[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 OW@"j;6 3`  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of gm=C0Sp?  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of yeBfzKI{b  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ZS=
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]6s/y  

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%fid=fopen('e21.dat','w'); hJ8%r_  
N = 128;                       % Number of Fourier modes (Time domain sampling points) eVB43]g  
M1 =3000;              % Total number of space steps F!Cn'*  
J =100;                % Steps between output of space T 1_B0H2  
T =10;                  % length of time windows:T*T0 hl] y):  
T0=0.1;                 % input pulse width oiC@
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MN1=0;                 % initial value for the space output location y?A*$6  
dt = T/N;                      % time step
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n = [-N/2:1:N/2-1]';           % Index qR_Np5nHF  
t = n.*dt;  
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 z`I%3U5(  
u20=u10.*0.0;                  % input to waveguide 2 <|]i3_Z  
u1=u10; u2=u20;                 b?VByJl  
U1 = u1;   mAY/J0_  
U2 = u2;                       % Compute initial condition; save it in U pGF;,h>  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. jTZi< Y:bB  
w=2*pi*n./T; g1_z=(i`Z  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #<U@SMv  
L=4;                           % length of evoluation to compare with S. Trillo's paper [O|c3;  
dz=L/M1;                       % space step, make sure nonlinear<0.05 *uP;rUY  
for m1 = 1:1:M1                                    % Start space evolution fe"w--v  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Da!vGr  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 1zw,;m n  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 0pl'*r*9  
   ca2 = fftshift(fft(u2));
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation /u`Opv&I
 
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ( ]0F3@k#s  
   u2 = ifft(fftshift(c2));                        % Return to physical space ' V*}d  
   u1 = ifft(fftshift(c1)); w5rtYTI  
if rem(m1,J) == 0                                 % Save output every J steps. lUp%1x+  
    U1 = [U1 u1];                                  % put solutions in U array KK]R@{ r  
    U2=[U2 u2]; $sZ4r>-  
    MN1=[MN1 m1]; g 4|ai*^  
    z1=dz*MN1';                                    % output location =|dm#w_L"  
  end AE`UnlUSF  
end Ux{QYjFE  
hg=abs(U1').*abs(U1');                             % for data write to excel 4>fj@X(3  
ha=[z1 hg];                                        % for data write to excel (~! @Uz5  
t1=[0 t']; 6 b?K-)kL  
hh=[t1' ha'];                                      % for data write to excel file T+rym8.p  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format nD>X?yz2  
figure(1) k`]76C7  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn zlTLp-^Y  
figure(2) N~or
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 20}]b*C}  
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非线性超快脉冲耦合的数值方法的Matlab程序 'O9Yu{M  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   _ Qek|>  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Z0D&ayzkh^  
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%  This Matlab script file solves the nonlinear Schrodinger equations q$IU!I4  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of NNTrH\SU#  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear SrOv* D3  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 JHVndK4L  
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C=1;                           #BS!J&a  
M1=120,                       % integer for amplitude z&um9rXR  
M3=5000;                      % integer for length of coupler eecIF0hp  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ;ByCtVm2  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ?qn4ea-\P  
T =40;                        % length of time:T*T0. e%{7CR'~TD  
dt = T/N;                     % time step P9Eh,
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n = [-N/2:1:N/2-1]';          % Index S"
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t = n.*dt;   ;i+(Q%LO  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.  :J)^gc  
w=2*pi*n./T; t*6C?zEAU  
g1=-i*ww./2; 0tMzVxS  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ^{++h?cS)  
g3=-i*ww./2; //Xz  
P1=0; qEdY]t   
P2=0; F^TOLwix  
P3=1; P>x88M  
P=0; K
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for m1=1:M1                 YxA nh  
p=0.032*m1;                %input amplitude P/]8+_K  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 BP4vOZ0$  
s1=s10; C)9-{Yp  
s20=0.*s10;                %input in waveguide 2 a<+Rw{  
s30=0.*s10;                %input in waveguide 3 5`
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s2=s20; ,c;#~y  
s3=s30; 6G-XZko~a  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   U^-J_yq  
%energy in waveguide 1 @OHNz!Lj:d  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   B8upv~U6  
%energy in waveguide 2 y6s/S.  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "[Tr"nI  
%energy in waveguide 3 : B1 "=ly  
for m3 = 1:1:M3                                    % Start space evolution \(5Bi3PA}  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 8@T0]vH&  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; F1
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   sca1 = fftshift(fft(s1));                       % Take Fourier transform =aehhs>  
   sca2 = fftshift(fft(s2)); PM {L}tEQ  
   sca3 = fftshift(fft(s3)); ~ r$I&8  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   qrt2uE{K  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 2fPMZ7Zd3  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 15DlD`QV  
   s3 = ifft(fftshift(sc3)); o i~,}E_  
   s2 = ifft(fftshift(sc2));                       % Return to physical space $ WWi2cI;  
   s1 = ifft(fftshift(sc1)); [F
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end z:{R4#(Q  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); -**fT?n  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ?C6`  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); h 'is#X 6:  
   P1=[P1 p1/p10]; O9p^P%U"  
   P2=[P2 p2/p10]; H"2,Q T  
   P3=[P3 p3/p10]; >v%UV:7ap  
   P=[P p*p]; EVbDI yFn  
end a$6pA@7}  
figure(1) /J,&G: Er  
plot(P,P1, P,P2, P,P3); m :]F&s  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~