.Xb  
g1=-i*ww./2; <?D[9Mk$  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Q "oI])r  
g3=-i*ww./2; ^ yh'lh/  
P1=0; o!Ev;'D  
P2=0; Cp^@zw*/  
P3=1; +,:^5{9{  
P=0; m`4R]L]  
for m1=1:M1                 x#~ x;)  
p=0.032*m1;                %input amplitude oIGrA-T}  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 EzW)'Zzw~  
s1=s10; ,1q_pep~?%  
s20=0.*s10;                %input in waveguide 2 P+
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s30=0.*s10;                %input in waveguide 3 m6eZ_&+u  
s2=s20; UV}73Sp  
s3=s30; Mcw4!{l`  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   l?Y_~Wuw  
%energy in waveguide 1 oHM ]  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   >Sa*`q3J  
%energy in waveguide 2 W$JebW<z(  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   kE.x+2  
%energy in waveguide 3 . .QB~  
for m3 = 1:1:M3                                    % Start space evolution oRN-xng  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }MR1^  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; DPrBFmHF  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Q|}aR:4  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform gADmN8G=  
   sca2 = fftshift(fft(s2)); H@X oqgI  
   sca3 = fftshift(fft(s3)); U(&oj e  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   M-NV_W&M  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); C0.'_  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); -3Avs9`5  
   s3 = ifft(fftshift(sc3)); d{et8N  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ?%Rw(E  
   s1 = ifft(fftshift(sc1)); @RD+xYm  
end 0,*%vG?Q  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ;TQf5|R
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); *fO3]+)d+  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); uBg 8h{>  
   P1=[P1 p1/p10]; 6Dws,_UAZ4  
   P2=[P2 p2/p10]; `&M{cfp_  
   P3=[P3 p3/p10]; *y`%]Hy<  
   P=[P p*p]; ZA~Z1Mro#"  
end ^IZ)#1U  
figure(1) `\=Gp'&Q+  
plot(P,P1, P,P2, P,P3); 1{pmKPu  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~