[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 XRJ<1w:  
,Xo9gn  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of qqS-0U2  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of TLPy/,  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Rk2ZdNc\  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /uW6P3M  
hk}M'  
%fid=fopen('e21.dat','w'); :==kC672  
N = 128;                       % Number of Fourier modes (Time domain sampling points) AG/nX?u7)t  
M1 =3000;              % Total number of space steps 9]1-J5iO  
J =100;                % Steps between output of space >
~>=[M0  
T =10;                  % length of time windows:T*T0 rS>njG;R  
T0=0.1;                 % input pulse width +_ K7x5g  
MN1=0;                 % initial value for the space output location qI:}3b;T  
dt = T/N;                      % time step #9#N+  
n = [-N/2:1:N/2-1]';           % Index %}+j4n  
t = n.*dt;   &p=|z2 J  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 YAC=V?U-#  
u20=u10.*0.0;                  % input to waveguide 2 Fr/8q:m&  
u1=u10; u2=u20;                 :9_K@f?n  
U1 = u1;   }\*dD2qNL}  
U2 = u2;                       % Compute initial condition; save it in U H]}Iw5Z  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ULjW589zb  
w=2*pi*n./T; \1aj!)  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T O0WzDD  
L=4;                           % length of evoluation to compare with S. Trillo's paper 67/hhO  
dz=L/M1;                       % space step, make sure nonlinear<0.05 ,yAvLY5P  
for m1 = 1:1:M1                                    % Start space evolution L a0H  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS wgkh}b   
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; !@ai=p  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 31Zl"-<#-  
   ca2 = fftshift(fft(u2)); 0-l @U{  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation QIBv}hgcy  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   76zi)f1f  
   u2 = ifft(fftshift(c2));                        % Return to physical space .;/@k%>   
   u1 = ifft(fftshift(c1)); /LPSI^l!m  
if rem(m1,J) == 0                                 % Save output every J steps. SZ1+h TY7d  
    U1 = [U1 u1];                                  % put solutions in U array DWm$:M4z  
    U2=[U2 u2];  UZmzk  
    MN1=[MN1 m1]; z/6kxV89  
    z1=dz*MN1';                                    % output location 8'Z9Z*^h#x  
  end jW?.>(  
end .~ZNlI {K  
hg=abs(U1').*abs(U1');                             % for data write to excel AM'-(x|  
ha=[z1 hg];                                        % for data write to excel k+JDbJ@  
t1=[0 t']; !Lk|eGd*  
hh=[t1' ha'];                                      % for data write to excel file p`33`25  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format rgu
C#Xt!4  
figure(1) Hd2Sou4-j  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn D-E30b]e  
figure(2) *1Nz VV  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn }"Hf/{E$_"  
1UyI.U]  
非线性超快脉冲耦合的数值方法的Matlab程序 Kn=P~,FaG3  
\qNj?;B  
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。   5a5I+* c  
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 Le|Ho^h,Y
 
`)1_^# k  
H5^'J`0\  
Co[  r
hs  
%  This Matlab script file solves the nonlinear Schrodinger equations gqyQ Zew  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of sW3-JA]  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear MFiX8zwhx+  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Vyu0OiGcR  
$@}6P,mg  
C=1;                           + [|2k(U  
M1=120,                       % integer for amplitude Y.[
^3  
M3=5000;                      % integer for length of coupler x)THeH@  
N = 512;                      % Number of Fourier modes (Time domain sampling points) <,HdX,5  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. P`T&zK  
T =40;                        % length of time:T*T0. 1;]cYIq  
dt = T/N;                     % time step WnvuB.(@3  
n = [-N/2:1:N/2-1]';          % Index {-7];e  
t = n.*dt;   "9&6bBa  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 6_^u}me  
w=2*pi*n./T; a}hpcr({?  
g1=-i*ww./2; az?B'|VX  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Y>R|Uf.o z  
g3=-i*ww./2; >m44U 9  
P1=0; ~ 9^
1m  
P2=0; j'X]bd'  
P3=1; TL1pv l  
P=0; \m*?5]m;  
for m1=1:M1                 jF_K*:gQ  
p=0.032*m1;                %input amplitude h=EJNz>U  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 0p*(<8D}  
s1=s10; 7t0\}e  
s20=0.*s10;                %input in waveguide 2 7K {/2k  
s30=0.*s10;                %input in waveguide 3 =5[}&W
 
s2=s20; )l\BZndf  
s3=s30; >e>Q'g{  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Hh$x8ADf  
%energy in waveguide 1 =S|SQz5%w  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   *&% kkbA  
%energy in waveguide 2 N6Vn/7I5%  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   $s)G0/~W  
%energy in waveguide 3 R`:Y&)c_$  
for m3 = 1:1:M3                                    % Start space evolution UqsVqi h(  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS :G9.}
VrU  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; n/=&?#m}d  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Me`jh8(K\6  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform {h7*a=  
   sca2 = fftshift(fft(s2)); neoT\HV  
   sca3 = fftshift(fft(s3)); ]9l=geZd%;  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Fwm{oypg%  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); "m3u}!`3  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ,xn+T)2I  
   s3 = ifft(fftshift(sc3)); *
h-_   
   s2 = ifft(fftshift(sc2));                       % Return to physical space =xS(Er`r  
   s1 = ifft(fftshift(sc1)); #hH"g  
end kbI:}b7H  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 0>)('Kv  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )67Kd]  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); p6A"_b^  
   P1=[P1 p1/p10]; z5=&qo|f9l  
   P2=[P2 p2/p10]; "qu%$L  
   P3=[P3 p3/p10]; HZ>Xm6DnC5  
   P=[P p*p]; K9mL1[B  
end I'`Q_5s5  
figure(1) wbUpD(  
plot(P,P1, P,P2, P,P3); ",B92[}Ar  
BikmAa  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~