[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 $WS?/H0C  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 'BOMFp7c  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 2Mo oqJp  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'YTSakNJ}  
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%fid=fopen('e21.dat','w'); zi
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N = 128;                       % Number of Fourier modes (Time domain sampling points) J=sj+:GS  
M1 =3000;              % Total number of space steps NwbX]pDT  
J =100;                % Steps between output of space b[s=FH]#N  
T =10;                  % length of time windows:T*T0
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T0=0.1;                 % input pulse width f5o##ia7:  
MN1=0;                 % initial value for the space output location &A!?:?3%O  
dt = T/N;                      % time step =jIP29+  
n = [-N/2:1:N/2-1]';           % Index G~nQR qv  
t = n.*dt;   *P0sl( &  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 fIwG9cR  
u20=u10.*0.0;                  % input to waveguide 2 jH~VjE>  
u1=u10; u2=u20;                 Ml
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U1 = u1;   {&,MkWgG  
U2 = u2;                       % Compute initial condition; save it in U V3v/hV:  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. >%1mx\y^  
w=2*pi*n./T; wx[Y2lUh6  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Zv&<r+<g  
L=4;                           % length of evoluation to compare with S. Trillo's paper 6TkV+\  
dz=L/M1;                       % space step, make sure nonlinear<0.05 _A]=45cn~  
for m1 = 1:1:M1                                    % Start space evolution gO%oA} !i  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Or<OmxJg  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; |B~^7RHXo  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform $3)Z>p  
   ca2 = fftshift(fft(u2)); :xy4JRcF  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 4RyQ^vL  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   O~DdM
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   u2 = ifft(fftshift(c2));                        % Return to physical space R8N*. [  
   u1 = ifft(fftshift(c1)); NSkIzaNY  
if rem(m1,J) == 0                                 % Save output every J steps. !}I+)@~
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    U1 = [U1 u1];                                  % put solutions in U array !si}m~K!_  
    U2=[U2 u2]; nv'YtmR  
    MN1=[MN1 m1]; V<ExR@|}.%  
    z1=dz*MN1';                                    % output location EAZLo;  
  end C2(VYw  
end O0RV>Ml'&  
hg=abs(U1').*abs(U1');                             % for data write to excel \9N )71n(  
ha=[z1 hg];                                        % for data write to excel m4x8W2q  
t1=[0 t']; `PS^o#  
hh=[t1' ha'];                                      % for data write to excel file Hkzx(yTi  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format D&*'|}RZ  
figure(1) zTS P8Q7  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn -F`uz,wZ  
figure(2) s~>0<3{5  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn (,^jgv|I  
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非线性超快脉冲耦合的数值方法的Matlab程序 7 V3r!y  
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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。   /vNHb_-  
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 Aq;WQyZ2  
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%  This Matlab script file solves the nonlinear Schrodinger equations J. $U_k  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 8>AS
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ^{g('BQx  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 v
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C=1;                            [yx8?5  
M1=120,                       % integer for amplitude pE381Cw  
M3=5000;                      % integer for length of coupler GZzBATx  
N = 512;                      % Number of Fourier modes (Time domain sampling points) QE4TvnhK  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. wu~?P`  
T =40;                        % length of time:T*T0. 3A!Qu$r9  
dt = T/N;                     % time step ypLt6(1j%  
n = [-N/2:1:N/2-1]';          % Index =`E{QCW  
t = n.*dt;   ;5&=I|xqe  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. "@(Sw>*o  
w=2*pi*n./T; b*TQKYT  
g1=-i*ww./2; ('1]f?:M  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; $0&<Jx  
g3=-i*ww./2; 9a$ 7$4m  
P1=0; 9o+e3TXp#  
P2=0; "U|u-ka8B  
P3=1; ukc<yc].+?  
P=0; `=P=
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for m1=1:M1                 o:PdPuZVR  
p=0.032*m1;                %input amplitude 6
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 a\*_b2 ^n  
s1=s10; h@j
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s20=0.*s10;                %input in waveguide 2 B\\M%!a>  
s30=0.*s10;                %input in waveguide 3 Qb#iT}!p%  
s2=s20; tQ,3nI!|xF  
s3=s30; q);@iiJ-  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   bkS-[rW  
%energy in waveguide 1 -Ra-Ux  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   v~:'t\n  
%energy in waveguide 2 <2t%<
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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))));   $Gs|Z$(  
%energy in waveguide 3 +wGFJLHJ  
for m3 = 1:1:M3                                    % Start space evolution Bmv5yc+;  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS NeR1}W  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @y8) "m"  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ~;vt{pk  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform kE854Ej  
   sca2 = fftshift(fft(s2)); ,:xses*7  
   sca3 = fftshift(fft(s3)); k-I
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   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   =3|5=ZU034  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); #Q/xQ`+|.  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); YQ`88z  
   s3 = ifft(fftshift(sc3)); >!PCEw<i  
   s2 = ifft(fftshift(sc2));                       % Return to physical space r#NR3_@9  
   s1 = ifft(fftshift(sc1)); B3W2?5p  
end D-Q54"^3  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); IHwoG(A~<  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); .#LvvAeh  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4VP$,|a  
   P1=[P1 p1/p10]; r#B{j$Rw   
   P2=[P2 p2/p10]; u-R;rf5%k  
   P3=[P3 p3/p10]; ]SUW"5L-  
   P=[P p*p]; s&M#]8x;x  
end juB/?'$~  
figure(1) _-z;  
plot(P,P1, P,P2, P,P3); "c
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~