[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 dpZ7eJ  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of kR^7Z7+#*  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ~D@V@sX  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear k(=\&T  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 jCW>=1:JGY  
fj0+a0h  
%fid=fopen('e21.dat','w'); qt/syF&s  
N = 128;                       % Number of Fourier modes (Time domain sampling points) =/6.4;8  
M1 =3000;              % Total number of space steps Z/q%%(fh 0  
J =100;                % Steps between output of space `m3@mJ!>\  
T =10;                  % length of time windows:T*T0 z:u`W#Rf  
T0=0.1;                 % input pulse width T_Z@uZom.  
MN1=0;                 % initial value for the space output location eN/sW!:P|  
dt = T/N;                      % time step c/;t.+g  
n = [-N/2:1:N/2-1]';           % Index L)8+/+  
t = n.*dt;   E=~H,~  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 s%GiM  
u20=u10.*0.0;                  % input to waveguide 2 ><LIOFqsS  
u1=u10; u2=u20;                 ~Zl`Ap  
U1 = u1;   -J[zJ4z#  
U2 = u2;                       % Compute initial condition; save it in U Cb=r8C  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. T~"
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w=2*pi*n./T; C>
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T (n" )  
L=4;                           % length of evoluation to compare with S. Trillo's paper @kvp2P+O  
dz=L/M1;                       % space step, make sure nonlinear<0.05 OOl{  
for m1 = 1:1:M1                                    % Start space evolution vR,HCI  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS t)cG_+rJ  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; a:zx&DwM  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform YL){o$-N"J  
   ca2 = fftshift(fft(u2)); 32~Tf,  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation WU<#_by g  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   X&
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   u2 = ifft(fftshift(c2));                        % Return to physical space + W@r p#  
   u1 = ifft(fftshift(c1)); ~|DF-t V  
if rem(m1,J) == 0                                 % Save output every J steps. V]q{N-Iq  
    U1 = [U1 u1];                                  % put solutions in U array ?b
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    U2=[U2 u2]; QMtt:f]?i  
    MN1=[MN1 m1]; ATnD~iACY  
    z1=dz*MN1';                                    % output location ]2h[.qa  
  end wW%I <M  
end L
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hg=abs(U1').*abs(U1');                             % for data write to excel I,YGm  
ha=[z1 hg];                                        % for data write to excel P?9CBhN  
t1=[0 t']; ]VwAHT&je  
hh=[t1' ha'];                                      % for data write to excel file jQb=N%5s  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 7]nPWz1%*  
figure(1) _Fz)2h,3  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn I]k'0LG*^  
figure(2) gKYn*  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn o8s&n3mY}y  
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非线性超快脉冲耦合的数值方法的Matlab程序 LL[+QcH  
hJ}G5pX  
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。   G x,D'H'  
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 +vU.#C_2  
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%  This Matlab script file solves the nonlinear Schrodinger equations 5Q%#Z L/'  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of qb"!  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 4k#B5^iJ  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [")
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C=1;                           8vT:icl  
M1=120,                       % integer for amplitude A%GJ|h,i  
M3=5000;                      % integer for length of coupler 3/[=  
N = 512;                      % Number of Fourier modes (Time domain sampling points) PH7L#H^  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ]$L[3qA.  
T =40;                        % length of time:T*T0. ?BLOc;I&a  
dt = T/N;                     % time step 3Y
Lnh@-  
n = [-N/2:1:N/2-1]';          % Index 1B1d>V$*  
t = n.*dt;   +$UfP(XmH  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. <=zGaU,  
w=2*pi*n./T; <;XJ::d  
g1=-i*ww./2; |hdh4P$+|  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; B}MJ?uvA  
g3=-i*ww./2; /C(L(
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P1=0; fk"{G>&8  
P2=0; 8odVdivh  
P3=1;
.H>Rqikj  
P=0; K&X'^|en  
for m1=1:M1                 I}q-J~s  
p=0.032*m1;                %input amplitude Gt1Up~\s  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 AH7k|6ku<*  
s1=s10; )a}5\
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s20=0.*s10;                %input in waveguide 2 9.@(&  
s30=0.*s10;                %input in waveguide 3 3jI.!xD`  
s2=s20; g@U#Y#b@"  
s3=s30; H 0h  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   =CVw0'yZ  
%energy in waveguide 1 asF-mf;D  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   2tbqmWw/s  
%energy in waveguide 2 H,I}R  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   cpy"1=K~M  
%energy in waveguide 3 O<E0L&4-&  
for m3 = 1:1:M3                                    % Start space evolution oby*.61?5l  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ]SPB c  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ~H$XSNPi  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; C=]3NB>Jc  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform e56#Qb@$\  
   sca2 = fftshift(fft(s2)); jG2w(h/"  
   sca3 = fftshift(fft(s3)); Cn55%:  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   MvW>ktkU  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); U;nC)'~YW9  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); {L=[1  
   s3 = ifft(fftshift(sc3)); x3P@AC$\  
   s2 = ifft(fftshift(sc2));                       % Return to physical space t,+S~Cj|  
   s1 = ifft(fftshift(sc1)); nZT@d;]U9  
end j*zK"n  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); N:<O  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 5_`}
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); J#kdyBmuO  
   P1=[P1 p1/p10]; G<z)Ydh_  
   P2=[P2 p2/p10]; f8 jaMn9o  
   P3=[P3 p3/p10]; xHGoCFB  
   P=[P p*p]; yRznP
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end nT12[@:Tr  
figure(1) ;1dz?'%V  
plot(P,P1, P,P2, P,P3); Chua>p!$g  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~