[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 J{XRltI+  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Y$./!lVY  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of :DuEv:;v  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /_8nZVu  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 K_.|FEV  
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%fid=fopen('e21.dat','w'); G$CSZrP.  
N = 128;                       % Number of Fourier modes (Time domain sampling points) e~R_bBQ0  
M1 =3000;              % Total number of space steps j|p=JrCJ  
J =100;                % Steps between output of space ?hURNlR_Q  
T =10;                  % length of time windows:T*T0 ``{GU}n  
T0=0.1;                 % input pulse width ,&* BhUC  
MN1=0;                 % initial value for the space output location "kIlxf3  
dt = T/N;                      % time step :eevc7  
n = [-N/2:1:N/2-1]';           % Index q$ j  
t = n.*dt;   N\?__WlBK7  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 OKu~Nb*  
u20=u10.*0.0;                  % input to waveguide 2 k!6m'}v  
u1=u10; u2=u20;                 i`iR7UmHeR  
U1 = u1;   [I<J6=  
U2 = u2;                       % Compute initial condition; save it in U W58%Zz4a  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ?T|0"|\"'  
w=2*pi*n./T; Aq>?G+  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 8&qtF.i-6  
L=4;                           % length of evoluation to compare with S. Trillo's paper cw0uLMqr`  
dz=L/M1;                       % space step, make sure nonlinear<0.05 nCA~=[&H  
for m1 = 1:1:M1                                    % Start space evolution AOV{@b(  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS :vaVghN\  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; %`/F>`  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform aQ&K a  
   ca2 = fftshift(fft(u2)); wMCgLh\wi  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation M}=>~TA@  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   3+iryW(\  
   u2 = ifft(fftshift(c2));                        % Return to physical space RfCu5Kn  
   u1 = ifft(fftshift(c1)); l=$?#^^ /  
if rem(m1,J) == 0                                 % Save output every J steps. yGX5
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    U1 = [U1 u1];                                  % put solutions in U array hb}QtQ  
    U2=[U2 u2]; G2P:|R  
    MN1=[MN1 m1]; NJQy*~P  
    z1=dz*MN1';                                    % output location 6%wlz%Fp  
  end -<" ;|v4  
end UDgX A  
hg=abs(U1').*abs(U1');                             % for data write to excel l%2 gM7WMY  
ha=[z1 hg];                                        % for data write to excel hyhm{RC?[  
t1=[0 t']; \uJ+~db
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hh=[t1' ha'];                                      % for data write to excel file # |OA>[  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 2{oQ  
figure(1) Q`-Xx  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn {qCFd  
figure(2) Hoe
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn D)Jac@,0  
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非线性超快脉冲耦合的数值方法的Matlab程序 ::cI4D  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   h$%h w+"4  
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 QDb8W*&<  
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%  This Matlab script file solves the nonlinear Schrodinger equations J L1]auO*  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of /^X)>1)j  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )FfS7 C\.  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 T?tZ?!6  
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C=1;                           BD]o+96qP  
M1=120,                       % integer for amplitude {V8uk
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M3=5000;                      % integer for length of coupler >Y|P+Z\7  
N = 512;                      % Number of Fourier modes (Time domain sampling points) j}fSz)`i  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. }n"gX>e~  
T =40;                        % length of time:T*T0. )Z\Zw~L  
dt = T/N;                     % time step ln6=X
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n = [-N/2:1:N/2-1]';          % Index QpS7nGev  
t = n.*dt;   $)6M@S  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 4sC)hAx&f  
w=2*pi*n./T; \i<7Lk  
g1=-i*ww./2; R+.kwq3CED  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; \vS >jB  
g3=-i*ww./2; VM;vLUu!e  
P1=0; Oa M~rze  
P2=0; 8CH9&N5W5t  
P3=1; ~4mRm!DP  
P=0; @,LU!#y(  
for m1=1:M1                 9eR";Wm])  
p=0.032*m1;                %input amplitude N0 mhgEA  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 -av=5hm  
s1=s10; >T{TE"XyO|  
s20=0.*s10;                %input in waveguide 2 O2U}jHsd  
s30=0.*s10;                %input in waveguide 3 ~Qf\DTM&  
s2=s20; d vo|9>  
s3=s30; ^E~1%Md.  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   7c6- o"A  
%energy in waveguide 1 ^)aj,U[  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   0}'/3Q  
%energy in waveguide 2 Rh)
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8m[o*E.4F  
%energy in waveguide 3 Rv.IHSQUo  
for m3 = 1:1:M3                                    % Start space evolution 9`KFJx6D  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS +HgyM0LFg  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ;3%Y@FS@  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; vTL/% SJ8  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform p=|S%  
   sca2 = fftshift(fft(s2)); sI{?4k  
   sca3 = fftshift(fft(s3)); su\`E&0V+  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   o'Y/0hkh  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); SQ'%a-Mct  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); V0%a/Hi v  
   s3 = ifft(fftshift(sc3)); b~<:k\EE  
   s2 = ifft(fftshift(sc2));                       % Return to physical space lAo4)  
   s1 = ifft(fftshift(sc1)); 7 ;2>kgf~  
end "_=t1UE  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <)Y jVGG  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ['3E'q,4&  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); $Yw~v36`t/  
   P1=[P1 p1/p10]; VA %lJ!$  
   P2=[P2 p2/p10]; ZoCk]hk  
   P3=[P3 p3/p10]; aN!,\D  
   P=[P p*p]; NSq29#  
end lwjA07i  
figure(1) 9hJ  a K  
plot(P,P1, P,P2, P,P3); =F5zU5`i  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~