[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 ~!2fUewEu  
/3rNX}tOMH  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of wG7>2
*(  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of >KP,67  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear gsEcvkj*  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &dWGa+e  
tbR  
%fid=fopen('e21.dat','w'); (M1YOK)I  
N = 128;                       % Number of Fourier modes (Time domain sampling points) gl`J(  
M1 =3000;              % Total number of space steps KWjhkRK4]  
J =100;                % Steps between output of space \WTKw x  
T =10;                  % length of time windows:T*T0 j7Y7&x"  
T0=0.1;                 % input pulse width =oh%-Sh:  
MN1=0;                 % initial value for the space output location C{^I}p  
dt = T/N;                      % time step U`EOun,  
n = [-N/2:1:N/2-1]';           % Index |hi,]D^Kc  
t = n.*dt;   J|^XD<Y  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 CC"
a2Hu/  
u20=u10.*0.0;                  % input to waveguide 2 DMsqTB`  
u1=u10; u2=u20;                 }T\.;$f  
U1 = u1;   gt.F[q3  
U2 = u2;                       % Compute initial condition; save it in U ?t6wozib2  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. tF-l=ph}`  
w=2*pi*n./T; ;qUB[Kw  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T j0~c2  
L=4;                           % length of evoluation to compare with S. Trillo's paper 9#hp]0S6  
dz=L/M1;                       % space step, make sure nonlinear<0.05 H<fi,"X^  
for m1 = 1:1:M1                                    % Start space evolution 2bw), W  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS O%>*=h`P  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; @|t]9  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform ^swj!da  
   ca2 = fftshift(fft(u2)); f'5 6IT  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 1,OkuyXy!>  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   %>9L}OAm  
   u2 = ifft(fftshift(c2));                        % Return to physical space :NWIUN  
   u1 = ifft(fftshift(c1)); Wp:vz']V  
if rem(m1,J) == 0                                 % Save output every J steps. d`flYNg4  
    U1 = [U1 u1];                                  % put solutions in U array ;8&/JSN M  
    U2=[U2 u2]; ?0KIM
* .  
    MN1=[MN1 m1]; d oEuKT  
    z1=dz*MN1';                                    % output location
KGc.YUoE  
  end Iq,h}7C8'  
end 2(~Zl\  
hg=abs(U1').*abs(U1');                             % for data write to excel H{N},B  
ha=[z1 hg];                                        % for data write to excel PknKzrEG:>  
t1=[0 t']; ~4FzA,,  
hh=[t1' ha'];                                      % for data write to excel file 2BF455e   
%dlmwrite('aa',hh,'\t');                           % save data in the excel format yevJA?C4 v  
figure(1) t,/8U  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2!W[ff@~7  
figure(2) >\:GFD{z  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Ths~8{dMb  
<Rn-B).3bs  
非线性超快脉冲耦合的数值方法的Matlab程序 +UX~
't_'v  
_U4@W+lhX_  
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。   O9?.J,,mVh  
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 P* &0HbJ  
l"`VvW[  
P/WGB~NH  
S~fP$L5  
%  This Matlab script file solves the nonlinear Schrodinger equations m(9I+
`  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ^;s/4  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear l8+)Xk>  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 rf
]z5;  
JtMl/h  
C=1;                           NhNd+SCZ@  
M1=120,                       % integer for amplitude Qt>kythi  
M3=5000;                      % integer for length of coupler 5+oY c-  
N = 512;                      % Number of Fourier modes (Time domain sampling points) \P":V  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. pYAKA1F  
T =40;                        % length of time:T*T0. Rm)hgmZ  
dt = T/N;                     % time step )jUPMIo  
n = [-N/2:1:N/2-1]';          % Index 1oiS
mW\  
t = n.*dt;   gk?H@b*  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. X|!@%wuGC  
w=2*pi*n./T; w<h8`K`3  
g1=-i*ww./2; ~J~R.r/  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ZQ`4'|"  
g3=-i*ww./2; z(.,BB[  
P1=0; : 4-pnn  
P2=0; MxX)&327  
P3=1; -W@nc QL}  
P=0; [Rq|;p  
for m1=1:M1                 `DSFaBj,  
p=0.032*m1;                %input amplitude {%k[Z9*tO  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 `~lG5|  
s1=s10; D'ZUbAh!  
s20=0.*s10;                %input in waveguide 2 lg )xQV  
s30=0.*s10;                %input in waveguide 3 ~(tt.l#  
s2=s20; 2g5 4<G*e  
s3=s30; 8q6Le{G  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   FwB xag:u  
%energy in waveguide 1 )Kl@dj  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   gG.+3=  
%energy in waveguide 2 0(u}z  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   !UPB4I  
%energy in waveguide 3 k^;/@:  
for m3 = 1:1:M3                                    % Start space evolution u^]Gc p  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS bW/T}FND  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; =Xid"$  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; l'2vo=IQ  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Df2$2VU  
   sca2 = fftshift(fft(s2)); W;!V_-:  
   sca3 = fftshift(fft(s3)); iKaS7lWH  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   3rN}iSF^  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @sZ' --Y  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); "^{Hta  
   s3 = ifft(fftshift(sc3)); 9)=bBQyr:  
   s2 = ifft(fftshift(sc2));                       % Return to physical space :TKx>~`  
   s1 = ifft(fftshift(sc1)); g%^/^<ei  
end KkzG#'I1  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); (NfB+Ue}  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); iDgc$'%?  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); In:V.'D/>t  
   P1=[P1 p1/p10]; mrKIiaU<J  
   P2=[P2 p2/p10]; 4T$jY}U  
   P3=[P3 p3/p10]; *Ev8f11i&  
   P=[P p*p]; wpQp1){%Q  
end x+'Ea.^  
figure(1) 4XiQ8
"C  
plot(P,P1, P,P2, P,P3); 9|@5eN:N  
-cn`D2RP  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~