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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 f*U3s N^y  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of }}L :6^  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 1P i_V  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NH+?7rf8  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 VrDSN  
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%fid=fopen('e21.dat','w'); gD`|N@W$5  
N = 128;                       % Number of Fourier modes (Time domain sampling points) ?Vg251-H  
M1 =3000;              % Total number of space steps =GH>-*qp  
J =100;                % Steps between output of space ZYf0FC=-  
T =10;                  % length of time windows:T*T0 n$]78\C  
T0=0.1;                 % input pulse width zY_?$9l0  
MN1=0;                 % initial value for the space output location X+6`]]  
dt = T/N;                      % time step oN3DM;  
n = [-N/2:1:N/2-1]';           % Index ob=](  
t = n.*dt;   [{R^!Az&b<  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 MPaF  
u20=u10.*0.0;                  % input to waveguide 2 rf@Cz%xDD  
u1=u10; u2=u20;                 :@x_& b  
U1 = u1;   :'hc&wk`  
U2 = u2;                       % Compute initial condition; save it in U p~LTu<*S  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. jTSN`R9@  
w=2*pi*n./T; 47<fg&T  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T M{(g"ha  
L=4;                           % length of evoluation to compare with S. Trillo's paper (}!xO?NA(  
dz=L/M1;                       % space step, make sure nonlinear<0.05 v*Dz4K#  
for m1 = 1:1:M1                                    % Start space evolution }.ZT?p\  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS st4WjX_Q  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; D^m`&asC  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform zeqwmV=  
   ca2 = fftshift(fft(u2)); 8D]&wBR:  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation =qWcw7!"  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   |XGj97#M  
   u2 = ifft(fftshift(c2));                        % Return to physical space =\ek;d0Tqb  
   u1 = ifft(fftshift(c1)); PH1jN?OEwZ  
if rem(m1,J) == 0                                 % Save output every J steps. . .5s 2  
    U1 = [U1 u1];                                  % put solutions in U array J=l\t7w  
    U2=[U2 u2]; D*_Z"q_B  
    MN1=[MN1 m1]; )(/Bw&$  
    z1=dz*MN1';                                    % output location &m PR[{  
  end 7=wPd4  
end {9c_T!c  
hg=abs(U1').*abs(U1');                             % for data write to excel >2^|r8l5  
ha=[z1 hg];                                        % for data write to excel lWyg_YO@  
t1=[0 t']; Efa3{ 7>{  
hh=[t1' ha'];                                      % for data write to excel file 8 *Y(wqH  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format hy}n&h  
figure(1) w3>.d(Q  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn j>I.d+   
figure(2) K%@#a}kRb  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn } Q1m  
^ZD0rp(l  
非线性超快脉冲耦合的数值方法的Matlab程序 zI& ).  
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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 3`z  
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 (GJX[$@  
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%  This Matlab script file solves the nonlinear Schrodinger equations Fu*Qci1Z  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of a IgV"3  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +*=?0\  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s g6e% 5  
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C=1;                           Lv<)Dur0K  
M1=120,                       % integer for amplitude lj+}5ySG/  
M3=5000;                      % integer for length of coupler m'"Ra-  
N = 512;                      % Number of Fourier modes (Time domain sampling points) G_5E#{u  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. r Cn"{.rI  
T =40;                        % length of time:T*T0. M^?=!!US^  
dt = T/N;                     % time step e =4k|8G  
n = [-N/2:1:N/2-1]';          % Index V?C_PMa  
t = n.*dt;   c 6$n:  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 0qk.NPMB0  
w=2*pi*n./T; nH(H k%~  
g1=-i*ww./2; L~} 2&w  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; TM$Ek^fQ.  
g3=-i*ww./2; I3D#wXW  
P1=0; ba"a!#wA  
P2=0; F<^93a9  
P3=1; lITZ|u  
P=0; *3We5  
for m1=1:M1                 x1ID6kI[{*  
p=0.032*m1;                %input amplitude g+iV0bbT  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 )gq(  
s1=s10; C},$(2>0+  
s20=0.*s10;                %input in waveguide 2 @5-+>\Hd^t  
s30=0.*s10;                %input in waveguide 3 dj0`Q:VZ  
s2=s20; k<3 _!?3  
s3=s30; 3tTz$$-#  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   y Yvv;E  
%energy in waveguide 1 TAu*lL(F  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   SY}iU@xo  
%energy in waveguide 2 ^2PQ75V@.  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   v1j]&3O  
%energy in waveguide 3 XU#nqvS`.  
for m3 = 1:1:M3                                    % Start space evolution S-:7P.#Q  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS (dC<N3  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ^Y:Q%?uB/  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; D{,B[5  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform r4xq%hy  
   sca2 = fftshift(fft(s2)); OQA3~\Vu  
   sca3 = fftshift(fft(s3)); Hvq< _&2  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   | We @p  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 6zLz<p?  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 4[!&L:tR  
   s3 = ifft(fftshift(sc3)); 7}r!%<^  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ++13m*fA  
   s1 = ifft(fftshift(sc1)); J 6S  
end k- sbZL  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); <!zItFMD[m  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); |"P5%k#6^>  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); @ec QVk  
   P1=[P1 p1/p10]; %'* |N [  
   P2=[P2 p2/p10]; 3MjMN%{P  
   P3=[P3 p3/p10]; 5Kv=;o=U  
   P=[P p*p]; (>0d+ KT  
end M14_w,  
figure(1) =QyO$:t  
plot(P,P1, P,P2, P,P3); !4jS=Lhe>  
FZA8@J|Q4  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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