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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 %/~6Qq  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of AR`X2m '  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of L{bcmo\U  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear .oH0yNFX  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r^ S 4 I&  
;WJ}zjo >  
%fid=fopen('e21.dat','w'); /tc*jXB  
N = 128;                       % Number of Fourier modes (Time domain sampling points) F)j-D(c4  
M1 =3000;              % Total number of space steps mC n,I  
J =100;                % Steps between output of space vi4u `  
T =10;                  % length of time windows:T*T0 5xwztcR-  
T0=0.1;                 % input pulse width *GbC`X)  
MN1=0;                 % initial value for the space output location ylLQKdcL  
dt = T/N;                      % time step 9bl&\Ykt.  
n = [-N/2:1:N/2-1]';           % Index r|:|\"Yk  
t = n.*dt;   uaNJTob  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 O;ZU{VY  
u20=u10.*0.0;                  % input to waveguide 2 VxLq,$B76  
u1=u10; u2=u20;                 l?NRQTG  
U1 = u1;   _Z.lr\  
U2 = u2;                       % Compute initial condition; save it in U M<r' j $g  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 7_.z3K m:  
w=2*pi*n./T; Fo3[KW)8I  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T {r`l  
L=4;                           % length of evoluation to compare with S. Trillo's paper Q mOG2  
dz=L/M1;                       % space step, make sure nonlinear<0.05 @R9zLL6#7  
for m1 = 1:1:M1                                    % Start space evolution Pr{?A]dQ  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS '$ ~.x|  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }C/u>89%q  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform L^KGY<hp4  
   ca2 = fftshift(fft(u2)); mwZesSxB_  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation <wFR%Y/j  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ^ox^gw)  
   u2 = ifft(fftshift(c2));                        % Return to physical space nj!)\U  
   u1 = ifft(fftshift(c1)); }+nC}A"BC  
if rem(m1,J) == 0                                 % Save output every J steps. %'kaNpBz  
    U1 = [U1 u1];                                  % put solutions in U array 4 `Z@^W  
    U2=[U2 u2]; ? 1?^>M  
    MN1=[MN1 m1]; ^5qX+!3r{  
    z1=dz*MN1';                                    % output location L=iaL[zdJ  
  end e7t).s)b{  
end sD1L P  
hg=abs(U1').*abs(U1');                             % for data write to excel muQH!Q  
ha=[z1 hg];                                        % for data write to excel R<Ojaj=V  
t1=[0 t']; mAhtC*  
hh=[t1' ha'];                                      % for data write to excel file mk~i (Ee  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format 9hHQWv7TgK  
figure(1) )@Z J3l.  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ({yuwH?tH  
figure(2) %:h)8e-;  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn T3[\;ib}  
KM g`O3_16  
非线性超快脉冲耦合的数值方法的Matlab程序 ^b~&}uU  
}pbyC  
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~cq T/\?  
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 %.r{+m  
FAjO-T4(  
K7F uMB  
F8;M++  
%  This Matlab script file solves the nonlinear Schrodinger equations p^&' C_?  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of hmtRs]7  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )-Zpr1kD  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tV9W4`Z2q  
6dV@.(][a  
C=1;                           o{4ya jt  
M1=120,                       % integer for amplitude l,1}1{k&  
M3=5000;                      % integer for length of coupler 1.o-2:]E  
N = 512;                      % Number of Fourier modes (Time domain sampling points) brb8C%j}9  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. QUaz;kNC7  
T =40;                        % length of time:T*T0. U`,&Q ]  
dt = T/N;                     % time step KunK.m  
n = [-N/2:1:N/2-1]';          % Index `4.Wdi-Si  
t = n.*dt;   ]cc4+}L~  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. uTpKT7t  
w=2*pi*n./T; lN,b@;  
g1=-i*ww./2; !aeL*`;  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 7$z")JB  
g3=-i*ww./2; !w[<?+%%n  
P1=0; :@wO' o  
P2=0; /&$'v:VB  
P3=1; }zj w\  
P=0; :M`|*~V~$  
for m1=1:M1                 9;&2LT7z  
p=0.032*m1;                %input amplitude S6 $S%$  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ,cWO Ak  
s1=s10; 82~UI'f \  
s20=0.*s10;                %input in waveguide 2 D=mU!rjr1  
s30=0.*s10;                %input in waveguide 3 nUQcoSY#  
s2=s20; mbsdiab#N  
s3=s30; ,yWTk ql  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   r%xp^j}  
%energy in waveguide 1 uwj/]#`  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   \_!FOUPz(  
%energy in waveguide 2 Uey.@2Q  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Y` LZ/Tgk  
%energy in waveguide 3 R 9o:{U]  
for m3 = 1:1:M3                                    % Start space evolution 6^ wg'u]c  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ?f1%)]>   
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; %bt2^  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _R1UEE3M  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform N(dn"`8  
   sca2 = fftshift(fft(s2)); %\}|&z6  
   sca3 = fftshift(fft(s3)); hAOXOj1  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   x]euNa  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Ar'}#6  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); dY~3 YD[  
   s3 = ifft(fftshift(sc3)); 7t\kof  
   s2 = ifft(fftshift(sc2));                       % Return to physical space u z ` H  
   s1 = ifft(fftshift(sc1)); 6](vnS;  
end 3! dD!'  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ?fXg_?+{'g  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); FMwT4]y  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); BXa1 [7Z  
   P1=[P1 p1/p10]; 6vX+- f  
   P2=[P2 p2/p10]; iEr|?,  
   P3=[P3 p3/p10]; |}es+<P  
   P=[P p*p]; K^J;iu4  
end N ]}Re$5  
figure(1) BNyDEFd  
plot(P,P1, P,P2, P,P3); 1|;WaO1Q  
s$C;31k  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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