[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 V(n7h
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of n!e4"|4~z  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of "HSAwe`5jU  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3(l^{YC+[7  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~Y
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%fid=fopen('e21.dat','w'); *T0{ yI  
N = 128;                       % Number of Fourier modes (Time domain sampling points) }DiMt4!ZC!  
M1 =3000;              % Total number of space steps n5h4]u  
J =100;                % Steps between output of space z/yNFY]i  
T =10;                  % length of time windows:T*T0 WZ`u"t^2V  
T0=0.1;                 % input pulse width ew8f7S[  
MN1=0;                 % initial value for the space output location z)N8#Y~vn  
dt = T/N;                      % time step :^7/+|}9p  
n = [-N/2:1:N/2-1]';           % Index 53X H|Ap  
t = n.*dt;   | wuUH  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Oo<L~7B  
u20=u10.*0.0;                  % input to waveguide 2 #wn`choT'  
u1=u10; u2=u20;                 j}~3m$  
U1 = u1;   x`/"1]Nf  
U2 = u2;                       % Compute initial condition; save it in U ,x#5.Koz  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 8V$pdz|[  
w=2*pi*n./T; G`3/${ti  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @*kQZRGK7  
L=4;                           % length of evoluation to compare with S. Trillo's paper :(gZ\q">k  
dz=L/M1;                       % space step, make sure nonlinear<0.05 t/xWJW2  
for m1 = 1:1:M1                                    % Start space evolution C{
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS N
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; M{:}.H<a  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform uR#aO''  
   ca2 = fftshift(fft(u2)); "i3wc&9!?W  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation %
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   [k qx%4q)  
   u2 = ifft(fftshift(c2));                        % Return to physical space fHK`u'  
   u1 = ifft(fftshift(c1)); O~Eju  
if rem(m1,J) == 0                                 % Save output every J steps. GcXh V  
    U1 = [U1 u1];                                  % put solutions in U array S[g{ )p)  
    U2=[U2 u2]; %dA6vHI,  
    MN1=[MN1 m1]; >6xZF'4  
    z1=dz*MN1';                                    % output location ;la sk4
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  end Fo  K!JX*  
end vV5dW  
hg=abs(U1').*abs(U1');                             % for data write to excel M@\A_x(Mas  
ha=[z1 hg];                                        % for data write to excel ;jC}.] _)w  
t1=[0 t'];  {*!L[)  
hh=[t1' ha'];                                      % for data write to excel file a B(_ZX'L  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format h+ixl#:  
figure(1) RE~9L5i5  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Z{<&2*  
figure(2) BllS3I}V  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn /{h@A~<96  
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非线性超快脉冲耦合的数值方法的Matlab程序 @K{1O|V  
{p -q&k&R|  
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。   )?es3Ehqq  
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 LHit9O[_/s  
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%  This Matlab script file solves the nonlinear Schrodinger equations l-?B1gd,l  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of :2+,?#W  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !h\>[
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 wrtJ8O(  
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C=1;                           @D$^- S6  
M1=120,                       % integer for amplitude yDmNPk/  
M3=5000;                      % integer for length of coupler O}$@|w(8;  
N = 512;                      % Number of Fourier modes (Time domain sampling points) hn-+]Y:  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. $hND!T+;  
T =40;                        % length of time:T*T0. {w/{)BnPG  
dt = T/N;                     % time step &d5n_:^  
n = [-N/2:1:N/2-1]';          % Index [w>T.b  
t = n.*dt;   l~_]k  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. +MHsdeGU1W  
w=2*pi*n./T; t(d$v_*y51  
g1=-i*ww./2; ,gag_o{*a  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 'MF|(`  
g3=-i*ww./2; {Y0Uln5u  
P1=0; BC*)@=
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P2=0; H rMH  
P3=1; 8\
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P=0; )1E[CIaXK  
for m1=1:M1                 1W@ C]n4  
p=0.032*m1;                %input amplitude :9nqQJ+~  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1
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s1=s10; aXOW +$,  
s20=0.*s10;                %input in waveguide 2 I%
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s30=0.*s10;                %input in waveguide 3 i
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s2=s20; }M
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s3=s30; YTb/ LeuT  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Ln&'5D#  
%energy in waveguide 1 |"gg2p  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   KM'*+.I  
%energy in waveguide 2  ~OdE!!  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   rzl0*
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%energy in waveguide 3 #Qir%\*V  
for m3 = 1:1:M3                                    % Start space evolution  Rix|LKk{  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Y.7iKMp(  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; '3<AzR2  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; &>jSuvVT  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform (vO\h8  
   sca2 = fftshift(fft(s2)); /Soc,PjZ  
   sca3 = fftshift(fft(s3)); %1\MW+  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   lMn1e6~K  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Ne!0`^`~  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); !@.9>"FU  
   s3 = ifft(fftshift(sc3)); cPx]:sC  
   s2 = ifft(fftshift(sc2));                       % Return to physical space G8sxg&bf{  
   s1 = ifft(fftshift(sc1)); 3zr95$Mt  
end w# iezo. 0  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); @.D1_A  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); L lNd97Z  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 3?n2/p 7=  
   P1=[P1 p1/p10]; 2kX

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   P2=[P2 p2/p10]; L\GjG&Y5  
   P3=[P3 p3/p10]; OrG1Mfx&2%  
   P=[P p*p]; 2:8p>^g=  
end Oh&k{DWE$  
figure(1) P5$L(x%~  
plot(P,P1, P,P2, P,P3); ^KlW"2:  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~