[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 w[XW>4xK  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 4dO>L"  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of eUl[gHP  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^,3 >}PU  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 IKt9=Tx  
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%fid=fopen('e21.dat','w'); =o {`vv  
N = 128;                       % Number of Fourier modes (Time domain sampling points) "3K0 wR5  
M1 =3000;              % Total number of space steps F~:5/-zs  
J =100;                % Steps between output of space &8N\ 6K=  
T =10;                  % length of time windows:T*T0 :?,&u,8  
T0=0.1;                 % input pulse width ,F1$Of/'@\  
MN1=0;                 % initial value for the space output location `JC!uc  
dt = T/N;                      % time step WJ%b9{<  
n = [-N/2:1:N/2-1]';           % Index N4Ym[l  
t = n.*dt;   -Bc.<pFqp  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 [4gv_g  
u20=u10.*0.0;                  % input to waveguide 2 9X-DR  
u1=u10; u2=u20;                 _T1e##Sq,  
U1 = u1;   T@L
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U2 = u2;                       % Compute initial condition; save it in U Sdn] f4  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. :=/DF  
w=2*pi*n./T; ~=71){4A  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T `hbM2cM  
L=4;                           % length of evoluation to compare with S. Trillo's paper U|>Js!$  
dz=L/M1;                       % space step, make sure nonlinear<0.05 W uQdz&s>  
for m1 = 1:1:M1                                    % Start space evolution _*+M'3&=  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Xd4~N:  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; tlW}lN}  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform uJ%ql5XDV  
   ca2 = fftshift(fft(u2)); }"szL=s  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation >uVG]  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift    d00r&Mc  
   u2 = ifft(fftshift(c2));                        % Return to physical space u+]zi"k^s  
   u1 = ifft(fftshift(c1)); , vR4x:W  
if rem(m1,J) == 0                                 % Save output every J steps. Aam2Y,B  
    U1 = [U1 u1];                                  % put solutions in U array M|\XFO  
    U2=[U2 u2]; y
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    MN1=[MN1 m1]; {BF
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    z1=dz*MN1';                                    % output location <fP|<>s$@1  
  end =lzjMRX(?  
end %rf<YZ.\  
hg=abs(U1').*abs(U1');                             % for data write to excel 7 `|-
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ha=[z1 hg];                                        % for data write to excel a+Z/=YUR  
t1=[0 t']; H.YntFtD'  
hh=[t1' ha'];                                      % for data write to excel file s}5;)>3~@  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format gG#M-2P  
figure(1) kw!! 5U;7  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Tfj%Sb,zM  
figure(2)
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn qLcs)&}/A  
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非线性超快脉冲耦合的数值方法的Matlab程序 ,Q^.SHP8  
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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。   -?j'<g0  
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 l{kum2DT  
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%  This Matlab script file solves the nonlinear Schrodinger equations d^w6_  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of BYRf MtT@+  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear P#iBwmwN+.  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^W;\faG  
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C=1;                           oh|Q&R  
M1=120,                       % integer for amplitude %
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M3=5000;                      % integer for length of coupler <"6}C)G  
N = 512;                      % Number of Fourier modes (Time domain sampling points) e~xN[Q\0]  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 6?r}bs6Msx  
T =40;                        % length of time:T*T0. &S/KR$^ %  
dt = T/N;                     % time step h^cM#L^B  
n = [-N/2:1:N/2-1]';          % Index "HlT-0F  
t = n.*dt;   ]5wc8Kh"  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. $)6y:t"  
w=2*pi*n./T; usU5q>1  
g1=-i*ww./2; l1nrJm8  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; jruwdm^  
g3=-i*ww./2; WS4J
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P1=0; !ouJ3Jn   
P2=0; ht)J#Di  
P3=1; Ub3^Js!b%  
P=0; uvi+#4~G  
for m1=1:M1                 ApR
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p=0.032*m1;                %input amplitude .O
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 4 1q|R[js!  
s1=s10; lx(kbSxF  
s20=0.*s10;                %input in waveguide 2 ("?V
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s30=0.*s10;                %input in waveguide 3 PCtf&U  
s2=s20; cJ=0zEv  
s3=s30; 4;=+qb  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   qi!+Ceo}  
%energy in waveguide 1 #L ffmS  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   WTbq)D(&[_  
%energy in waveguide 2 <<4U:  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8(]*J8/wt  
%energy in waveguide 3 22$M6Qof]n  
for m3 = 1:1:M3                                    % Start space evolution p%[/ _ -7  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS $9bLD >.  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; fgdqp8~  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; GUSEbIz):  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform vq=nG]cE)  
   sca2 = fftshift(fft(s2)); /6
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   sca3 = fftshift(fft(s3)); GKIO@!@[  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   m7!Mstu  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3RJsH:u8  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); vnc-W3N  
   s3 = ifft(fftshift(sc3)); ^Y,nv,gYn  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 7Ji|x{``  
   s1 = ifft(fftshift(sc1)); 2!QQypQ  
end O%}?DiSl  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); t>Lq "]1  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); (ZSd7qH"  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ip8%9fG\>  
   P1=[P1 p1/p10]; bf@H(gCW=  
   P2=[P2 p2/p10]; t\S=u y  
   P3=[P3 p3/p10]; %?2y2O,;  
   P=[P p*p]; gjFpM.D-.  
end iC2``[m"  
figure(1) 4 ))ZBq?  
plot(P,P1, P,P2, P,P3); []OmztB  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~