[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 gHVD,Jr  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of V#V<Kz  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @|@6
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 g HKA:j`c  

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%fid=fopen('e21.dat','w'); ?wMS[Kj  
N = 128;                       % Number of Fourier modes (Time domain sampling points) iLf*m~Q  
M1 =3000;              % Total number of space steps [ejl #'*5  
J =100;                % Steps between output of space G_6!w//  
T =10;                  % length of time windows:T*T0 {Ty?OZ  
T0=0.1;                 % input pulse width ;>jOB>b{h  
MN1=0;                 % initial value for the space output location kl#)0yqN0  
dt = T/N;                      % time step 6?= ^8  
n = [-N/2:1:N/2-1]';           % Index
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t = n.*dt;   L7s _3\  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 _&PF(/w  
u20=u10.*0.0;                  % input to waveguide 2 @;>Xy!G  
u1=u10; u2=u20;                 9D51@b6k  
U1 = u1;   xd]7?L@h.I  
U2 = u2;                       % Compute initial condition; save it in U |}<!O@<|  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. I.)9:7  
w=2*pi*n./T; GD#W=O  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 
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L=4;                           % length of evoluation to compare with S. Trillo's paper Ir3|PehB  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ux>LciNq  
for m1 = 1:1:M1                                    % Start space evolution | @p  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS da5fKK/s  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; B-tLRLWn   
   ca1 = fftshift(fft(u1));                        % Take Fourier transform O\^D 6\ v  
   ca2 = fftshift(fft(u2)); G3de<?K.[V  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation AI3\
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   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   c.h_&~0qf  
   u2 = ifft(fftshift(c2));                        % Return to physical space $TavvO%#  
   u1 = ifft(fftshift(c1)); pcPRkYT[M  
if rem(m1,J) == 0                                 % Save output every J steps. 5z"[{#/  
    U1 = [U1 u1];                                  % put solutions in U array ]V
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    U2=[U2 u2]; "IJcKoB  
    MN1=[MN1 m1]; lsB.>NlU  
    z1=dz*MN1';                                    % output location KL8WT6!RZ  
  end ;;n=(cM|z  
end FO?I}G22  
hg=abs(U1').*abs(U1');                             % for data write to excel .jRv8x b
 
ha=[z1 hg];                                        % for data write to excel 8iN@n8O  
t1=[0 t']; $kn"S>jV  
hh=[t1' ha'];                                      % for data write to excel file SNtOHTQ  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format )iCg,?SSw=  
figure(1) a`S3v  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ;Yn_*M/*  
figure(2) Ct}rj-L<i  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn `}*jjnr"  
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非线性超快脉冲耦合的数值方法的Matlab程序 t++\&!F  
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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。   FSS~E [(DL  
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 cb9@ 0^-  
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%  This Matlab script file solves the nonlinear Schrodinger equations x DX_s:A  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of L&qY709  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @wW)#!Mou  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 S-G#+Ue2  
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C=1;                           ,\E5et4  
M1=120,                       % integer for amplitude jp+#N pH  
M3=5000;                      % integer for length of coupler Dlo4Wy  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 1Yy*G-7}  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. uCGn9]  
T =40;                        % length of time:T*T0. g<N3 L[
 
dt = T/N;                     % time step f{f|frs  
n = [-N/2:1:N/2-1]';          % Index %{^kmlO  
t = n.*dt;   &^@IAjxn  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. <N\#6m  
w=2*pi*n./T; _@ @"'  
g1=-i*ww./2; \DRYqLT`  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; vKNxL^x  
g3=-i*ww./2; v@ OM  
P1=0; ~n!7 ?4%U  
P2=0; u"M^qRhD  
P3=1; wfc+E9E  
P=0; %~YQlN  
for m1=1:M1                 ED R*1!d  
p=0.032*m1;                %input amplitude i+B
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s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 )J!=X`b  
s1=s10; h_ J|uu  
s20=0.*s10;                %input in waveguide 2 |Xa|%f  
s30=0.*s10;                %input in waveguide 3 hOF>Dj  
s2=s20; )z2hyGX  
s3=s30; Se&%Dr3Nv  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [:C!g#o  
%energy in waveguide 1 t&Z:G<;  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Vr%!rQ  
%energy in waveguide 2 }8&L?B;90  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   t!}?nw%$  
%energy in waveguide 3 ];G$~[  
for m3 = 1:1:M3                                    % Start space evolution H1g"09?h6o  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS oi}\;TG  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; D1<$]r,  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; E[E[Za^Y  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform L~xzfO  
   sca2 = fftshift(fft(s2)); 7q,M2v;  
   sca3 = fftshift(fft(s3)); /-jk_8@a  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   =8)q-{p3  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); IOi6' 1l  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); sy.U]QG  
   s3 = ifft(fftshift(sc3)); v_Y'o _  
   s2 = ifft(fftshift(sc2));                       % Return to physical space Gn%gSH/  
   s1 = ifft(fftshift(sc1)); .]W A/}  
end [XP3  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ;'J{ylRQ  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); &`4v,l^Zi6  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 7A[`%.!F6  
   P1=[P1 p1/p10]; $N1UEvC%Q  
   P2=[P2 p2/p10]; u6(>?r-  
   P3=[P3 p3/p10]; L(!mm  
   P=[P p*p]; zSFqy'b.M-  
end S\O6B1<:  
figure(1) ^04|tda  
plot(P,P1, P,P2, P,P3); y*5bF0  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~