[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 i?a]v 5  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of D@3|n
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of X!"y>J  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear U?}Maf  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 P"~B2__*  
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%fid=fopen('e21.dat','w'); !X,S2
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N = 128;                       % Number of Fourier modes (Time domain sampling points) fW\u*dMMZE  
M1 =3000;              % Total number of space steps -Z
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J =100;                % Steps between output of space A,iXiDb3pK  
T =10;                  % length of time windows:T*T0 PzF)Vg  
T0=0.1;                 % input pulse width M0]fh5O  
MN1=0;                 % initial value for the space output location %ZxKN;  
dt = T/N;                      % time step w68qyG|wM  
n = [-N/2:1:N/2-1]';           % Index ?Jma^ S  
t = n.*dt;   x^;nfqn|  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 o3`Z@-.G  
u20=u10.*0.0;                  % input to waveguide 2 EZ=M^0=Hpf  
u1=u10; u2=u20;                 Oc8+an1m  
U1 = u1;   3b_#xr-  
U2 = u2;                       % Compute initial condition; save it in U ROfmAc  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 1n5&PNu  
w=2*pi*n./T; jALo;PDJ  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T kiECJ@5p  
L=4;                           % length of evoluation to compare with S. Trillo's paper kP|!!N  
dz=L/M1;                       % space step, make sure nonlinear<0.05 5<S1,u5  
for m1 = 1:1:M1                                    % Start space evolution ES+&e/G"ds  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Z@*Z@]
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform .p5*&i7  
   ca2 = fftshift(fft(u2)); 6suc0  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ]~oM'?&!  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   SHaZ-d  
   u2 = ifft(fftshift(c2));                        % Return to physical space o]FQ)WRB  
   u1 = ifft(fftshift(c1)); <.AIVp  
if rem(m1,J) == 0                                 % Save output every J steps. ar{e<&Bny  
    U1 = [U1 u1];                                  % put solutions in U array NN$`n*;l  
    U2=[U2 u2]; hV
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    MN1=[MN1 m1]; eFx*lYjA  
    z1=dz*MN1';                                    % output location A/.cNen  
  end G cbal:q  
end $~2Ao[  
hg=abs(U1').*abs(U1');                             % for data write to excel vD*KJ3(c  
ha=[z1 hg];                                        % for data write to excel i0R=P[  
t1=[0 t']; l==T3u r  
hh=[t1' ha'];                                      % for data write to excel file Hnaq+ _]  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format  Ne4A  
figure(1) 6$zUFIk  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn $~j]/U  
figure(2) ]f\rB8k|&  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn x 1_(j  
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非线性超快脉冲耦合的数值方法的Matlab程序 ;P{ *'@  
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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。   VP"L_Um  
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 D`gY6wX  
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%  This Matlab script file solves the nonlinear Schrodinger equations N$3F4b%+  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of .c',?[S/vH  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear UOwj"#  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Z<wg`  
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C=1;                           ND`~|6
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M1=120,                       % integer for amplitude -V+fQGZe  
M3=5000;                      % integer for length of coupler vbWX`skU  
N = 512;                      % Number of Fourier modes (Time domain sampling points) >sP;B5S  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Z2ZS5a  
T =40;                        % length of time:T*T0. `zvYuKQ.}  
dt = T/N;                     % time step xE}q(.]  
n = [-N/2:1:N/2-1]';          % Index e5AiIVlv  
t = n.*dt;   $V+ze*ra  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ](O!6_'d  
w=2*pi*n./T; 5-sxTp  
g1=-i*ww./2; sPhh#VCw{  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @U9ov >E  
g3=-i*ww./2; [[)HPHSQ  
P1=0; %@IR7v~  
P2=0; +yYz;, \  
P3=1; lKa}Bcd  
P=0; #\"5:.H Oz  
for m1=1:M1                 7[K$os5al  
p=0.032*m1;                %input amplitude M^bujGD  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 sQ_{zOUPh  
s1=s10; Nc7YMxk'H  
s20=0.*s10;                %input in waveguide 2 S2Wxf>bt2  
s30=0.*s10;                %input in waveguide 3 *v&g>Ni  
s2=s20; :JOF!Q  
s3=s30; t
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [3\}Ca1  
%energy in waveguide 1 d6Z;\f7[  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   '91Ak,cWB  
%energy in waveguide 2 HID;~Ne  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   uh GL1{  
%energy in waveguide 3 | 0&~fY  
for m3 = 1:1:M3                                    % Start space evolution , n+dB2\  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS KI#hII[Q.  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; OW6i2>Or  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Va{`es)hky  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 0R; ;ou  
   sca2 = fftshift(fft(s2)); e}Db-7B_~  
   sca3 = fftshift(fft(s3)); 9 Z4H5!:(  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift    ]@<O!fS  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); No h*1u*  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); J0{0B=d;  
   s3 = ifft(fftshift(sc3)); BK-{z).)  
   s2 = ifft(fftshift(sc2));                       % Return to physical space {>syZZ,h  
   s1 = ifft(fftshift(sc1)); WyO10yvR  
end hnyZXk1|  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); T]0qd^\4w  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); **oN/5  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); `i<U;?=0'  
   P1=[P1 p1/p10]; n}YRE`>D  
   P2=[P2 p2/p10]; b2ZKhS8  
   P3=[P3 p3/p10]; p-;*K(#X  
   P=[P p*p]; g<tr |n  
end .)Du ;  
figure(1) pvcD 61,  
plot(P,P1, P,P2, P,P3); Bl(we/r  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~