[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 9LUP{(uq  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of WllCcD1  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of "
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear t(Cq(.u`:  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 bt.K<Y0  
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%fid=fopen('e21.dat','w'); 3RG/X  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *m2d#f  
M1 =3000;              % Total number of space steps ant-\w>}  
J =100;                % Steps between output of space V~tu<"%  
T =10;                  % length of time windows:T*T0 .oB'ttF1  
T0=0.1;                 % input pulse width :X]lXock
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MN1=0;                 % initial value for the space output location p2M?pV  
dt = T/N;                      % time step c'm-XL_La  
n = [-N/2:1:N/2-1]';           % Index +Uc&%Px  
t = n.*dt;   AF07KA#  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 M]pel\{M  
u20=u10.*0.0;                  % input to waveguide 2 oc,U4+T  
u1=u10; u2=u20;                 Ra*k  
U1 = u1;   gDjd{+LUo  
U2 = u2;                       % Compute initial condition; save it in U RJ7/I/yD|  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. cviN$oL  
w=2*pi*n./T; 9^=t@  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T FeincZ!M  
L=4;                           % length of evoluation to compare with S. Trillo's paper ?`BED6$`G9  
dz=L/M1;                       % space step, make sure nonlinear<0.05 '3Y0D1`v  
for m1 = 1:1:M1                                    % Start space evolution J/H#d')c  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS '8((;N|I^  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 8M5!5Jzv  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ()rx>?x5  
   ca2 = fftshift(fft(u2)); QvT-&|  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation *U5>j#,  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   M2;(+8 b  
   u2 = ifft(fftshift(c2));                        % Return to physical space N:sECGS,  
   u1 = ifft(fftshift(c1)); <yb=!  
if rem(m1,J) == 0                                 % Save output every J steps. [0%Gu5_\  
    U1 = [U1 u1];                                  % put solutions in U array OQX{<pQ6  
    U2=[U2 u2]; bsmoLT  
    MN1=[MN1 m1]; {{#a%O  
    z1=dz*MN1';                                    % output location b{ubp  
  end dk, I?c&  
end d5E
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hg=abs(U1').*abs(U1');                             % for data write to excel cWy*K4O  
ha=[z1 hg];                                        % for data write to excel R*c0NJF
 
t1=[0 t']; M<|~MR  
hh=[t1' ha'];                                      % for data write to excel file eUUD|U*b   
%dlmwrite('aa',hh,'\t');                           % save data in the excel format vVv
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figure(1) n?ZH2dI\0  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn VNh,pQ(  
figure(2) #uDBF
 
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn K:Xrfn{s  
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非线性超快脉冲耦合的数值方法的Matlab程序 He$mu=$q{  
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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。   [laL6  
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 IbNTdg]/F`  
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%  This Matlab script file solves the nonlinear Schrodinger equations `peJ s~V  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of y^+[eT&  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear XC8z|A-@  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?p/kuv{\o#  
yP=isi#dDY  
C=1;                           _bV=G#qKK  
M1=120,                       % integer for amplitude j~0ZE -e  
M3=5000;                      % integer for length of coupler m3v*,~  
N = 512;                      % Number of Fourier modes (Time domain sampling points) < c4RmnA  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. /dP8F  
T =40;                        % length of time:T*T0. x /Ky: Ky  
dt = T/N;                     % time step eG)/&zQ8  
n = [-N/2:1:N/2-1]';          % Index .f!eRV.&  
t = n.*dt;   <t|9`l_XW  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. =[-- Hf  
w=2*pi*n./T; Iy 8E$B;  
g1=-i*ww./2; e4_aKuA  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 5Vm}<8{  
g3=-i*ww./2; +cOI`4`$  
P1=0; TH}ycue  
P2=0; @p'v.;~#  
P3=1; 01d26`G$i~  
P=0; rp[oH=&  
for m1=1:M1                 _ JJ0pc9t  
p=0.032*m1;                %input amplitude %'~<:>:"E  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 
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s1=s10; d4eCBqx  
s20=0.*s10;                %input in waveguide 2 eR 2T<7G  
s30=0.*s10;                %input in waveguide 3 "
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s2=s20; ).`a-Pv  
s3=s30; F vk:c-  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   7JwWM2N?V  
%energy in waveguide 1 tMk>Bx9[  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   .aH?H]^  
%energy in waveguide 2 qQRYHo>/e  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   f*&JfP  
%energy in waveguide 3 g~sNY|%  
for m3 = 1:1:M3                                    % Start space evolution 21EUP6}8j  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 5pyvs;As  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; nR'EuI~(}  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; GSb)|mj  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 4qXUk:C@m  
   sca2 = fftshift(fft(s2)); "._WdY[  
   sca3 = fftshift(fft(s3)); %v)'`|i  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   KX}dn:;(3  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); _89G2)U=C  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); $u.T1v  
   s3 = ifft(fftshift(sc3)); : MmXH&yR  
   s2 = ifft(fftshift(sc2));                       % Return to physical space t-'GRme  
   s1 = ifft(fftshift(sc1)); m%(JRh  
end nMvIL2:3  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); (_5+`YsV  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 67:<X(u+!  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Id
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   P1=[P1 p1/p10]; hGHzO  
   P2=[P2 p2/p10]; @I.OT  
   P3=[P3 p3/p10]; aC]l({-0  
   P=[P p*p]; qtwmTT)  
end \$
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figure(1) eQIi}\`  
plot(P,P1, P,P2, P,P3); Kqu7DZ+W  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~