[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 Fsnw3/Nr  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 5Xp$yX =  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9vB9k@9  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cZPbD;e:  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 l :f9Ih  
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%fid=fopen('e21.dat','w'); rd|@*
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N = 128;                       % Number of Fourier modes (Time domain sampling points) (3)C_Z  
M1 =3000;              % Total number of space steps pA*D/P-  
J =100;                % Steps between output of space ;:v]NZtc  
T =10;                  % length of time windows:T*T0 L#@l(8.  
T0=0.1;                 % input pulse width _Cu[s?,kS  
MN1=0;                 % initial value for the space output location }T?i%l  
dt = T/N;                      % time step XMjI}SPG  
n = [-N/2:1:N/2-1]';           % Index s#'|{  
t = n.*dt;   *O2^{
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 trID#DT~  
u20=u10.*0.0;                  % input to waveguide 2 {Bav$kw;?e  
u1=u10; u2=u20;                 'e+-,CGdY\  
U1 = u1;   FCsyKdM  
U2 = u2;                       % Compute initial condition; save it in U F2Nb5WT  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. z'5;f;  
w=2*pi*n./T; $K=K?BV[  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T pkrl@jv >  
L=4;                           % length of evoluation to compare with S. Trillo's paper Y2RxD\!Z  
dz=L/M1;                       % space step, make sure nonlinear<0.05 6Y0/i,d*  
for m1 = 1:1:M1                                    % Start space evolution O^QR;<t'  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS |HKHN?)  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; jldcvW  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform V Z4nAG  
   ca2 = fftshift(fft(u2)); YHwVj?6W  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation VWnu#_(  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   avYh\xZ  
   u2 = ifft(fftshift(c2));                        % Return to physical space (E2lv#[  
   u1 = ifft(fftshift(c1)); )W_ Y3M,  
if rem(m1,J) == 0                                 % Save output every J steps. O3slabE#
 
    U1 = [U1 u1];                                  % put solutions in U array :epitpJ  
    U2=[U2 u2]; *~\;&G29Y  
    MN1=[MN1 m1]; r9p?@P\:[  
    z1=dz*MN1';                                    % output location hr/xpQW  
  end $6Q2)^LJ  
end \?5[RR  
hg=abs(U1').*abs(U1');                             % for data write to excel `Z;B
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ha=[z1 hg];                                        % for data write to excel $G^H7|PzdC  
t1=[0 t']; i]hR7g<  
hh=[t1' ha'];                                      % for data write to excel file MSxU>FX0  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format rm7*l<v6  
figure(1) 
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waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;DT
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figure(2) ThT.iD[  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Q!BkS=H30K  
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非线性超快脉冲耦合的数值方法的Matlab程序 P~b%;*m}8  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   r`mzsO-'  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 o$qFa9|Ec?  
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%  This Matlab script file solves the nonlinear Schrodinger equations !T&
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of )nbyV a  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear MO(5-R`  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6i?kkULBS  
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C=1;                           l")o!N?  
M1=120,                       % integer for amplitude Bt`r6v;\  
M3=5000;                      % integer for length of coupler `qYc#_ELv  
N = 512;                      % Number of Fourier modes (Time domain sampling points) *I;Mp  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ;Kq<',u~  
T =40;                        % length of time:T*T0. i >/@]2  
dt = T/N;                     % time step O7L6Htya  
n = [-N/2:1:N/2-1]';          % Index #q^>qX y  
t = n.*dt;   QVA!z##  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. sVZ}nq{  
w=2*pi*n./T;  hE?GO,  
g1=-i*ww./2; w-q=.RSTn=  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; swe8  
g3=-i*ww./2; 'KW+Rr~tZn  
P1=0; N]<~NG:6b  
P2=0; 2Xk1AS  
P3=1; .jG.90  
P=0; G@l|u  
for m1=1:M1                 *^&iw$Qx3  
p=0.032*m1;                %input amplitude $(<*pU  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 EZNB`gO  
s1=s10; U]R|ej  
s20=0.*s10;                %input in waveguide 2 B+e~k?O]1  
s30=0.*s10;                %input in waveguide 3 jak|LOp  
s2=s20; ^,\se9=(  
s3=s30; _ZvX"{y~  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   XQ?)  
%energy in waveguide 1 H6+st`{  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ^dp[Z,[1z  
%energy in waveguide 2 =*O9)$b  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   @o-evH;G  
%energy in waveguide 3 vA $BBXX  
for m3 = 1:1:M3                                    % Start space evolution N'1[t  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3k
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Y_ u7 0@`  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; k?_$h<Y  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform I[YfF  
   sca2 = fftshift(fft(s2)); F^[Rwzv>c  
   sca3 = fftshift(fft(s3)); 8B
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   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   (j\UoKLRt  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Xwn|.  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); O
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   s3 = ifft(fftshift(sc3)); _KlPbyLU  
   s2 = ifft(fftshift(sc2));                       % Return to physical space aG&kl O>m  
   s1 = ifft(fftshift(sc1)); P24  
end pz z`4VS:  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); EC&19  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Ql!6I(  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 'G By^hj?  
   P1=[P1 p1/p10]; pRfHbPV?  
   P2=[P2 p2/p10]; (5\d[||9g  
   P3=[P3 p3/p10]; < oG\)!O  
   P=[P p*p]; v,
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end ` G/QJH{I  
figure(1) t3kh]2t  
plot(P,P1, P,P2, P,P3); :j!_XMyT:  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~