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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 q6a7o=BP]  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of FvVR \a  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of n 0rAOkW  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /_.1f|{B  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1b4/  
 "yA=Tw  
%fid=fopen('e21.dat','w'); g ;To}0H  
N = 128;                       % Number of Fourier modes (Time domain sampling points) i^2-PKPg{  
M1 =3000;              % Total number of space steps yHIZpU|(j  
J =100;                % Steps between output of space |fhYft  
T =10;                  % length of time windows:T*T0 W34_@,GD  
T0=0.1;                 % input pulse width `_Fxb@"R  
MN1=0;                 % initial value for the space output location h}SP`  
dt = T/N;                      % time step x}B_;&>&"_  
n = [-N/2:1:N/2-1]';           % Index lz >>{  
t = n.*dt;   ~H1 ZQ[  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 %|\Af>o4d  
u20=u10.*0.0;                  % input to waveguide 2 6Ud6F t6  
u1=u10; u2=u20;                 Tw0GG8(c  
U1 = u1;   %Z]c[V.  
U2 = u2;                       % Compute initial condition; save it in U |O4LR,{G.w  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 3]cW08"c  
w=2*pi*n./T; `y0u(m5  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T n1J;)VyR  
L=4;                           % length of evoluation to compare with S. Trillo's paper Ka+N5 T.f  
dz=L/M1;                       % space step, make sure nonlinear<0.05 L-z9n@=8\  
for m1 = 1:1:M1                                    % Start space evolution h5^qo ^;g7  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS yh:Wg$qx  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;  J*FUJT  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform R?L? 6~/q  
   ca2 = fftshift(fft(u2)); fs,]%g^  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 0LD$"0v/C3  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   %(YU*Tf~  
   u2 = ifft(fftshift(c2));                        % Return to physical space Wkj0z ]]?  
   u1 = ifft(fftshift(c1)); CD:$22*]  
if rem(m1,J) == 0                                 % Save output every J steps. YQ$EN>.eO  
    U1 = [U1 u1];                                  % put solutions in U array K);)$8K  
    U2=[U2 u2]; G%FLt[  
    MN1=[MN1 m1]; i2&I<:  
    z1=dz*MN1';                                    % output location 4157!w'\y  
  end " .<>(bE  
end 7Adg;  
hg=abs(U1').*abs(U1');                             % for data write to excel "%E<%g  
ha=[z1 hg];                                        % for data write to excel %|AXVv7IN>  
t1=[0 t']; >O$ JS,  
hh=[t1' ha'];                                      % for data write to excel file Xt9vTCox  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format ;]\>jC  
figure(1) gUWW}*\ U  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn tQWjNP~  
figure(2) sEzl4I  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +Z=%4  
Hzc5BC  
非线性超快脉冲耦合的数值方法的Matlab程序 -,a@bF:  
J5"d|i  
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。   ;m#_Rj6  
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 wmB_)`QNP  
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p>9|JMk  
%  This Matlab script file solves the nonlinear Schrodinger equations ;}KT 3Q<^  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Y?#aUQc  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ?DgeKA"A  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 C/#?S=w`4  
X+[h]A  
C=1;                           7xh91EU:4  
M1=120,                       % integer for amplitude w:nLm,  
M3=5000;                      % integer for length of coupler S8k<}5  
N = 512;                      % Number of Fourier modes (Time domain sampling points) !D|c2  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. f)1*%zg%  
T =40;                        % length of time:T*T0. w`I+ 4&/h  
dt = T/N;                     % time step L}=t"y  
n = [-N/2:1:N/2-1]';          % Index zGaqYbQD  
t = n.*dt;   Oj8xc!d'  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. r)|6H"n#]S  
w=2*pi*n./T; ;Z.sK-NJ4  
g1=-i*ww./2; j.kv!;Rj=  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; w JF(&P  
g3=-i*ww./2; YkF52_^_  
P1=0; 3g87ir  
P2=0; ~B\O{5W  
P3=1; $bFH%EA.  
P=0; utU ;M*  
for m1=1:M1                 &fe67#0r)  
p=0.032*m1;                %input amplitude 4L/nEZ!Nsu  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 +FH@|~^O  
s1=s10; oS^g "hQ`\  
s20=0.*s10;                %input in waveguide 2 4 z^7T  
s30=0.*s10;                %input in waveguide 3 oq9gFJG(  
s2=s20; ]]9 VI0   
s3=s30; 1Vx>\A  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   _sAcvKH  
%energy in waveguide 1 a"m-&mN  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   3w}ul~>j  
%energy in waveguide 2 6 \}.l  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   $6]1T>  
%energy in waveguide 3 Q9k;PJ`@  
for m3 = 1:1:M3                                    % Start space evolution 2(k m]H^  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS z:oi @q  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; m:Fdgu9  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; *X uIA-9  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform eCjyx|:J  
   sca2 = fftshift(fft(s2)); 4m!w<c0NL  
   sca3 = fftshift(fft(s3)); xbz O' C  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   cq~~a(IS  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); v;#0h7qd  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ?OFfU  4  
   s3 = ifft(fftshift(sc3)); 4mvnFY}   
   s2 = ifft(fftshift(sc2));                       % Return to physical space gjzU%{T ?  
   s1 = ifft(fftshift(sc1));  Y-+JDrK  
end Ym?VF{e,  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); N<XMSt  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); DD}YbuO7  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); M_h8{  
   P1=[P1 p1/p10]; <07]w$m/  
   P2=[P2 p2/p10]; w\a6ga!xt"  
   P3=[P3 p3/p10]; =w7+Yt  
   P=[P p*p]; |3BxNFe`%  
end  0:$pJtx"  
figure(1) e4FR)d0x  
plot(P,P1, P,P2, P,P3); <B!DwMk;.  
piFZu/~Gq\  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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