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tianmen 2011-06-12 18:33

求解光孤子或超短脉冲耦合方程的Matlab程序

计算脉冲在非线性耦合器中演化的Matlab 程序 :OvTZ ?\  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of (jB_uMuS  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of qGPIKu  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear FW7@7cVoF  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *^b<CZd9  
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%fid=fopen('e21.dat','w'); &fu J%  
N = 128;                       % Number of Fourier modes (Time domain sampling points) vynchZ+g]  
M1 =3000;              % Total number of space steps Oe:_B/l  
J =100;                % Steps between output of space [j^c&}0  
T =10;                  % length of time windows:T*T0 `L1lGlt  
T0=0.1;                 % input pulse width ( [m[<  
MN1=0;                 % initial value for the space output location M<"H1>q@  
dt = T/N;                      % time step !>Ru= $9  
n = [-N/2:1:N/2-1]';           % Index /6Vn WrN_  
t = n.*dt;   ra*(.<&  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 +`H{  
u20=u10.*0.0;                  % input to waveguide 2 %~A$cc  
u1=u10; u2=u20;                 D%NVqk|  
U1 = u1;   1ZK~i  
U2 = u2;                       % Compute initial condition; save it in U voAen&>!  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. -3 2?]LN}  
w=2*pi*n./T; z3X:.%  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T _onEXrM  
L=4;                           % length of evoluation to compare with S. Trillo's paper >4N=P0=  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Udbz;^(  
for m1 = 1:1:M1                                    % Start space evolution Kgw_c:/'  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS  %SSBXWP  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; f-b#F2I  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform loPBHoE3@H  
   ca2 = fftshift(fft(u2)); r=o\!sh[  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation P:8P>#L  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ehCZhi~  
   u2 = ifft(fftshift(c2));                        % Return to physical space 6*92I  
   u1 = ifft(fftshift(c1)); +GqV9x 8  
if rem(m1,J) == 0                                 % Save output every J steps. 7 ,![oY[  
    U1 = [U1 u1];                                  % put solutions in U array (#"iZv,  
    U2=[U2 u2]; jJfV_#'N'  
    MN1=[MN1 m1]; M~/R1\'&j  
    z1=dz*MN1';                                    % output location MH8Selnv  
  end _x ;fTW0  
end b=-LQkcZhK  
hg=abs(U1').*abs(U1');                             % for data write to excel qIIl,!&}A  
ha=[z1 hg];                                        % for data write to excel hz8Z)xjJ V  
t1=[0 t']; HECZZnM  
hh=[t1' ha'];                                      % for data write to excel file > l@ o\  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 9?xc3F2EBD  
figure(1) ^.f`6 6/  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;0!rq^JG  
figure(2) 82bOiN15  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn &InMI#0mV  
jdF~0#vH  
非线性超快脉冲耦合的数值方法的Matlab程序 pd1V8PZSG  
O)4P)KAO<  
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。   EhBYmc" &  
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 d^Jf(NE0Yo  
AX= 4{b'  
DY~zi  
qAF.i^  
%  This Matlab script file solves the nonlinear Schrodinger equations DE^@b+6  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of itg PG  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear - #ta/*TT:  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 mq(*4KFWJ2  
XtV=Gr8"  
C=1;                           l$s8O0-'T  
M1=120,                       % integer for amplitude %?7j Q  
M3=5000;                      % integer for length of coupler 9se ,c  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Qs^Rh F\d  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Td`0;R'<}c  
T =40;                        % length of time:T*T0. sP+ZE>7  
dt = T/N;                     % time step 3;h%mk KQ+  
n = [-N/2:1:N/2-1]';          % Index A]FjV~PB  
t = n.*dt;   ~e)`D nJ  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. gZ^NdDBO  
w=2*pi*n./T; ,X2CV INb}  
g1=-i*ww./2; %Z"I=;=nxI  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; l{7q(  
g3=-i*ww./2;  #)r  
P1=0; MJ )aY2  
P2=0; 9z:P#=Q:  
P3=1; iw$n*1M  
P=0; ua^gG3n0  
for m1=1:M1                 pd[?TyVK;  
p=0.032*m1;                %input amplitude 9Xu O\+z  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 *UJ&9rQ  
s1=s10; \Q5Jg  
s20=0.*s10;                %input in waveguide 2 r3hUa4^97  
s30=0.*s10;                %input in waveguide 3 j/FFxlFNL  
s2=s20; !P6\-.  
s3=s30; m R3km1T  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   b\U p(]  
%energy in waveguide 1 "[*W=6m0  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   (RL5L=,u  
%energy in waveguide 2 uH6QK\  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   k3 65.nc  
%energy in waveguide 3 16p$>a<6  
for m3 = 1:1:M3                                    % Start space evolution ;LBq!  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS whzV7RT  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; #_, l7q8U  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 22|a~"Z  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform V ?10O  
   sca2 = fftshift(fft(s2)); dh~+0FZ{A  
   sca3 = fftshift(fft(s3)); )T=cd   
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   "Zh6j)[o  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); f/r@9\x  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 4;*o}E  
   s3 = ifft(fftshift(sc3)); K'`N(WiL  
   s2 = ifft(fftshift(sc2));                       % Return to physical space M=57 d7  
   s1 = ifft(fftshift(sc1)); hY?x14m$3  
end c&+p{hH+  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); kc3dWWPe  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); -L&FguoVB  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); <V}^c/c!  
   P1=[P1 p1/p10]; 9K>$  
   P2=[P2 p2/p10]; O;N QJ$^bI  
   P3=[P3 p3/p10]; !;YmLJk;hN  
   P=[P p*p]; eQ}o;vJN  
end A&$oiLc  
figure(1) f2sv$#'  
plot(P,P1, P,P2, P,P3); l>i<J1  
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转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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