[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 `62iW3y  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of j1sZRl)D  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of LKx<hl$O  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear b-Q%cxJ  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FkS$x'~2$  
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%fid=fopen('e21.dat','w'); F6vN{FI  
N = 128;                       % Number of Fourier modes (Time domain sampling points) $!Pm*s  
M1 =3000;              % Total number of space steps L]_1z  
J =100;                % Steps between output of space T`?{Is['(  
T =10;                  % length of time windows:T*T0 |;[%ZE"  
T0=0.1;                 % input pulse width =D@+_7\?  
MN1=0;                 % initial value for the space output location XLeQxp=  
dt = T/N;                      % time step s>VpbJ3S  
n = [-N/2:1:N/2-1]';           % Index n!Dy-)!`O  
t = n.*dt;   a#_=c>h;  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ap7Z
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u20=u10.*0.0;                  % input to waveguide 2 ~53uUT|B  
u1=u10; u2=u20;                 SBNeN]  
U1 = u1;   D^Cpgha  
U2 = u2;                       % Compute initial condition; save it in U 2L!wbeTb;  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. [ BpZ{Ql  
w=2*pi*n./T; Xc!0'P0T  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T aJmSagr69C  
L=4;                           % length of evoluation to compare with S. Trillo's paper $XOs(>~"r  
dz=L/M1;                       % space step, make sure nonlinear<0.05 !i`HjV0wS  
for m1 = 1:1:M1                                    % Start space evolution \*(A1Vk  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 1_aUU,|.  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; $}*bZ~  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ?)#qBE ]  
   ca2 = fftshift(fft(u2)); !pwY@}oL  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation =gYKAr^p5  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   C(Bh<
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   u2 = ifft(fftshift(c2));                        % Return to physical space 7 B<  
   u1 = ifft(fftshift(c1)); }K8W%h
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if rem(m1,J) == 0                                 % Save output every J steps. i 1{Lx)  
    U1 = [U1 u1];                                  % put solutions in U array &:3uK`  
    U2=[U2 u2]; )e1&[0  
    MN1=[MN1 m1]; ]V4Fm{]  
    z1=dz*MN1';                                    % output location $0f(Gc|  
  end |lnMT)^D  
end [nx OGa2  
hg=abs(U1').*abs(U1');                             % for data write to excel "Q>gQKgL  
ha=[z1 hg];                                        % for data write to excel )Td;2  
t1=[0 t']; &m8#^]*  
hh=[t1' ha'];                                      % for data write to excel file PqhR^re0.  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format YoT<]'  
figure(1) )$.::[pNA  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6w )mo)<X  
figure(2) ^E)*i#."4  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^ |xSU_wa  
19r4J(pV  
非线性超快脉冲耦合的数值方法的Matlab程序 5\?\|*WT  
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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。   &"h 9Awn2  
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 ^~iFG+g5  
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%  This Matlab script file solves the nonlinear Schrodinger equations `[&) X  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ]WO0v`xh  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }u>F}mUa  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 P Tc@MH)  
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C=1;                           YM:;mX5B  
M1=120,                       % integer for amplitude gq'}LcV  
M3=5000;                      % integer for length of coupler *i=+["A  
N = 512;                      % Number of Fourier modes (Time domain sampling points) U)P
NY  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. S~ff<A>f  
T =40;                        % length of time:T*T0. &$,%6X"  
dt = T/N;                     % time step ?bq S{KF  
n = [-N/2:1:N/2-1]';          % Index !bPsJbIo>  
t = n.*dt;   {#Lj,o  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. \h#,qTE  
w=2*pi*n./T; /F(wb_!  
g1=-i*ww./2; #TXN\YNP  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 1&Fty'p  
g3=-i*ww./2; n{b(~eL?  
P1=0; 5 aT>8@$Z^  
P2=0; {DI
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P3=1; "<
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P=0; Ez= Q{g  
for m1=1:M1                 JB_<Haj  
p=0.032*m1;                %input amplitude /^F_~.u{  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 T~238C{vh  
s1=s10; "M GX(SQ  
s20=0.*s10;                %input in waveguide 2 )t$<FP  
s30=0.*s10;                %input in waveguide 3 :3uCW1  
s2=s20; nO^m  
s3=s30; w;=fi}<G|e  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   iq25|{1$  
%energy in waveguide 1 8Moe8X#3  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   h6yXW!8  
%energy in waveguide 2 
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   #dvH0LX?  
%energy in waveguide 3 7lC );  
for m3 = 1:1:M3                                    % Start space evolution /uh?F  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS L7gZ4Hu=`  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; !zu YO3:  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 015 ;'V#we  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform )@IDmz>  
   sca2 = fftshift(fft(s2)); xbN)
z  
   sca3 = fftshift(fft(s3)); sULCYiT|Hn  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   4;rt|X77  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); FnoE\2}9  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); sQ)D.9\~  
   s3 = ifft(fftshift(sc3)); i42M.M6D$  
   s2 = ifft(fftshift(sc2));                       % Return to physical space J'Z!`R|  
   s1 = ifft(fftshift(sc1)); jGeil qPC  
end z]^u@]@NC  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); g
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); CQ4MQ<BJ.  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); (}1:]D{)@V  
   P1=[P1 p1/p10]; ]uikE2nn  
   P2=[P2 p2/p10]; }!&Vcf  
   P3=[P3 p3/p10]; \$g,Hgp/<  
   P=[P p*p]; PNSV?RT*pG  
end q&:UP  
figure(1) z'W8t|m}Pb  
plot(P,P1, P,P2, P,P3); q_hkI]  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~