[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 ;Uy}(  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of m6gMVon  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 5as5{"l  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear GR 1%(,  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 wuSotbc/  
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%fid=fopen('e21.dat','w'); ~JS@$#  
N = 128;                       % Number of Fourier modes (Time domain sampling points) }-9 c1&m  
M1 =3000;              % Total number of space steps VAqZ`y  
J =100;                % Steps between output of space 4#ikdjB;  
T =10;                  % length of time windows:T*T0 Z=a~0&G  
T0=0.1;                 % input pulse width TWfkr  
MN1=0;                 % initial value for the space output location ,,ML^ey  
dt = T/N;                      % time step g{K
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n = [-N/2:1:N/2-1]';           % Index WQBV~.<Yv  
t = n.*dt;   /`y^z"!  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 KUHkjA_  
u20=u10.*0.0;                  % input to waveguide 2 8{6`?qst@  
u1=u10; u2=u20;                 W
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U1 = u1;   [N"=rY4G  
U2 = u2;                       % Compute initial condition; save it in U !>GDp>0  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. BD]o+96qP  
w=2*pi*n./T; {V8uk
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g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 3l$D%y  
L=4;                           % length of evoluation to compare with S. Trillo's paper > -(Zx  
dz=L/M1;                       % space step, make sure nonlinear<0.05 }I18|=TB  
for m1 = 1:1:M1                                    % Start space evolution l=#b7rBP  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS E, oR.B  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ^_W] @m2  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ,F "P/`i'  
   ca2 = fftshift(fft(u2)); ##Qy6Dc  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation :H:+XIgoR  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   >q ,Z*s>?  
   u2 = ifft(fftshift(c2));                        % Return to physical space &(|Ot`el]v  
   u1 = ifft(fftshift(c1)); h&~9?B  
if rem(m1,J) == 0                                 % Save output every J steps. ~b4kV)[ q  
    U1 = [U1 u1];                                  % put solutions in U array ocpM6b.fK  
    U2=[U2 u2]; '#Do( U'  
    MN1=[MN1 m1]; C+dz0u3s  
    z1=dz*MN1';                                    % output location 5FsfJpw  
  end jc,Qg2  
end k3
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hg=abs(U1').*abs(U1');                             % for data write to excel us.IdG  
ha=[z1 hg];                                        % for data write to excel 19%zcYTe  
t1=[0 t']; ~w.y9)",  
hh=[t1' ha'];                                      % for data write to excel file Xc~BHEp  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format !:}m-iqQ1  
figure(1) bh3yH>Zns  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn SN[ar&I  
figure(2) TJZarNc$  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn HC6v#-( `{  
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非线性超快脉冲耦合的数值方法的Matlab程序 Zvr
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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。   $0+&xJVn  
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 {Eqx'j  
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%  This Matlab script file solves the nonlinear Schrodinger equations _3#_6>=M  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of bik lja  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear $ % B  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 cxx8I  
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C=1;                           6^2='y~e  
M1=120,                       % integer for amplitude |Nadk(}  
M3=5000;                      % integer for length of coupler BH}M]<5  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ~&"'>C#  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. $Yw~v36`t/  
T =40;                        % length of time:T*T0. VA %lJ!$  
dt = T/N;                     % time step ZoCk]hk  
n = [-N/2:1:N/2-1]';          % Index aN!,\D  
t = n.*dt;   NSq29#  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. lwjA07i  
w=2*pi*n./T; 9hJ  a K  
g1=-i*ww./2; =F5zU5`i  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; /_yAd,^-+  
g3=-i*ww./2; k?1e+ \  
P1=0; -<e_^  
P2=0; 8m#y>`  
P3=1; 90ov[|MkM  
P=0; }%^3  
for m1=1:M1                 ^),;`YXZ  
p=0.032*m1;                %input amplitude ~B7<Yg  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Gh<#wa['}  
s1=s10; qca=a}  
s20=0.*s10;                %input in waveguide 2 4H{$zMq8  
s30=0.*s10;                %input in waveguide 3 8N3rYx;d~  
s2=s20; d ]#`?}  
s3=s30; Bw9
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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))));   ;1>V7+/  
%energy in waveguide 1 st>%U9  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   g!)*CP#;  
%energy in waveguide 2 iP1yy5T  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   =c%gV]>G  
%energy in waveguide 3 Zv9%}%7p  
for m3 = 1:1:M3                                    % Start space evolution x&$8;2&.  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 7y$U$6  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; -$,'|\Y  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; i?|u$[^=+  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Or55_E  
   sca2 = fftshift(fft(s2)); p[;@9!t  
   sca3 = fftshift(fft(s3)); >4Qj+ou  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   =4OV }z=I  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Y^XZ.R  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); NFf`V  
   s3 = ifft(fftshift(sc3)); tg9{(_t/W  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ):n'B` f}z  
   s1 = ifft(fftshift(sc1)); _,f7D/dq  
end nB}eJD|  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); _T;Kn'Gz(&  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); A-h[vP!v|  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); +,)Iv_Xl$  
   P1=[P1 p1/p10]; D4?cnwU  
   P2=[P2 p2/p10]; K 28s<i`  
   P3=[P3 p3/p10]; 
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   P=[P p*p]; Ql,WKoj*  
end *q@3yB}  
figure(1) OU*skc>  
plot(P,P1, P,P2, P,P3); U}l=1B  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~