[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 mgBxcmv  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of R)GDsgXy  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of l{3ZN"`I  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear liH1r1M  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 w8-L2)Q}I  
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%fid=fopen('e21.dat','w'); /.m}y$@GV  
N = 128;                       % Number of Fourier modes (Time domain sampling points) *zDL
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M1 =3000;              % Total number of space steps }ev+WIERQV  
J =100;                % Steps between output of space 5R#:ALwX:  
T =10;                  % length of time windows:T*T0 {?uswbk.  
T0=0.1;                 % input pulse width Qlhm:[  
MN1=0;                 % initial value for the space output location pR~"p#Y  
dt = T/N;                      % time step ?D=%k8)Y  
n = [-N/2:1:N/2-1]';           % Index V5d|Lpm  
t = n.*dt;   ; 5!8LmZ0#  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Hd~fSXFl  
u20=u10.*0.0;                  % input to waveguide 2 vg[zRWh8  
u1=u10; u2=u20;                 D+Z,;X
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U1 = u1;   nZkMyRk  
U2 = u2;                       % Compute initial condition; save it in U .J9\Fr@  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 2}#VB;B  
w=2*pi*n./T; /C[XC7^4'  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 4' <y  
L=4;                           % length of evoluation to compare with S. Trillo's paper a~`,zQ -@  
dz=L/M1;                       % space step, make sure nonlinear<0.05 (7}Zh|@W  
for m1 = 1:1:M1                                    % Start space evolution )Z@hk]@?_[  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ;UWp0d%  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ._}Dqg$  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform M cbiO)@I  
   ca2 = fftshift(fft(u2)); \'Ca
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation lKy4Nry9  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   [{rne2sA  
   u2 = ifft(fftshift(c2));                        % Return to physical space U,^jN|v  
   u1 = ifft(fftshift(c1)); Z+! 96LR  
if rem(m1,J) == 0                                 % Save output every J steps. T04&Tl'CT  
    U1 = [U1 u1];                                  % put solutions in U array OMN|ea.O  
    U2=[U2 u2]; ZvW&%*k=  
    MN1=[MN1 m1]; G)y'exk  
    z1=dz*MN1';                                    % output location C<iOa)_@Q  
  end LfG$?<}hR  
end \AB*C_Ri  
hg=abs(U1').*abs(U1');                             % for data write to excel ZY> u4v.  
ha=[z1 hg];                                        % for data write to excel 4S,/Z{ J.  
t1=[0 t']; ,koG*sn  
hh=[t1' ha'];                                      % for data write to excel file ))#_@CwRr  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format }{ "RgT-qG  
figure(1) fn\&%`U  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn H6-{(: *<  
figure(2) 15`
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn +8
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?nx 1{2[  
非线性超快脉冲耦合的数值方法的Matlab程序 3O'X;s2\d  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   .1?7)k v  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 5[>N[}Ck>  
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%  This Matlab script file solves the nonlinear Schrodinger equations N`i`[ f  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of H.: [# a  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >R8eAR$N  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ffE>%M*  
s2\6\8Ipn  
C=1;                           +\`t@Ht#  
M1=120,                       % integer for amplitude ,V:RE y  
M3=5000;                      % integer for length of coupler "]{"4qV1=  
N = 512;                      % Number of Fourier modes (Time domain sampling points) o[CjRQY]P  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 'QEQyJ0EB  
T =40;                        % length of time:T*T0. vE+OL8V  
dt = T/N;                     % time step \%:]o-+"I  
n = [-N/2:1:N/2-1]';          % Index  al:c2o  
t = n.*dt;   f@= lK?Pfh  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 0_5j(  
w=2*pi*n./T; $8,/[V A  
g1=-i*ww./2; #o-CG PE  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; w*s#=]6
 
g3=-i*ww./2; Ty>g:#bogI  
P1=0; Zr@
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P2=0; }]?U. ]-  
P3=1; o+Kh2;$)  
P=0; lw"5p)aB  
for m1=1:M1                 $C !Mk  
p=0.032*m1;                %input amplitude *Ad7GG1/u  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 P(BV J_n  
s1=s10; 6 bnuC  
s20=0.*s10;                %input in waveguide 2 mh8~w~/[  
s30=0.*s10;                %input in waveguide 3 tqo!WuZAj  
s2=s20; HR83{B21  
s3=s30; "ZyWU f  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ]tVXao  
%energy in waveguide 1 2i~qihx5^  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   j?n:"@!G/  
%energy in waveguide 2 R9z^=QKcH  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   f~D> *<L4-  
%energy in waveguide 3 p;rGaLo:u  
for m3 = 1:1:M3                                    % Start space evolution nu#_,x<LS  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS XK5q
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   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; r?=7#/]  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; R'q:Fc  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform R?Or=W)i  
   sca2 = fftshift(fft(s2)); '{:Yg3K  
   sca3 = fftshift(fft(s3)); Rl"" aZ  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   -cHX3UAEI  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); h}U\2$5  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }3Y3f).ZW  
   s3 = ifft(fftshift(sc3)); H19C
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   s2 = ifft(fftshift(sc2));                       % Return to physical space z<F.0~)jb  
   s1 = ifft(fftshift(sc1)); R]Q4+  
end k&1~yW  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); mTzzF9n"Y  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ZkJYPXdn?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); SAEr$F^  
   P1=[P1 p1/p10]; e1RtoNF^  
   P2=[P2 p2/p10]; %8V/QimHU  
   P3=[P3 p3/p10];  -'|pt,)  
   P=[P p*p]; +0O{"XM  
end k'BLos1W  
figure(1) ^m   
plot(P,P1, P,P2, P,P3); 4{\h53j$  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~