[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 9XobTi3+'  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of YA{Kgc^  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of jqb,^T|j;m  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2/B(T5PY@  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 x9-K}s]%  
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%fid=fopen('e21.dat','w'); "9kEqz4a  
N = 128;                       % Number of Fourier modes (Time domain sampling points) KGP2,U6  
M1 =3000;              % Total number of space steps Yk?uxZ4)H  
J =100;                % Steps between output of space asPD>jc  
T =10;                  % length of time windows:T*T0 d 'x;]#S  
T0=0.1;                 % input pulse width "pMXTRb  
MN1=0;                 % initial value for the space output location 8Q#&=]W$  
dt = T/N;                      % time step uZ<Bfrc  
n = [-N/2:1:N/2-1]';           % Index >tib21*  
t = n.*dt;   +n2x@ 0op  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ,1^)JshZ~  
u20=u10.*0.0;                  % input to waveguide 2 WYEvW<Hv  
u1=u10; u2=u20;                 <XCH{Te1  
U1 = u1;   Y<a/(`  
U2 = u2;                       % Compute initial condition; save it in U FCqs'  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. mc!
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w=2*pi*n./T; 9Ki86  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T s_D7?o  
L=4;                           % length of evoluation to compare with S. Trillo's paper <KHB/7  
dz=L/M1;                       % space step, make sure nonlinear<0.05 {D`F$=Dlw  
for m1 = 1:1:M1                                    % Start space evolution GbB&kE3KP  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ~X`vRSrH  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; D=9x/ ) *G  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ELY$ ]^T  
   ca2 = fftshift(fft(u2)); P5] cEZ n  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation \f /<#'  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ~@itZ,d\  
   u2 = ifft(fftshift(c2));                        % Return to physical space ^B1vvb  
   u1 = ifft(fftshift(c1)); nqiy)ZN#R  
if rem(m1,J) == 0                                 % Save output every J steps. ~)oC+H@{  
    U1 = [U1 u1];                                  % put solutions in U array LoBKR c2t  
    U2=[U2 u2]; tC|5;'m.2  
    MN1=[MN1 m1]; IO v4Zx<)  
    z1=dz*MN1';                                    % output location %[Nef
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  end `pII-dSC%  
end LjxTRtB_  
hg=abs(U1').*abs(U1');                             % for data write to excel P d*}0a~  
ha=[z1 hg];                                        % for data write to excel 3bE^[V8/  
t1=[0 t']; "uZ'oN  
hh=[t1' ha'];                                      % for data write to excel file xu& v(C9  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 0qR;Z{k  
figure(1) l9P~,Ec4''  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 'e{e>>03  
figure(2) ;=B&t@  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn M}38uxP  
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非线性超快脉冲耦合的数值方法的Matlab程序 |6_<4lmTxF  
}=XL^a|V  
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。   XUW~8P  
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 ;]<$p[m  
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%  This Matlab script file solves the nonlinear Schrodinger equations ckhW?T>l  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of .>CqZN,^  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear U%w-/!p  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 < >f12pu  
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C=1;                           OaU$ [Z'8  
M1=120,                       % integer for amplitude 1*>a  
M3=5000;                      % integer for length of coupler nSd?P'PFg  
N = 512;                      % Number of Fourier modes (Time domain sampling points) &Hh%pY"  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. FA4bv9:hi  
T =40;                        % length of time:T*T0. (qB$I\  
dt = T/N;                     % time step 173/A=]  
n = [-N/2:1:N/2-1]';          % Index p1X lni%=  
t = n.*dt;   `$MO.K{  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. >@ge[MuS  
w=2*pi*n./T; <V>vDno\  
g1=-i*ww./2; d@] 0 =Ax  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; O-  r"G  
g3=-i*ww./2; 3~Ipcr B  
P1=0; b?H
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P2=0; 3n6_
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P3=1; =;@5Ue J  
P=0; 299; N  
for m1=1:M1                 <M+ZlF-`  
p=0.032*m1;                %input amplitude -Frx{3  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 tLV9b %i(  
s1=s10; x#Hq74H,  
s20=0.*s10;                %input in waveguide 2 T(3"bS.,  
s30=0.*s10;                %input in waveguide 3 ! daXF&q  
s2=s20; 7%)4cHZ^$?  
s3=s30; 6aMqU?-
 
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));  
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%energy in waveguide 1 `n5|4yaG~  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   JNX7]j\  
%energy in waveguide 2  D&N5)   
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   o?hya.;h4  
%energy in waveguide 3 DZLSn Ax  
for m3 = 1:1:M3                                    % Start space evolution !;iySRZr  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS DSET!F;PG  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; lBPZB%  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; cB?HMLbG>  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform e ~*qi&,4  
   sca2 = fftshift(fft(s2)); i:{a-Bd  
   sca3 = fftshift(fft(s3)); c9f~^}jNb  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   WERK JA  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); &XgB-}^:  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); pD`7N<F 3  
   s3 = ifft(fftshift(sc3)); ZH~m%sA  
   s2 = ifft(fftshift(sc2));                       % Return to physical space 5:56l>0  
   s1 = ifft(fftshift(sc1)); =@{H7z(p&  
end hc~--[1c:  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); hQl3F6-ud  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 9\Yj`,i
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 6,s@>8n  
   P1=[P1 p1/p10]; 2r[Q$GPM<  
   P2=[P2 p2/p10]; dos$d3B4  
   P3=[P3 p3/p10]; r=qb[4HiV  
   P=[P p*p]; f]o DZO%^  
end e2/&X;2  
figure(1) QLIm+)T  
plot(P,P1, P,P2, P,P3); 1Qf5H!5vx  
#sNa}292"  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~