[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 gMXs&`7P  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of #}M\ J0QG  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of j-~x==c-;  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear =sm<B^yj  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 (Dat`
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%fid=fopen('e21.dat','w'); n
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N = 128;                       % Number of Fourier modes (Time domain sampling points) "|N58%  
M1 =3000;              % Total number of space steps ar&j1""  
J =100;                % Steps between output of space W4OL{p-\/  
T =10;                  % length of time windows:T*T0 3(2WO^zX {  
T0=0.1;                 % input pulse width /Pbytu);ds  
MN1=0;                 % initial value for the space output location BE0Ov{'  
dt = T/N;                      % time step (-}:'5|Yj  
n = [-N/2:1:N/2-1]';           % Index K#"J8h;x  
t = n.*dt;   1iA0+Ex(j  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 EF>vu+YK  
u20=u10.*0.0;                  % input to waveguide 2 i2+r#Hw#5R  
u1=u10; u2=u20;                 \eF_Xk[  
U1 = u1;   #}PQ !gZ  
U2 = u2;                       % Compute initial condition; save it in U A&?8 rc  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 5taR[ukM  
w=2*pi*n./T; UWW^g@d4  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 0sMNp  
L=4;                           % length of evoluation to compare with S. Trillo's paper bA_/6r)u  
dz=L/M1;                       % space step, make sure nonlinear<0.05 kC,=E9)O  
for m1 = 1:1:M1                                    % Start space evolution J#>)+  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS O'Mo/ u1-  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; %fT%,( w}t  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform jo-2D[Q{  
   ca2 = fftshift(fft(u2)); !Y8+Z&^2  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation T}}T`Ce  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Vjdu9Ez  
   u2 = ifft(fftshift(c2));                        % Return to physical space ._E 6?  
   u1 = ifft(fftshift(c1)); |2Vhj<6  
if rem(m1,J) == 0                                 % Save output every J steps. 3 as~yF0  
    U1 = [U1 u1];                                  % put solutions in U array qix$ }(P  
    U2=[U2 u2]; VGYx(  
    MN1=[MN1 m1]; ndmsXls  
    z1=dz*MN1';                                    % output location 8t;vZ&  
  end XnwVK  
end 7"_m?c8  
hg=abs(U1').*abs(U1');                             % for data write to excel QGCg~TV;  
ha=[z1 hg];                                        % for data write to excel > `1K0?_  
t1=[0 t']; +P &S0/  
hh=[t1' ha'];                                      % for data write to excel file exZgk2[0  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format H|Y*TI2vf8  
figure(1) `<3%`4z/  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn /Hs\`Kg"!  
figure(2) A'tv[Td8,  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn } =
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非线性超快脉冲耦合的数值方法的Matlab程序 -k?K|w*X  
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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。   4<j7F4  
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 S.z
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%  This Matlab script file solves the nonlinear Schrodinger equations O:]e4r,'  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of yMz dM&a!*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear [t6Y,yo&h4  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 cq`!17"k  
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C=1;                           3Q#
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M1=120,                       % integer for amplitude `Hx JE"/  
M3=5000;                      % integer for length of coupler N!//m?}  
N = 512;                      % Number of Fourier modes (Time domain sampling points) hcqg94R#_  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. {UFs1  
T =40;                        % length of time:T*T0. hz+O.k],?  
dt = T/N;                     % time step vn+~P9SHQ  
n = [-N/2:1:N/2-1]';          % Index [ KDNKK  
t = n.*dt;   }*P?KV (  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. [k]3#<sS  
w=2*pi*n./T; n%ypxY0  
g1=-i*ww./2; |})v, oB  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; NI:3hfs  
g3=-i*ww./2; 35H.ZXQp-  
P1=0; Qp;FVUw9  
P2=0; V2SHF  
P3=1; ~_F<"
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P=0; eMLcmZJR  
for m1=1:M1                 Y<t(
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p=0.032*m1;                %input amplitude KJ7-Vl>  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 0m,q3  
s1=s10; aF{1V\e  
s20=0.*s10;                %input in waveguide 2 #=T^XHjQ  
s30=0.*s10;                %input in waveguide 3 Ov#G7a"  
s2=s20; (@Kc(>(: Y  
s3=s30; ^&lkh@Y1q  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   6IJH%qUx'  
%energy in waveguide 1 z?t75#u9.  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ,B:r^(}0j  
%energy in waveguide 2 p
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   iOtf7.@  
%energy in waveguide 3 fCbd]X  
for m3 = 1:1:M3                                    % Start space evolution n}dLfg*  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Db*&'32W  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6@VgLa,  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; e0M'\'J  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform y q!{\@-  
   sca2 = fftshift(fft(s2)); !-m 'diE  
   sca3 = fftshift(fft(s3)); 25;(`Td5  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   FY)US>  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); N<O<wtXIj  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); *LEI@  
   s3 = ifft(fftshift(sc3)); C;%1XFzM  
   s2 = ifft(fftshift(sc2));                       % Return to physical space X2E=2tXl`7  
   s1 = ifft(fftshift(sc1)); K@vU_x0Sl  
end bZ#5\L2  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); VsDY,=Ww  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 3i#'osq  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4>Y*owa4  
   P1=[P1 p1/p10]; s &f\gp1  
   P2=[P2 p2/p10]; BZ,{gy7g7X  
   P3=[P3 p3/p10]; +
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   P=[P p*p]; 2AW*PDncxP  
end {TvB3QOsj  
figure(1) mRy0zN>?  
plot(P,P1, P,P2, P,P3); 3:>hHQi  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~