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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 4|:{apH  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of H!45w;,I  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of SH`"o  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !J:DBtGT  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 LI nN-b#  
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%fid=fopen('e21.dat','w'); DF&C7+hO  
N = 128;                       % Number of Fourier modes (Time domain sampling points) txL5' mK  
M1 =3000;              % Total number of space steps Bj]0Cz  
J =100;                % Steps between output of space H=yD}!j  
T =10;                  % length of time windows:T*T0 1":{$A?OB  
T0=0.1;                 % input pulse width a)Wf* <B  
MN1=0;                 % initial value for the space output location g#70Sg*d  
dt = T/N;                      % time step `*N0 Lbl]  
n = [-N/2:1:N/2-1]';           % Index 4Y)3<=kDG  
t = n.*dt;   L)w& f  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 r/{VL3}F_e  
u20=u10.*0.0;                  % input to waveguide 2 A: @=?(lI3  
u1=u10; u2=u20;                 -D(Ubk Pw  
U1 = u1;   ?>AhC{  
U2 = u2;                       % Compute initial condition; save it in U I&(cdKY z  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. !'[sV^ ds  
w=2*pi*n./T; ]1Q\wsB  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T B2,! 0Re  
L=4;                           % length of evoluation to compare with S. Trillo's paper 8KAyif@1::  
dz=L/M1;                       % space step, make sure nonlinear<0.05 +h9CcBd  
for m1 = 1:1:M1                                    % Start space evolution ]X-ZRmB`  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS :))AZ7_  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 1DLQ Zq  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform \|T0@V  
   ca2 = fftshift(fft(u2)); Xbu >8d?n  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation c9'#G>&h~^  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   >2v_fw  
   u2 = ifft(fftshift(c2));                        % Return to physical space 6%yr>BFtVV  
   u1 = ifft(fftshift(c1)); 9(@bjL465  
if rem(m1,J) == 0                                 % Save output every J steps. WQ*$y3%  
    U1 = [U1 u1];                                  % put solutions in U array z_Qw's  
    U2=[U2 u2]; p@Qzg /X  
    MN1=[MN1 m1]; o0<T|zgF5,  
    z1=dz*MN1';                                    % output location dj]sr!q+  
  end ?]7ITF  
end I|`K;a  
hg=abs(U1').*abs(U1');                             % for data write to excel gbInSp`4  
ha=[z1 hg];                                        % for data write to excel =a {Z7W  
t1=[0 t']; cJhf{{_oR  
hh=[t1' ha'];                                      % for data write to excel file ^iI^)  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format OOv"h\,  
figure(1) {`3;Pd`  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn T}\U:@b  
figure(2) G;^iwxzhO  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn r^ "mPgY  
WUHx0I  
非线性超快脉冲耦合的数值方法的Matlab程序 P, Vq/Tt  
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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。   I5bi^!i  
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 6}|vfw  
hwXp=not(  
w6E?TI  
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%  This Matlab script file solves the nonlinear Schrodinger equations ]Wy V bIu  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of n@%'Nbc>b  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear / _cOg? o  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 HQE#O4  
:}GxJT4  
C=1;                           Q \{\u J x  
M1=120,                       % integer for amplitude "qDEI}  
M3=5000;                      % integer for length of coupler qt1# P  
N = 512;                      % Number of Fourier modes (Time domain sampling points) [UI bO@e  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. JTb<uC  
T =40;                        % length of time:T*T0. ):\ pD]e  
dt = T/N;                     % time step Q2NS>[  
n = [-N/2:1:N/2-1]';          % Index =* (d+[_  
t = n.*dt;   @TH \hr]  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. A] F K\  
w=2*pi*n./T; `QkzWy~V3  
g1=-i*ww./2; &R8zuD`#  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 5fLCmLM`  
g3=-i*ww./2; {<]abO  
P1=0; B;-oa;m:E=  
P2=0; ;0BCM(>Wo  
P3=1; `Y[zF1$kz^  
P=0; ;N j5NB7  
for m1=1:M1                 /qp`xJ  
p=0.032*m1;                %input amplitude gr S,PKH  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 :J<S-d=  
s1=s10; !BY=HFT  
s20=0.*s10;                %input in waveguide 2 %v|,-B7Yx  
s30=0.*s10;                %input in waveguide 3 PCU6E9~t2  
s2=s20; e@q[Dv'mu  
s3=s30; Fj5^_2MU:  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   7;_5 [_  
%energy in waveguide 1 AI)9E=D%  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   eIEcj<f  
%energy in waveguide 2 zMG4oRPP  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   r!zNcN(%cs  
%energy in waveguide 3 %_ z]iz4  
for m3 = 1:1:M3                                    % Start space evolution $DQ -.WI  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS V}J W@  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; I|PiZ1]2 Y  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; '}OrFN  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Uvuvr_IP  
   sca2 = fftshift(fft(s2)); ~k J#IA  
   sca3 = fftshift(fft(s3)); ]xS< \{og  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   FIS-xpv$  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 5I<?HsK@  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ())|x[>JS+  
   s3 = ifft(fftshift(sc3)); <h;P<4JX  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Im Tq`  
   s1 = ifft(fftshift(sc1)); S1=c_!q%9  
end x7/2e{p uu  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); # ._!.P  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); dk.da&P  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 2.x3^/  
   P1=[P1 p1/p10]; p*N+B o  
   P2=[P2 p2/p10]; +FJ o!~1  
   P3=[P3 p3/p10]; jK{CjfCNz  
   P=[P p*p]; C :e 'wmA  
end cis ~]x%  
figure(1) z1L.  
plot(P,P1, P,P2, P,P3); &,#VhT![  
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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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