[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 +t&)Z  
COw!a\Jl  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of }aXSMxCd  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of qxHn+O!h  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear jTV4iX  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 0c!^=(  
aj .7t=^  
%fid=fopen('e21.dat','w'); 4^nHq 4_  
N = 128;                       % Number of Fourier modes (Time domain sampling points) V6((5o#  
M1 =3000;              % Total number of space steps (V'w5&f(L  
J =100;                % Steps between output of space G973n  
T =10;                  % length of time windows:T*T0 IuAu_`,Ndi  
T0=0.1;                 % input pulse width )8}k.t>'s  
MN1=0;                 % initial value for the space output location v''J@F7  
dt = T/N;                      % time step 8'TIDu  
n = [-N/2:1:N/2-1]';           % Index dBovcc  
t = n.*dt;   `nEqw/I  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 GVn'p Wg  
u20=u10.*0.0;                  % input to waveguide 2 #8M^;4N>[  
u1=u10; u2=u20;                 8*{jxN'M  
U1 = u1;  
gp$Rf9\  
U2 = u2;                       % Compute initial condition; save it in U
QkHG`yW  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. i1KjQ1\a+  
w=2*pi*n./T; gae=+@z  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T h4h
p5M  
L=4;                           % length of evoluation to compare with S. Trillo's paper @]2aPs} }6  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ;/?w-)n?  
for m1 = 1:1:M1                                    % Start space evolution F|.tn`j]U  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 2|B@s3a  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; nec}g
rA  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform h?B1Emlq  
   ca2 = fftshift(fft(u2)); .v'`TD).6  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 0CXXCa7!  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ! os@G  
   u2 = ifft(fftshift(c2));                        % Return to physical space X !0 7QKs  
   u1 = ifft(fftshift(c1)); 6o9&FU  
if rem(m1,J) == 0                                 % Save output every J steps. Df*<3G  
    U1 = [U1 u1];                                  % put solutions in U array >py[g
0J  
    U2=[U2 u2]; k2,`W2]^E  
    MN1=[MN1 m1]; ru`U/6n  
    z1=dz*MN1';                                    % output location VGxab;#,:3  
  end :~srl)|)  
end whP5u/857  
hg=abs(U1').*abs(U1');                             % for data write to excel 9(z) ^G  
ha=[z1 hg];                                        % for data write to excel .;ofRx<  
t1=[0 t']; 2g?q4e,  
hh=[t1' ha'];                                      % for data write to excel file v.>K )%`#  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format |/%5~=%7  
figure(1)
\)>#`X  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn YN<vOv  
figure(2) 5=<KA  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn kz6fU\U  
T:2f*!r  
非线性超快脉冲耦合的数值方法的Matlab程序 }m5()@Q}a  
"XLtrAu{  
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。   QUvSeNSp  
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 PN<VqtW  
y^n
T G  
BtKor6ba  
:2 :VMIa  
%  This Matlab script file solves the nonlinear Schrodinger equations GXQ%lQ  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ZUS5z+o  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear `{ HWk^  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d]^m^
 
W(4$.uZ)  
C=1;                           JZ5";*,  
M1=120,                       % integer for amplitude .oTS7rYw  
M3=5000;                      % integer for length of coupler xVX:kDX  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ~jHuJ`]DF  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. &ynAB)  
T =40;                        % length of time:T*T0. H<<t^,E^.t  
dt = T/N;                     % time step 9rT^rTV  
n = [-N/2:1:N/2-1]';          % Index ScD E)r  
t = n.*dt;   2e-bt
@0t  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. "Y^9g/  
w=2*pi*n./T; YX)Rs Vf  
g1=-i*ww./2; /QVwZrch  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; w{2CV\^>5  
g3=-i*ww./2; .j^BWr  
P1=0; mD&I6F[s  
P2=0; S^p^) fAmF  
P3=1; 8Lx1XbwK  
P=0; 3"v>y]$U  
for m1=1:M1                 S^==$TT  
p=0.032*m1;                %input amplitude w{k^O7
~  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 y06**f)  
s1=s10; qz3 Z'  
s20=0.*s10;                %input in waveguide 2 B]()  
s30=0.*s10;                %input in waveguide 3 IvY3iRq6  
s2=s20; 5~jz| T}s  
s3=s30; t0@AfO.'1  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Ml{ ]{n  
%energy in waveguide 1 Mlo,F1'?>  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   YwF&-~mp7n  
%energy in waveguide 2 19y,O0# _  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   P2aFn=f  
%energy in waveguide 3 Cj`~ntMN  
for m3 = 1:1:M3                                    % Start space evolution fsw[R0B  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS v@q&B|0  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; U.I w/T-5  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; u7RlxA:  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform X;UEq]kcmn  
   sca2 = fftshift(fft(s2)); ~"J1@<  
   sca3 = fftshift(fft(s3)); 'xG J;pY  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   D|m3.si  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); GQhy4ji'z  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); _xm<zy{`S  
   s3 = ifft(fftshift(sc3)); s2|.LmC3|B  
   s2 = ifft(fftshift(sc2));                       % Return to physical space =7H\llL4BC  
   s1 = ifft(fftshift(sc1)); kV T |(Y  
end dhnX\/  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 39 zfbxX  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 6B7*|R>  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); "!AtS  
   P1=[P1 p1/p10]; )`'a1y|  
   P2=[P2 p2/p10]; G6W|l2P!  
   P3=[P3 p3/p10]; $':5uU1}  
   P=[P p*p]; Y%0rji  
end %cUC~, g_(  
figure(1) [M%?[E}>  
plot(P,P1, P,P2, P,P3); AzZhIhWl">  
5Ww,vSCV)  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~