[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 M%d
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of x?:[:Hf   
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ,c@^u6a  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear {q%wr*  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ISI\<qx  
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%fid=fopen('e21.dat','w'); a W`q  
N = 128;                       % Number of Fourier modes (Time domain sampling points) uoYG@L2  
M1 =3000;              % Total number of space steps yVvO!  
J =100;                % Steps between output of space 3[E3]]OVa  
T =10;                  % length of time windows:T*T0 C:/O]slH  
T0=0.1;                 % input pulse width gRS}Y8  
MN1=0;                 % initial value for the space output location TKpka]nJ  
dt = T/N;                      % time step Sni Ck*T,  
n = [-N/2:1:N/2-1]';           % Index .v36xXK(  
t = n.*dt;   XO+^q9  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 4tR:O#($V  
u20=u10.*0.0;                  % input to waveguide 2 (PjC]`FK  
u1=u10; u2=u20;                 84UH& b'n  
U1 = u1;   |*W`}i  
U2 = u2;                       % Compute initial condition; save it in U |1zoT|}q  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. .az+'1  
w=2*pi*n./T; Y]aVa2!Wb  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 5A,@$yp+  
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 m$ZPQ0X  
for m1 = 1:1:M1                                    % Start space evolution f"zXiUV  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; bI 3o|  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 6]yYiz2Xn  
   ca2 = fftshift(fft(u2)); v/{LC
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ufE;rcYE  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   >4>!zZ  
   u2 = ifft(fftshift(c2));                        % Return to physical space `9BZ))Pg  
   u1 = ifft(fftshift(c1)); ct+ ;W  
if rem(m1,J) == 0                                 % Save output every J steps. S"ZH5O(  
    U1 = [U1 u1];                                  % put solutions in U array LeDty_  
    U2=[U2 u2]; U|QLc  
    MN1=[MN1 m1]; QH:k5V~  
    z1=dz*MN1';                                    % output location XdX1GH*C  
  end jj2 [Zh/h  
end YvD+Lk'hm  
hg=abs(U1').*abs(U1');                             % for data write to excel 6?I,sZW  
ha=[z1 hg];                                        % for data write to excel q}[
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t1=[0 t']; h+)XLs  
hh=[t1' ha'];                                      % for data write to excel file ~u-DuOZ8  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format egMl(~D  
figure(1) C7#ji"t  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn D#}t)$"  
figure(2) f%fD>a  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn fYrC;&n  
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非线性超快脉冲耦合的数值方法的Matlab程序 wVU.j$+_#  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   Y5nj _xQJL  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \c1u$'|v  
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%  This Matlab script file solves the nonlinear Schrodinger equations a*?bnw?  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Fk(nf9M%  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear :.8@ xVH  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 VfWU-lJ  
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C=1;                           iNj*Gj  
M1=120,                       % integer for amplitude v_M-:e3`  
M3=5000;                      % integer for length of coupler }LK +w+h~  
N = 512;                      % Number of Fourier modes (Time domain sampling points) T1,Nb>gBq^  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. En01LrC?  
T =40;                        % length of time:T*T0. h9<*+T  
dt = T/N;                     % time step M)sM G C  
n = [-N/2:1:N/2-1]';          % Index +9LIpU&5  
t = n.*dt;   \ZN>7?Vs  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. .nDB{@#  
w=2*pi*n./T; jSi\/(E  
g1=-i*ww./2;
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g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; mhh^kwW  
g3=-i*ww./2; {}gx;v)  
P1=0; %gBulvg
 
P2=0; kAc8[Hn  
P3=1; u={A4A#  
P=0; 90g=&O5@O  
for m1=1:M1                 >\f'QQ  
p=0.032*m1;                %input amplitude v_U+wga  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Tvp~~Dk  
s1=s10; jEK{QOq0  
s20=0.*s10;                %input in waveguide 2
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s30=0.*s10;                %input in waveguide 3 d\eTyN'rA  
s2=s20; M N-j$-y}  
s3=s30; l!S}gbM  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \%],pZsA~  
%energy in waveguide 1 =:neGqd\_E  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   %=w@c  
%energy in waveguide 2 "~V|p3  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   6gr?#D -F  
%energy in waveguide 3 IOL5p*:gz  
for m3 = 1:1:M3                                    % Start space evolution 4Nylc.2mi  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS M~h^~:Lk  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ]2zzY::Sd=  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 9Rf})$o+  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform `1xJ1z#  
   sca2 = fftshift(fft(s2)); _;zIH5 H  
   sca3 = fftshift(fft(s3)); r<)>k.] !  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   d ,"L8  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); PiL[&_8g  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); P3e}G-Oz  
   s3 = ifft(fftshift(sc3)); 3'*}ZDC  
   s2 = ifft(fftshift(sc2));                       % Return to physical space v35!? 5{  
   s1 = ifft(fftshift(sc1)); :o37 V!  
end yb/v?q?Fk  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); K^6fg,&  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); @Z+(J:Grm5  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); z5tOsU  
   P1=[P1 p1/p10]; n0 q$/Y.  
   P2=[P2 p2/p10]; dj}y6V&  
   P3=[P3 p3/p10]; tNbL)  
   P=[P p*p]; ~;AJB  
end :qAF}|6  
figure(1) fkHCfcU  
plot(P,P1, P,P2, P,P3); ^X\{MW'>4  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~