[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 HP7~Zn)c  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of {\k }:)  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of #Mk3cp^Yl  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear o; 6^:  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Aua}.Fl,  
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%fid=fopen('e21.dat','w'); ?x
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N = 128;                       % Number of Fourier modes (Time domain sampling points) r#oJch=  
M1 =3000;              % Total number of space steps h=6D=6c  
J =100;                % Steps between output of space # bjK]+  
T =10;                  % length of time windows:T*T0 a~R.">>$  
T0=0.1;                 % input pulse width 0)zJG |  
MN1=0;                 % initial value for the space output location BK)<~I  
dt = T/N;                      % time step 2rC&  
n = [-N/2:1:N/2-1]';           % Index YvuE:ia  
t = n.*dt;   |Y6;8e`H  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 %TAS4hnu%  
u20=u10.*0.0;                  % input to waveguide 2 a>-qHX-l  
u1=u10; u2=u20;                 B[h^]k  
U1 = u1;   4o";p}[b  
U2 = u2;                       % Compute initial condition; save it in U LPs5LE[Pm  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. <_
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w=2*pi*n./T; _u;pD-  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @+~>utr  
L=4;                           % length of evoluation to compare with S. Trillo's paper Xf"< >M  
dz=L/M1;                       % space step, make sure nonlinear<0.05 j(k%w  
for m1 = 1:1:M1                                    % Start space evolution /kw;q{>?o  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS .x] pJ9  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; eU`O=uE   
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 2wPc yD  
   ca2 = fftshift(fft(u2)); b>i5r$S8G  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Q`.q,T8I  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   (GGosXU-v  
   u2 = ifft(fftshift(c2));                        % Return to physical space gMZ+kP`  
   u1 = ifft(fftshift(c1)); \ q
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if rem(m1,J) == 0                                 % Save output every J steps. EbX!;z  
    U1 = [U1 u1];                                  % put solutions in U array qQ3pe:n?  
    U2=[U2 u2]; ] >w@@A  
    MN1=[MN1 m1]; q7_Ttjn-DV  
    z1=dz*MN1';                                    % output location dIh+h|:  
  end ^~vM*.j~j  
end lIx./Nf  
hg=abs(U1').*abs(U1');                             % for data write to excel L<iRqayn  
ha=[z1 hg];                                        % for data write to excel X@:Y./  
t1=[0 t'];
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hh=[t1' ha'];                                      % for data write to excel file 01&E.A  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format <s\ZqL$f  
figure(1) z%T|L[(6  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn $`%Om WW{  
figure(2) gs/ocu  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn .p o,.}  
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非线性超快脉冲耦合的数值方法的Matlab程序 SsZSR.tD  
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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。   %I!2dXNFRF  
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 Wb cm1I)  
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%  This Matlab script file solves the nonlinear Schrodinger equations 2P^qZDG 8I  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of );
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear eV(9I v[  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 KUm?gFh  
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C=1;                           34N~<-9AY  
M1=120,                       % integer for amplitude E]m?R 4  
M3=5000;                      % integer for length of coupler QX<x2U  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ~LOE^6C+~o  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. )u=W?5%=}  
T =40;                        % length of time:T*T0. mW{>  
dt = T/N;                     % time step
T,>L  
n = [-N/2:1:N/2-1]';          % Index 0WSZhzNyY  
t = n.*dt;   |S|'o*u  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. S
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w=2*pi*n./T; :{lP9%J-  
g1=-i*ww./2; \weg%
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g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; v*dw'i  
g3=-i*ww./2; to,\n"$~!  
P1=0; LGW_7&0<<  
P2=0; { %]imf|g.  
P3=1; >zL5*:G  
P=0; GPL%8 YY  
for m1=1:M1                 ).(y#zJ7P  
p=0.032*m1;                %input amplitude ]cmX f
 
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 bJD$!*r\%!  
s1=s10;  |Nj6RB7  
s20=0.*s10;                %input in waveguide 2 t8xXGWk0  
s30=0.*s10;                %input in waveguide 3 NT5
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s2=s20; 02*qf:kTnA  
s3=s30; 0{8L^ jB/  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   !d!u{1Y&  
%energy in waveguide 1 kL0K[O
 
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   {N/%%O.b  
%energy in waveguide 2 hKWWN`;b !  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   $YcB=l  
%energy in waveguide 3 |Rhqi  
for m3 = 1:1:M3                                    % Start space evolution 0('ec60u  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS HDZl
;=  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ^V96lKt/  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; *0eU_*A^zO  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform u{\'/c7G  
   sca2 = fftshift(fft(s2)); "2sk1  
   sca3 = fftshift(fft(s3)); Q1?*+]  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   9jEH"`qqk  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); rZaO^}u]  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); YE{t?Y\5  
   s3 = ifft(fftshift(sc3)); ]SRpMZ  
   s2 = ifft(fftshift(sc2));                       % Return to physical space wB \`3u4  
   s1 = ifft(fftshift(sc1)); (uDd_@a9t  
end q^EY?;Y  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); |3@DCbT  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ?&~q^t?u  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 3Ioe#*5\  
   P1=[P1 p1/p10]; bSX/)')jU  
   P2=[P2 p2/p10]; @&WHX#  
   P3=[P3 p3/p10]; g""GQeR  
   P=[P p*p]; B#SVN Lv  
end }shxEsq  
figure(1) l&qCgw  
plot(P,P1, P,P2, P,P3); ZCPUNtOl  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~