[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 #k2&2W=x  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of nB"r<?n<  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 'U ',9  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 9Axk-c  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 YSwAu,$jf  
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%fid=fopen('e21.dat','w'); 02E-|p;  
N = 128;                       % Number of Fourier modes (Time domain sampling points) jv7-i'I@  
M1 =3000;              % Total number of space steps }M?\BH&  
J =100;                % Steps between output of space 3
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T =10;                  % length of time windows:T*T0 hR,VE'A  
T0=0.1;                 % input pulse width &.z: i5&o!  
MN1=0;                 % initial value for the space output location m^cr-'  
dt = T/N;                      % time step `
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n = [-N/2:1:N/2-1]';           % Index p\I,P2on  
t = n.*dt;   4zuM?Dp  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 [uK*=K/v  
u20=u10.*0.0;                  % input to waveguide 2 '9^+J7iO(+  
u1=u10; u2=u20;                 <>/0;J1<  
U1 = u1;   j<H`<S  
U2 = u2;                       % Compute initial condition; save it in U "?EoYF_  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ?dMyhU}  
w=2*pi*n./T; @igGfYy  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T N*z_rZE  
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 xc)A`(g  
for m1 = 1:1:M1                                    % Start space evolution Yqz(@( %  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ucP}( $  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; K{)N:|y%!$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform %!%G\nv  
   ca2 = fftshift(fft(u2)); t mAj  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation mh`~1aEr  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   u&Q2/Y  
   u2 = ifft(fftshift(c2));                        % Return to physical space ;u`zZb=,[  
   u1 = ifft(fftshift(c1)); JJ@O5  
if rem(m1,J) == 0                                 % Save output every J steps. P0O5CaR  
    U1 = [U1 u1];                                  % put solutions in U array `^HAWo;J  
    U2=[U2 u2]; ,]HH%/h  
    MN1=[MN1 m1]; :*
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    z1=dz*MN1';                                    % output location lZoy(kdc  
  end SXX6EIJr|  
end 1SIhW:C  
hg=abs(U1').*abs(U1');                             % for data write to excel XnC`JO+7M  
ha=[z1 hg];                                        % for data write to excel \49LgN@\  
t1=[0 t']; BeP]M1\?>  
hh=[t1' ha'];                                      % for data write to excel file pvCn
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format :SFcnYv0  
figure(1) k(l  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn h+EG) <  
figure(2) ;M{@|z[Nv  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1_JtD|Jy  
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非线性超快脉冲耦合的数值方法的Matlab程序 nXHU|5.I  
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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。   Cv7FVl-I  
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 Zz
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%  This Matlab script file solves the nonlinear Schrodinger equations I*cB Ha  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of SF$'$6x}  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ["l1\YCi  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 3^p<Wx  
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C=1;                           E?%SOU<  
M1=120,                       % integer for amplitude ygt7;};!  
M3=5000;                      % integer for length of coupler [@ExR*  
N = 512;                      % Number of Fourier modes (Time domain sampling points) CBaU$`5  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.  N7%iz+  
T =40;                        % length of time:T*T0. 5 :O7cBr  
dt = T/N;                     % time step  L~F"  
n = [-N/2:1:N/2-1]';          % Index }.md$N_F  
t = n.*dt;   :4 9ttJl  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. Glz)-hjJ:n  
w=2*pi*n./T; [I/f(GK  
g1=-i*ww./2; s7j#Yg  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 8@`"ZzM  
g3=-i*ww./2; so[i"ZM)  
P1=0; a/d'(]  
P2=0; ZJUTtiD  
P3=1; Yphru"\$  
P=0; aH@Ux?-}  
for m1=1:M1                 U)IW6)q  
p=0.032*m1;                %input amplitude "#7~}ZB  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 zY?GO"U"  
s1=s10; Jpi\n- d!  
s20=0.*s10;                %input in waveguide 2 #H]cb#  
s30=0.*s10;                %input in waveguide 3 -]8cw#y 0A  
s2=s20; >T'=4n['  
s3=s30; 7.hgne'<  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   z[xi  
%energy in waveguide 1 QwaCaYoh  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   tqI]S X  
%energy in waveguide 2 w!$|IC  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   S $wx>715  
%energy in waveguide 3 N}ur0 'J0  
for m3 = 1:1:M3                                    % Start space evolution Rw4"co6  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ~ Iin|  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; UhQsT^b_  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; WzM9{c  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform &,?bX])  
   sca2 = fftshift(fft(s2)); ~G0\57;h  
   sca3 = fftshift(fft(s3)); R"Ol'y{  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   J*)Vpk  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); j$Tto
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   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); T KpX]H`  
   s3 = ifft(fftshift(sc3)); 6=V&3|"  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Jt4&%b-T  
   s1 = ifft(fftshift(sc1)); &Nf10%J'<  
end &\(p<TF  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); =-#>NlB$w  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); J%|!KQl  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); $umh&z/  
   P1=[P1 p1/p10]; )vH6N_  
   P2=[P2 p2/p10]; r>fx55dw  
   P3=[P3 p3/p10]; 5<o8prtB  
   P=[P p*p]; aAHx
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end .~#<>  
figure(1) /jJi`'{U  
plot(P,P1, P,P2, P,P3); D ==H{c1F  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~