[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 'a"Uw"/p[  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of M*aYcIU((  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of SZvC4lOn#  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear kkXe=f%  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 m",G;VN  
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%fid=fopen('e21.dat','w'); (t,mtdD#1  
N = 128;                       % Number of Fourier modes (Time domain sampling points) XY<KLO%  
M1 =3000;              % Total number of space steps 8tzL.P^  
J =100;                % Steps between output of space ]hZk#rp}  
T =10;                  % length of time windows:T*T0 }Ggn2 X  
T0=0.1;                 % input pulse width Is9.A_0h  
MN1=0;                 % initial value for the space output location @2TfW]6  
dt = T/N;                      % time step (R(NEN  
n = [-N/2:1:N/2-1]';           % Index )M@^Z(W/a  
t = n.*dt;   ^1Bk*?Yx\x  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 gBZNO! a,d  
u20=u10.*0.0;                  % input to waveguide 2 %1)JRc  
u1=u10; u2=u20;                 ?',Wn3A  
U1 = u1;   4G RHvA.  
U2 = u2;                       % Compute initial condition; save it in U Ii>#
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ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. }6*
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w=2*pi*n./T; P=X)Ktmv  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T m<!CF3g  
L=4;                           % length of evoluation to compare with S. Trillo's paper EF;B)y=  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Wj, {lJ,  
for m1 = 1:1:M1                                    % Start space evolution #;UoZJ B  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS FA;B:O@:'  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }TDq7-(g  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 4v2JrC;  
   ca2 = fftshift(fft(u2)); TJuS)AZ C  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation S5~(3I )v  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   C}\kp0mz  
   u2 = ifft(fftshift(c2));                        % Return to physical space JC}T*h>Ee  
   u1 = ifft(fftshift(c1)); %h v-3L#V  
if rem(m1,J) == 0                                 % Save output every J steps. [5Zi\'~UH)  
    U1 = [U1 u1];                                  % put solutions in U array kqGydGh*"  
    U2=[U2 u2]; 0\+$j5;  
    MN1=[MN1 m1]; A@reIt  
    z1=dz*MN1';                                    % output location _,w*Rv5=  
  end ozA%u,\7k  
end =.,XJIw&  
hg=abs(U1').*abs(U1');                             % for data write to excel }{v0}-~@  
ha=[z1 hg];                                        % for data write to excel Z 2lX^z  
t1=[0 t']; ^b*ub(5Ot  
hh=[t1' ha'];                                      % for data write to excel file nyOvB#f  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format N8X)/W  
figure(1) 4ZB]n,pfT  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Kc+9n%sp  
figure(2) 8an_s%,AW  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn {(h!JeQ  
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非线性超快脉冲耦合的数值方法的Matlab程序 Htep
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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。   ='(;!3ZH  
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 Z*'_/Grv?  
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%  This Matlab script file solves the nonlinear Schrodinger equations u2*."W\  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 1119YeL  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear K:Z|# i-  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 OO;I^`Yn  
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C=1;                           O\
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M1=120,                       % integer for amplitude d/E0opv  
M3=5000;                      % integer for length of coupler xP 3>8Y  
N = 512;                      % Number of Fourier modes (Time domain sampling points) q4Y'yp`?K;  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. l Ng)k1  
T =40;                        % length of time:T*T0. t_qX7P8+'  
dt = T/N;                     % time step 7QaZ|\c  
n = [-N/2:1:N/2-1]';          % Index ]Yf8  
t = n.*dt;   w^S]HzMd  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. b+$-f:m
j  
w=2*pi*n./T; s$/Z+"f(  
g1=-i*ww./2; i^eDM.#X  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 0:eK}tC  
g3=-i*ww./2; Hlj3z3  
P1=0; RG-,<G`  
P2=0; C(}Kfi@6N  
P3=1; oSP^ .BJ$  
P=0; Qq\hD@Z|  
for m1=1:M1                 Rz33_ qA  
p=0.032*m1;                %input amplitude ~bfjP2 g  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 kqLpt  
s1=s10; 9A}n
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s20=0.*s10;                %input in waveguide 2 5~"m$/yE  
s30=0.*s10;                %input in waveguide 3 dVBr-+  
s2=s20; G)%r|meKGB  
s3=s30; $oZ
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p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   i.+#a2   
%energy in waveguide 1 x%RE3J-  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Ft8ii|-  
%energy in waveguide 2 > Cx;h=  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   h'A #Yp0,  
%energy in waveguide 3 wodff_l  
for m3 = 1:1:M3                                    % Start space evolution MUp{2_RA  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Gdlx0i  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6)9X+U@  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Y IVN;:B.  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform wQX%*GbL2  
   sca2 = fftshift(fft(s2)); *w1R>  
   sca3 = fftshift(fft(s3)); s?&UFyYb,  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   )eBCO~HS  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); )(`,!s,8)  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); !(qaudX{>k  
   s3 = ifft(fftshift(sc3)); =UFmN"  
   s2 = ifft(fftshift(sc2));                       % Return to physical space /x&52~X5-  
   s1 = ifft(fftshift(sc1)); R?l={N=Wf  
end 0EUC8Ni  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); yzz(<s:o/  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); s=)1:jYk  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); @.
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   P1=[P1 p1/p10]; 2tdr1+U?g  
   P2=[P2 p2/p10]; X6o iOs  
   P3=[P3 p3/p10]; T28Q(\C:}  
   P=[P p*p]; ](^BQc  
end .4,l0Nn`W  
figure(1) gOn^}%4.I  
plot(P,P1, P,P2, P,P3); ~`VD}{[,B  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~