[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 cP`f\\c  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of a[]=*(AZI  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of GN?^7kI  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear di>"\On-  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?P
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%fid=fopen('e21.dat','w'); z
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N = 128;                       % Number of Fourier modes (Time domain sampling points) UGj!I  
M1 =3000;              % Total number of space steps @bOhnd#W  
J =100;                % Steps between output of space 8]]uk=P  
T =10;                  % length of time windows:T*T0 #Z)e]4{!l  
T0=0.1;                 % input pulse width LoSblV  
MN1=0;                 % initial value for the space output location v*<hE>J0  
dt = T/N;                      % time step WW\u}z.QJ  
n = [-N/2:1:N/2-1]';           % Index z4b2t}  
t = n.*dt;   d+rrb>-OU  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 \Pi\
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u20=u10.*0.0;                  % input to waveguide 2 oS0l Tf\  
u1=u10; u2=u20;                 
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U1 = u1;   wUW^ O  
U2 = u2;                       % Compute initial condition; save it in U
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. X#'DS&{  
w=2*pi*n./T; ' 7+x,TszI  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T  gPh;  
L=4;                           % length of evoluation to compare with S. Trillo's paper ,dhJ\cQ~  
dz=L/M1;                       % space step, make sure nonlinear<0.05 :JH#*5%gQ:  
for m1 = 1:1:M1                                    % Start space evolution K'%2'd  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS f6vhW66:?x  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ayfR{RYi  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform O;z:?  
   ca2 = fftshift(fft(u2)); {^=T&aCYdS  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation yhv(KI  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   1K?RA*aj  
   u2 = ifft(fftshift(c2));                        % Return to physical space g>-pC a  
   u1 = ifft(fftshift(c1)); ]$Pl[Vegy  
if rem(m1,J) == 0                                 % Save output every J steps. FM;NA{  
    U1 = [U1 u1];                                  % put solutions in U array 3u#bx1  
    U2=[U2 u2]; z/!LC;
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    MN1=[MN1 m1]; nNz1gV:0X  
    z1=dz*MN1';                                    % output location ^MIF+/bQ  
  end cWjb149@)  
end 0gO_dyB  
hg=abs(U1').*abs(U1');                             % for data write to excel m0QE S  
ha=[z1 hg];                                        % for data write to excel k>E^FB=  
t1=[0 t']; a?jUm.  
hh=[t1' ha'];                                      % for data write to excel file YbtsJ <w  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format |eykb?j`  
figure(1) L#O1>  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn waI?X2  
figure(2) g%Bh-O9\  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Wip@MGtJ  

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非线性超快脉冲耦合的数值方法的Matlab程序 yJQ>u  
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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。  
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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 fh_+M"Y0`  
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%  This Matlab script file solves the nonlinear Schrodinger equations 9$[6\jMh  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Ak3cE_*Y/  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _P
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9d&@;&al  
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C=1;                           "uCO?hv0  
M1=120,                       % integer for amplitude $B%wK`J  
M3=5000;                      % integer for length of coupler hr$Wt?B  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 3LGX ^J<f  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Drm#z05i[g  
T =40;                        % length of time:T*T0. /2^"c+/'p  
dt = T/N;                     % time step !LI6_Oq  
n = [-N/2:1:N/2-1]';          % Index JLd-{}A""-  
t = n.*dt;   "5<:Dj/W  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.
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w=2*pi*n./T; m)AF9#aT2  
g1=-i*ww./2; n*A?>NV  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 0JFS%Yjw[  
g3=-i*ww./2; riR(CJ}Ff  
P1=0; +YZ*>ki  
P2=0; E{;F4wT_@  
P3=1; [|".j#ZlK  
P=0; Fn>KdoByN  
for m1=1:M1                 }1fi
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p=0.032*m1;                %input amplitude PRJ  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 UQZl:DYa  
s1=s10; +*RaX (&  
s20=0.*s10;                %input in waveguide 2 e5RF6roxO  
s30=0.*s10;                %input in waveguide 3 &F- \t5X=i  
s2=s20; j,n\`7dD$  
s3=s30; O22Q g  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   )ifjK6*  
%energy in waveguide 1 U$yy7}g  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   8Y4mTW  
%energy in waveguide 2 R + ~b@  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   hrNB"W|?x  
%energy in waveguide 3 s$%t2UaV  
for m3 = 1:1:M3                                    % Start space evolution !"2S'oQKS  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS .n n&K}h  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; |\zzOfaO  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; |v:oLgUdH  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform acrR  
   sca2 = fftshift(fft(s2)); +7\d78U  
   sca3 = fftshift(fft(s3)); 6k_Uq.<X  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   6Hbu7r*tm  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); SZ29B  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 2FR+Z3&z  
   s3 = ifft(fftshift(sc3)); SJB^dI**/d  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ;6eBfMhL  
   s1 = ifft(fftshift(sc1)); /#WvC;B  
end @(bg#  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); aFaioE#h(  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); _9g-D9  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); hkb&]XWi[  
   P1=[P1 p1/p10]; -MRX@a^1  
   P2=[P2 p2/p10]; 9X?RJ."J  
   P3=[P3 p3/p10]; Ptz##o'{5  
   P=[P p*p]; FnKC|X  
end Fc#Sn2p*  
figure(1) ^T:L6:  
plot(P,P1, P,P2, P,P3); }DQTy.d;P  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~