[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 P)h
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 5C03)Go3Z  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of :n1^Xw0q  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear LyEM^d]  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^|h5*Tb  
}3G`f> s  
%fid=fopen('e21.dat','w'); -ahSFBZlg  
N = 128;                       % Number of Fourier modes (Time domain sampling points) fSe$
w#*I  
M1 =3000;              % Total number of space steps MMyVm"w  
J =100;                % Steps between output of space
%t*_Rtz\o  
T =10;                  % length of time windows:T*T0 u`%Kh_  
T0=0.1;                 % input pulse width (}$pf6s  
MN1=0;                 % initial value for the space output location *2K/)(  
dt = T/N;                      % time step ]u;Ma G=;  
n = [-N/2:1:N/2-1]';           % Index vr/O%mD
p  
t = n.*dt;   RyI(6TZl  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 X\?PnD`,  
u20=u10.*0.0;                  % input to waveguide 2 $:{r#mM  
u1=u10; u2=u20;                 {'.[N79xP  
U1 = u1;   Ch3{q/-g  
U2 = u2;                       % Compute initial condition; save it in U ?CaMn b8  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ^/K]id7 2  
w=2*pi*n./T; FXpI-?#E<  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Ro&s\T+d  
L=4;                           % length of evoluation to compare with S. Trillo's paper 5xHP5+&  
dz=L/M1;                       % space step, make sure nonlinear<0.05 h.A@o#x  
for m1 = 1:1:M1                                    % Start space evolution jRk"#:  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 3ID1>  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; (?9@nS  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 'p%\fb6`  
   ca2 = fftshift(fft(u2)); 9-Y.8:A`  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ;IN!H@bq  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   =5a|'O  
   u2 = ifft(fftshift(c2));                        % Return to physical space DEdJH4  
   u1 = ifft(fftshift(c1)); 3#=%2\  
if rem(m1,J) == 0                                 % Save output every J steps. lT`y=qR|  
    U1 = [U1 u1];                                  % put solutions in U array |.OXe!uU41  
    U2=[U2 u2]; ("G _{tVU  
    MN1=[MN1 m1]; 8uj;RG  
    z1=dz*MN1';                                    % output location 0QWc1L  
  end &, =Z  
end k&|#(1CFY  
hg=abs(U1').*abs(U1');                             % for data write to excel ?3f-"K_r  
ha=[z1 hg];                                        % for data write to excel OKXELP  
t1=[0 t']; T^"-;  
hh=[t1' ha'];                                      % for data write to excel file Yy,i,c`r  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format kOu C@~,  
figure(1) %OI4}!z@l  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn *%[L @WF  
figure(2) s)gUvS\  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn G*oqhep  
nUp, %z[  
非线性超快脉冲耦合的数值方法的Matlab程序 j %3wD2 l  
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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。   B+8lp4V9%  
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 OMl<=;^:|  
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%  This Matlab script file solves the nonlinear Schrodinger equations 2 Nr*  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of IB'gY0*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear E41ay:duAl  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 iSiez'  
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C=1;                           <Mt>v2a3Y  
M1=120,                       % integer for amplitude !=-{$& {  
M3=5000;                      % integer for length of coupler ;ui=7[Us  
N = 512;                      % Number of Fourier modes (Time domain sampling points) /t4#-vz  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ZxDh94w/  
T =40;                        % length of time:T*T0. X(YR).a~  
dt = T/N;                     % time step lhp.zl  
n = [-N/2:1:N/2-1]';          % Index ;J]
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t = n.*dt;   +!@@55I-  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. q_J)68BR  
w=2*pi*n./T; sI&|qK-(  
g1=-i*ww./2; AW6"1(D  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 3Z taj^v  
g3=-i*ww./2; d=*&=r0!C{  
P1=0; h;+bHrKji  
P2=0; x_X%|f  
P3=1; km 0LLYG  
P=0; wjRv=[  
for m1=1:M1                 [v,Y-}wQ)  
p=0.032*m1;                %input amplitude .huk>   
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 8<2 [ F  
s1=s10; w1N-`S:  
s20=0.*s10;                %input in waveguide 2 H N )@sLPc  
s30=0.*s10;                %input in waveguide 3 \DgWp:|  
s2=s20; cBGR%w\t%  
s3=s30; 0q!
  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   WxgA{q7:  
%energy in waveguide 1 t>Ot)d  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   E U# M.  
%energy in waveguide 2 GIs *;ps7w  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   DJ]GM|?  
%energy in waveguide 3 '1f:8  
for m3 = 1:1:M3                                    % Start space evolution n0T>sE-9  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS RaX:&PE  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; /XeCJxo8  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; O{Y_j&1  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform _d J"2rx  
   sca2 = fftshift(fft(s2)); GcHy`bQbiX  
   sca3 = fftshift(fft(s3)); r ?e''r  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   +{7/+Zz  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @D3|Ak1  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); asLvJ{d8s  
   s3 = ifft(fftshift(sc3)); /Y7YyjMi  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ]Av)N6$&-Z  
   s1 = ifft(fftshift(sc1)); #[<XNs!"  
end xDtJ&6uFw  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); V\=QAN^  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); V=+wsc  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); v;_k*y[VV$  
   P1=[P1 p1/p10]; BT3X7Cx  
   P2=[P2 p2/p10]; |PY*"Ul  
   P3=[P3 p3/p10]; :tTP3t5  
   P=[P p*p]; FTk`Mq  
end 920 o]Dh=t  
figure(1) 'xn3g;5  
plot(P,P1, P,P2, P,P3); `yXJaTbo  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~