[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 GB0] |z5  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of !!9V0[  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of x`$4  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear E0YXgQa  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 M/BBNT  
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%fid=fopen('e21.dat','w'); PffRV7qU0  
N = 128;                       % Number of Fourier modes (Time domain sampling points) #JVcl $0Y  
M1 =3000;              % Total number of space steps yCwQ0|  
J =100;                % Steps between output of space I)6)~[:'  
T =10;                  % length of time windows:T*T0 JI.ad_IR
 
T0=0.1;                 % input pulse width GDk/85cv0$  
MN1=0;                 % initial value for the space output location lGxG$0`;;  
dt = T/N;                      % time step s3q65%D  
n = [-N/2:1:N/2-1]';           % Index [;c#LJ/y  
t = n.*dt;   Ls9G:>'rR  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 qh=lF_%uj  
u20=u10.*0.0;                  % input to waveguide 2 ZI1[jM{4^F  
u1=u10; u2=u20;                 $v+g3+7  
U1 = u1;   es.`:^
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U2 = u2;                       % Compute initial condition; save it in U C; ! )<(Vw  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ]R0^ }sI  
w=2*pi*n./T; R!:1{1  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T :
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L=4;                           % length of evoluation to compare with S. Trillo's paper C6GYhG]  
dz=L/M1;                       % space step, make sure nonlinear<0.05 /q8n_NR  
for m1 = 1:1:M1                                    % Start space evolution 2Ddrxc>48  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS srUpG&Bcx  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; <#:"v
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform k)4   
   ca2 = fftshift(fft(u2)); qUCiB}  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation <MY_
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   gCd9"n-e  
   u2 = ifft(fftshift(c2));                        % Return to physical space GMFp,Df  
   u1 = ifft(fftshift(c1)); y>|7'M
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if rem(m1,J) == 0                                 % Save output every J steps. R:11w#m7w  
    U1 = [U1 u1];                                  % put solutions in U array D>05F,a  
    U2=[U2 u2]; UeE&rA]  
    MN1=[MN1 m1]; )PZ'{S  
    z1=dz*MN1';                                    % output location 'H+pwp"M@  
  end f ^z7K  
end O0wD"V^W  
hg=abs(U1').*abs(U1');                             % for data write to excel (G:$/fK  
ha=[z1 hg];                                        % for data write to excel ceAK;v o  
t1=[0 t']; kpEES{f  
hh=[t1' ha'];                                      % for data write to excel file Aj-}G^>#  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format X=-pNwO   
figure(1) \3x,)~m  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn +,If|5>(  
figure(2) 'H:lR1(,  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Z?X ^7<  
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非线性超快脉冲耦合的数值方法的Matlab程序 K" Y,K  
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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。   &%rXRP  
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 +\SbrB P  
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%  This Matlab script file solves the nonlinear Schrodinger equations qd"*Td  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of tPc'#.  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Bm1yBKjO  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 KD=T04v  
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C=1;                           x-Yt@}6mvl  
M1=120,                       % integer for amplitude Jt@7y"<  
M3=5000;                      % integer for length of coupler zAS&L%^tV  
N = 512;                      % Number of Fourier modes (Time domain sampling points) jO3Z2/#  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. DtR-NzjB  
T =40;                        % length of time:T*T0. 's+ Fd~'  
dt = T/N;                     % time step :U^a0s%B  
n = [-N/2:1:N/2-1]';          % Index t: r   
t = n.*dt;   Lr_+)l  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. RR*<txdN  
w=2*pi*n./T; c(i-~_  
g1=-i*ww./2; ZI-)'  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; lhKd<Y"  
g3=-i*ww./2; >DpnIWn  
P1=0; e=QnGT*b5  
P2=0; UIIR$,XB  
P3=1; oe# :EfT  
P=0; Fn yA;,*  
for m1=1:M1                 % =br-c  
p=0.032*m1;                %input amplitude _z#zF[%  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 AS'a'x>8>,  
s1=s10; x/R|i%u-s  
s20=0.*s10;                %input in waveguide 2 8it|yK.G@&  
s30=0.*s10;                %input in waveguide 3 qJKD|=_  
s2=s20; P1
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s3=s30; Cir==7A0  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   8S&`  
%energy in waveguide 1 mN!>BqvN  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   <$K%u?  
%energy in waveguide 2 1B}6 zJ  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   &S]\)&Yt  
%energy in waveguide 3 A !x"*  
for m3 = 1:1:M3                                    % Start space evolution eOE7A'X  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS A!x_R {,yH  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; %DbL|;z1  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; >x eKO2o  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform TY],H=  
   sca2 = fftshift(fft(s2)); ?S36)oZzg  
   sca3 = fftshift(fft(s3)); gQCkoQi:j  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   cL7je  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); uL1e
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   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 3W5|Y@0  
   s3 = ifft(fftshift(sc3)); pdngM8n  
   s2 = ifft(fftshift(sc2));                       % Return to physical space b(&2/|hd
 
   s1 = ifft(fftshift(sc1)); j_H{_Ug  
end { %vX/Ek  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ~6Vs>E4G  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); (&=-o(  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); P*BA  
   P1=[P1 p1/p10]; 5rr7lwWZ  
   P2=[P2 p2/p10]; ]3BTL7r  
   P3=[P3 p3/p10]; =hH>]$J[  
   P=[P p*p]; y4tM0h  
end ;^^u_SuH  
figure(1) ={o>g'  
plot(P,P1, P,P2, P,P3); J$%mG*Y(  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~