[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 ={@6{-tl  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of UhQj Qaa~  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Od,qbU4O  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @O^6&\s>  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @YTaSz$L  
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%fid=fopen('e21.dat','w'); =R$u[~Xl2X  
N = 128;                       % Number of Fourier modes (Time domain sampling points) )W _v:?A9  
M1 =3000;              % Total number of space steps Tq
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J =100;                % Steps between output of space CU2*z(]&  
T =10;                  % length of time windows:T*T0 w-L=LWL\  
T0=0.1;                 % input pulse width q ,]L$  
MN1=0;                 % initial value for the space output location ra gXn  
dt = T/N;                      % time step mLLDE;7|}  
n = [-N/2:1:N/2-1]';           % Index 8\A#CQ5b  
t = n.*dt;   sLT3Y}IO  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 uo%)1NS!  
u20=u10.*0.0;                  % input to waveguide 2 !Pfr,a  
u1=u10; u2=u20;                 q Y?j#fzi  
U1 = u1;   Pw`8Wj  
U2 = u2;                       % Compute initial condition; save it in U w;:*P  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. IDriGZZ<)6  
w=2*pi*n./T; u[=r,^YQ  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T YWO)HsjP  
L=4;                           % length of evoluation to compare with S. Trillo's paper ">,|V-H  
dz=L/M1;                       % space step, make sure nonlinear<0.05 A&Usddcp  
for m1 = 1:1:M1                                    % Start space evolution jZkcBIK2  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS yEoF4bt  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; >rmqBDKaQ  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform >7T'OC  
   ca2 = fftshift(fft(u2)); w4{<n/"  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ]dmrkZz:  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ~1AgD-:Jz  
   u2 = ifft(fftshift(c2));                        % Return to physical space \aUC(K~o\;  
   u1 = ifft(fftshift(c1)); By",rD- r  
if rem(m1,J) == 0                                 % Save output every J steps. WUXx;9>  
    U1 = [U1 u1];                                  % put solutions in U array :g=qz~2Xk  
    U2=[U2 u2]; .|>3k'<l  
    MN1=[MN1 m1]; goOCu  
    z1=dz*MN1';                                    % output location Y0dEH^I  
  end cj|80$cSA  
end Ma']?Rb`  
hg=abs(U1').*abs(U1');                             % for data write to excel g63(E,;;J  
ha=[z1 hg];                                        % for data write to excel J7Hl\Q[D1  
t1=[0 t']; @&3EJ1  
hh=[t1' ha'];                                      % for data write to excel file i
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%dlmwrite('aa',hh,'\t');                           % save data in the excel format `*cxH..  
figure(1) m{cGK`/\  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn CMG&7(MR  
figure(2) H0gbSd+  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn t[;LD_  
JWhdMU  
非线性超快脉冲耦合的数值方法的Matlab程序 */^q{PsN  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   p\tm:QWD;  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *-=(Q`3  
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%  This Matlab script file solves the nonlinear Schrodinger equations }mYx_=+VX  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of FQ7T'G![  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear SpLzm A  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 BB!THj69a6  
z2_*%S@  
C=1;                           HIR~"It$  
M1=120,                       % integer for amplitude i$:*Pb3mV  
M3=5000;                      % integer for length of coupler c"n\cNP<  
N = 512;                      % Number of Fourier modes (Time domain sampling points) wc NOLUl  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.  gmO!  
T =40;                        % length of time:T*T0. y^,1a[U.  
dt = T/N;                     % time step oWim}Er=  
n = [-N/2:1:N/2-1]';          % Index rq/yD,I,  
t = n.*dt;   ?FeYN+qR  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. T@:Wp4>69  
w=2*pi*n./T; L
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g1=-i*ww./2; 7Oa#c<2]  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ^& t
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g3=-i*ww./2; tqvN0vY5  
P1=0; "$Z= %.3Q  
P2=0; 7$vYo _  
P3=1; Pw7]r<Q  
P=0; nQX:T;WL@  
for m1=1:M1                 *8yAG]z  
p=0.032*m1;                %input amplitude F3v!AvA|  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [#<-ZC#T*  
s1=s10; 8>2.UrC  
s20=0.*s10;                %input in waveguide 2 b8`)y<7  
s30=0.*s10;                %input in waveguide 3 G C),N\@Q  
s2=s20; [LjT*bi  
s3=s30; g:'xae/]S  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   qPX~@^`9  
%energy in waveguide 1 L O_k@3  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   \=?a/  
%energy in waveguide 2 cz#rb*b  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   '8RsN-w  
%energy in waveguide 3 UqFO|r"M  
for m3 = 1:1:M3                                    % Start space evolution "/*\1v9  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS R[h9"0Y^  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; xjuN
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 8`q:Gz=M\  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform t9kzw*U9  
   sca2 = fftshift(fft(s2)); $<dH?%!7  
   sca3 = fftshift(fft(s3)); k$z_:X  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   <y2U3;t  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); fnjPSts0  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); _JzEGpeG  
   s3 = ifft(fftshift(sc3)); ITE{@1  
   s2 = ifft(fftshift(sc2));                       % Return to physical space *KZYv=s,u  
   s1 = ifft(fftshift(sc1)); ?yrX)3hyH  
end =t#llgi~  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); iW]j9}t  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); q 6:dy  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); &=@IzmA  
   P1=[P1 p1/p10]; 'Vzp2  
   P2=[P2 p2/p10]; '1P2$#  
   P3=[P3 p3/p10]; ?(' wn<  
   P=[P p*p]; zsEc(  
end G}9Jg  
figure(1) .;y.]Z/;  
plot(P,P1, P,P2, P,P3); m)ky*"(  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~