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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 n`2LGc[rP  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of K1[(% <Gp  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of kCZxv"Ts  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 71!'k>]h  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d2[R{eNX=  
,1|0]:  
%fid=fopen('e21.dat','w'); u<K{=94!e  
N = 128;                       % Number of Fourier modes (Time domain sampling points) h^ =9R6im  
M1 =3000;              % Total number of space steps ~k780  
J =100;                % Steps between output of space MgUjB~)Y  
T =10;                  % length of time windows:T*T0 muKCCWy#  
T0=0.1;                 % input pulse width M"|({+9eG  
MN1=0;                 % initial value for the space output location @86?!0bt  
dt = T/N;                      % time step _"c:Z!L  
n = [-N/2:1:N/2-1]';           % Index ;}E$>]*Yn  
t = n.*dt;   YB3?Ftgw  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 El4SL'E@  
u20=u10.*0.0;                  % input to waveguide 2 _&|<(m&."  
u1=u10; u2=u20;                 ;iT ZzmB  
U1 = u1;   {;E]#=|  
U2 = u2;                       % Compute initial condition; save it in U LQ3J$N  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ;P!x/Ct  
w=2*pi*n./T; <n{-& ;>  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Rg6/6/ IN  
L=4;                           % length of evoluation to compare with S. Trillo's paper ~e#QAaXD#5  
dz=L/M1;                       % space step, make sure nonlinear<0.05 "6zf-++%  
for m1 = 1:1:M1                                    % Start space evolution SQJ }$#=  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS *zTEK:+_  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;  V4q v7  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 6 P U]I+  
   ca2 = fftshift(fft(u2)); FCA]zR1  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation @]xH t&j  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   q_[V9  
   u2 = ifft(fftshift(c2));                        % Return to physical space l~c# X3E  
   u1 = ifft(fftshift(c1)); [ %:%C]4  
if rem(m1,J) == 0                                 % Save output every J steps. o0\d`0-el  
    U1 = [U1 u1];                                  % put solutions in U array d<+@cf_9  
    U2=[U2 u2]; HlC[Nu^6U  
    MN1=[MN1 m1]; (4oO8 aBB  
    z1=dz*MN1';                                    % output location VSW"/{Lp  
  end L+J)  
end K6M_b?XekA  
hg=abs(U1').*abs(U1');                             % for data write to excel Zt H{2j0  
ha=[z1 hg];                                        % for data write to excel Gn} ^BJN  
t1=[0 t']; 6qH^&O][  
hh=[t1' ha'];                                      % for data write to excel file odNHyJS0  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format a0=>@?  
figure(1) YqNI:znm-  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn v!77dj 6I  
figure(2) hR(p{$-T  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn sTChbks  
:1,xse  
非线性超快脉冲耦合的数值方法的Matlab程序 Xl\yOMfp  
7zEpuw  
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。   BFH=cs  
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 nMU[S +  
h(MS>=  
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sm96Ye{O{  
%  This Matlab script file solves the nonlinear Schrodinger equations T,SCK^  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of  3JcI}w  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear UgAG2  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 m. DC  
L$4nbOu\~  
C=1;                           ;/|3U7{c  
M1=120,                       % integer for amplitude IM9P5?kJ ?  
M3=5000;                      % integer for length of coupler [>wvVv  
N = 512;                      % Number of Fourier modes (Time domain sampling points) F|{F'UXj|  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. kV:C=MLI  
T =40;                        % length of time:T*T0. tDwj~{a~  
dt = T/N;                     % time step 9_I#{ ?  
n = [-N/2:1:N/2-1]';          % Index W9%B9~\G;+  
t = n.*dt;   9d1 G u"  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. r,-9 ]?i  
w=2*pi*n./T; vB;$AFh{  
g1=-i*ww./2; rN5;W  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @!:_r5R~N  
g3=-i*ww./2; nps"nggk  
P1=0; tF=Y3W+L  
P2=0; %eDJ]\*^X  
P3=1; CKgbb4;<m[  
P=0; 1?N$I}?  
for m1=1:M1                 k=8LhO  
p=0.032*m1;                %input amplitude bhg OLh#  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 l<YCX[%E  
s1=s10; Z5%TpAu[  
s20=0.*s10;                %input in waveguide 2 J0a#QvX!  
s30=0.*s10;                %input in waveguide 3 xzjG|"a[GB  
s2=s20; hDc)\vzr  
s3=s30; jFThW N  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   <=7N2t)s4  
%energy in waveguide 1 k>;a5'S  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   RFzMah?Q=j  
%energy in waveguide 2 KXTx{R  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   z~+gche>  
%energy in waveguide 3 I'%(f@u~  
for m3 = 1:1:M3                                    % Start space evolution 8`S6BkfC|  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 8 y+Nl&"V  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; wM#BQe3t#  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 1[Ffl^\ARp  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform *2tG07kI  
   sca2 = fftshift(fft(s2)); TSCc=c  
   sca3 = fftshift(fft(s3)); p-1 \4  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   oHI/tS4 _  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); sB>ZN3ptH^  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); J4;F k  
   s3 = ifft(fftshift(sc3)); b$Ch2Qz0q  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ^&-H"jF  
   s1 = ifft(fftshift(sc1)); ^S'tMT_  
end _$Hx:^p:  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); A}cGag+sp  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); WJN}d-S=^  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); uRu)iBd D  
   P1=[P1 p1/p10]; <dA1n:3o  
   P2=[P2 p2/p10]; l-mf~{   
   P3=[P3 p3/p10]; !j|93*  
   P=[P p*p]; 6bW:&IPQ;  
end \d)~.2$G*  
figure(1) V*U*_Y  
plot(P,P1, P,P2, P,P3); :n?K[f?LfY  
/P-Eg86V'  
转自:http://blog.163.com/opto_wang/
ciomplj 2014-06-22 22:57
谢谢哈~!~
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