[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 Xh?J"kjof  
TQL_K8k@_  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of 0Qr|!B:+9)  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of /Z1>3=G by  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear O*lMIWx  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 BbG=vy8'l  
iezY+`x4  
%fid=fopen('e21.dat','w'); H tx)MEZ  
N = 128;                       % Number of Fourier modes (Time domain sampling points) c~)H" n  
M1 =3000;              % Total number of space steps M<K}H8?  
J =100;                % Steps between output of space 70F(`;  
T =10;                  % length of time windows:T*T0 Iy;bzHXs  
T0=0.1;                 % input pulse width dTVh{~/  
MN1=0;                 % initial value for the space output location gg?O0W{  
dt = T/N;                      % time step u`gY/]y!  
n = [-N/2:1:N/2-1]';           % Index z{(c-7*  
t = n.*dt;   WqRaD=R->;  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 3J}/<
&wv  
u20=u10.*0.0;                  % input to waveguide 2 OrRU$5Lo  
u1=u10; u2=u20;                 AVO$R\1YR  
U1 = u1;   Tqm)-|[  
U2 = u2;                       % Compute initial condition; save it in U 1Q!^%{Y;  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ,R*YI  
w=2*pi*n./T; 4"et4Y7  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T F*_ytL  
L=4;                           % length of evoluation to compare with S. Trillo's paper |>v8yS5  
dz=L/M1;                       % space step, make sure nonlinear<0.05 l0BYv&tu  
for m1 = 1:1:M1                                    % Start space evolution #eY?6Kjn  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS }kF*I@:g  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; !{S HlS  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform BDcA_=^R&  
   ca2 = fftshift(fft(u2)); evE$$# 6R  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation !glGW[r/7  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   &\5%C\0Z<  
   u2 = ifft(fftshift(c2));                        % Return to physical space l~#%j( Yo  
   u1 = ifft(fftshift(c1)); 1z-Q~m@@  
if rem(m1,J) == 0                                 % Save output every J steps. iX6'3\Q3A  
    U1 = [U1 u1];                                  % put solutions in U array qwvch^?>FQ  
    U2=[U2 u2];  t@+z r3  
    MN1=[MN1 m1]; zuYz"-(L  
    z1=dz*MN1';                                    % output location pP*`b<|  
  end >mp"=Y  
end `y*o-St3  
hg=abs(U1').*abs(U1');                             % for data write to excel JU!vVA_  
ha=[z1 hg];                                        % for data write to excel mApl}I  
t1=[0 t']; 6B&ERdoX  
hh=[t1' ha'];                                      % for data write to excel file qVr?st  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format (R^Ca7F  
figure(1) p77  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn F(;95TB  
figure(2) #TD0)C/  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn vFH1hm  
QmY1Bn?s  
非线性超快脉冲耦合的数值方法的Matlab程序 cE7IHQ  
N6uKFQL:{  
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。   9RnXp&w  
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 +*Pj,+;W  
3sz?49tX  
.*c%A^>  
11BfJvs:  
%  This Matlab script file solves the nonlinear Schrodinger equations #2Z\K>L  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ?gl[=NV  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear gB}UzEj^<  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $?dutbE  
8BggK6X  
C=1;                          
[|dQZ  
M1=120,                       % integer for amplitude Sj9NhtF]f  
M3=5000;                      % integer for length of coupler {"@E_{\  
N = 512;                      % Number of Fourier modes (Time domain sampling points) ['\u?m  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. {on+ ;,  
T =40;                        % length of time:T*T0. rEY5,'?YHv  
dt = T/N;                     % time step z|WDqB%/I  
n = [-N/2:1:N/2-1]';          % Index N-<m/RS  
t = n.*dt;   Z >F5rkJ  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. {aYCrk1  
w=2*pi*n./T; YN($rAkL  
g1=-i*ww./2; 6
^vHFJ$  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; > @n?W"  
g3=-i*ww./2; )+v'@]r  
P1=0; TptXH?  
P2=0; FX:'38-fk  
P3=1; WoX,F1o  
P=0; (g#,AX  
for m1=1:M1                 P'p5-l UK  
p=0.032*m1;                %input amplitude bT#re  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 X0Zr?$q  
s1=s10; "M4gl  
s20=0.*s10;                %input in waveguide 2 _do(   
s30=0.*s10;                %input in waveguide 3 Wz-7oP%;I  
s2=s20; =d`/BDD  
s3=s30; X7{ h/^  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Kk<MS$Ov  
%energy in waveguide 1 5Q.z#]Lg  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   dT4e[4l  
%energy in waveguide 2 Hpq?I-g<^  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   RlnJl
Y/  
%energy in waveguide 3 u|uPvbM  
for m3 = 1:1:M3                                    % Start space evolution @T8$/  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS .m \y6  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; /%5X:*:H  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; z{ydP Ra  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Th\t6K~  
   sca2 = fftshift(fft(s2)); +Rb0:r>kU  
   sca3 = fftshift(fft(s3)); Tv`-h  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   #+6t|  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 4KCJ(<p|  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); a~"<lzu|$  
   s3 = ifft(fftshift(sc3)); 0Rze9od]$  
   s2 = ifft(fftshift(sc2));                       % Return to physical space z8\;XR  
   s1 = ifft(fftshift(sc1)); 3f^~mTY9>]  
end ^VAvQ(b!:i  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); -|&5aH]  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); s5SKQ#,@P  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); L#X!.  
   P1=[P1 p1/p10]; RmcQGQ
 
   P2=[P2 p2/p10]; Rr3<ln  
   P3=[P3 p3/p10]; +7|Qd}\X  
   P=[P p*p]; DV">9{"5']  
end  LAfv1  
figure(1) Nw=mSW^E  
plot(P,P1, P,P2, P,P3); cp\A xWtUZ  
c<n <!!
vi  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~