[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 5|:t$  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of W[BwHNxyg  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of h=*eOxR"4^  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cI#! Y  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'j&+Pg)@  
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%fid=fopen('e21.dat','w'); 0vYHx V  
N = 128;                       % Number of Fourier modes (Time domain sampling points) D^dos`L0b  
M1 =3000;              % Total number of space steps R-[t4BHn  
J =100;                % Steps between output of space Fx!NRY_  
T =10;                  % length of time windows:T*T0 X7."hGu@  
T0=0.1;                 % input pulse width $*-U
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MN1=0;                 % initial value for the space output location 1[4 2f#  
dt = T/N;                      % time step Ng,<4;  
n = [-N/2:1:N/2-1]';           % Index CQ;.}=j ,  
t = n.*dt;   x b6X8:  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 HEBKRpt  
u20=u10.*0.0;                  % input to waveguide 2 {V
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u1=u10; u2=u20;                 P[q 'Y^\  
U1 = u1;   ))9w)A@  
U2 = u2;                       % Compute initial condition; save it in U _-6IB>  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. VV'*3/I  
w=2*pi*n./T; _@] uHp|  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ,Y+J.8.H  
L=4;                           % length of evoluation to compare with S. Trillo's paper 1^v?Ly8  
dz=L/M1;                       % space step, make sure nonlinear<0.05 SJ0IEPk  
for m1 = 1:1:M1                                    % Start space evolution -h%!#g  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 1ZZ}ojq  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; P70]
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   ca1 = fftshift(fft(u1));                        % Take Fourier transform | > t,1T.  
   ca2 = fftshift(fft(u2)); 7iijATc  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 3q}fDM(@J  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   L!qXt(`  
   u2 = ifft(fftshift(c2));                        % Return to physical space 0pW?v:!H  
   u1 = ifft(fftshift(c1)); I%?ia5]H  
if rem(m1,J) == 0                                 % Save output every J steps. GeydVT-  
    U1 = [U1 u1];                                  % put solutions in U array Or:a\qQ1  
    U2=[U2 u2]; h+d  \u  
    MN1=[MN1 m1]; I7C*P~32{n  
    z1=dz*MN1';                                    % output location Kf>]M|G c  
  end J{w[vcf  
end \g;o9}@3~  
hg=abs(U1').*abs(U1');                             % for data write to excel ud`!X#e~  
ha=[z1 hg];                                        % for data write to excel
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t1=[0 t']; \+3P<?hD#  
hh=[t1' ha'];                                      % for data write to excel file IUZ@n0/T  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format jt6q8  
figure(1) $-#|g  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn oU
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figure(2) S9VD/  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn "I}]]?y  
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非线性超快脉冲耦合的数值方法的Matlab程序 6 {j}Z*)m  
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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。   jM07&o]D  
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 "tX=^4
 
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%  This Matlab script file solves the nonlinear Schrodinger equations Xe.
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%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of [+8in\T i  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear #[LnDU8
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%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 NpLO_-  
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C=1;                           r2.f8U  
M1=120,                       % integer for amplitude Jv[c?6He  
M3=5000;                      % integer for length of coupler ;jZfVRl  
N = 512;                      % Number of Fourier modes (Time domain sampling points) [G#PK5C  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. }:zTz%_K  
T =40;                        % length of time:T*T0. XI/LVP,.  
dt = T/N;                     % time step Ro:DAxi@L  
n = [-N/2:1:N/2-1]';          % Index b,r{wrLe)  
t = n.*dt;   \LbBK ~l-I  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. -#agWqUM|T  
w=2*pi*n./T; BK/_hNz  
g1=-i*ww./2; PYhRP00}M  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; |08'd5  
g3=-i*ww./2; duT'$}2@>  
P1=0; tX'2 $}  
P2=0; ='z4bU  
P3=1; [5T{`&  
P=0; +>*! 3x+sE  
for m1=1:M1                 $AyE6j_1gX  
p=0.032*m1;                %input amplitude *kM^l!<g  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 +5xVgIk#  
s1=s10; *%p`Jk-U  
s20=0.*s10;                %input in waveguide 2 1Ax{Y#<  
s30=0.*s10;                %input in waveguide 3 *+rWn*L  
s2=s20; lD41+x7  
s3=s30; X1Vj"4'wT  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   kh5VuXpe  
%energy in waveguide 1 wRsh@I<  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   P7D__hoE  
%energy in waveguide 2 L,7+26XV"B  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   2Q81#i'Cm  
%energy in waveguide 3 }Y
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for m3 = 1:1:M3                                    % Start space evolution MIx,#]C&  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS P g.j]  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ~[
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   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; .tQeOZW'  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform glI4Jb_[  
   sca2 = fftshift(fft(s2)); =4_Er{AT  
   sca3 = fftshift(fft(s3)); H$44,8,m  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   W^8MsdM  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); zNRR('B?  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); jn,_Ncd#  
   s3 = ifft(fftshift(sc3)); W^"C|4G}  
   s2 = ifft(fftshift(sc2));                       % Return to physical space K}a3Bj,  
   s1 = ifft(fftshift(sc1)); LAjreC<W  
end l)K8.(2  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Z#
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   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); |SSe n#PYp  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); }P*x/z~  
   P1=[P1 p1/p10]; \\iX9-aI<  
   P2=[P2 p2/p10]; ==]BrhZK  
   P3=[P3 p3/p10]; dh0nB  
   P=[P p*p]; Je &O  
end Bp9_\4  
figure(1) 9ymx;  
plot(P,P1, P,P2, P,P3); >p?Vv0*  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~