[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 V/zmbo)  
\C4wWh-A  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ^)C#  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of [a?bv7K
z  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ngI+afo   
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 y9
w,Su2  
>qmNT/  
%fid=fopen('e21.dat','w'); w^,Xa  
N = 128;                       % Number of Fourier modes (Time domain sampling points) y,w_x,m  
M1 =3000;              % Total number of space steps $RUK<JN$6  
J =100;                % Steps between output of space zS h9`F  
T =10;                  % length of time windows:T*T0 }}k*i0  
T0=0.1;                 % input pulse width qVH.I6)  
MN1=0;                 % initial value for the space output location 9<3fH J?vq  
dt = T/N;                      % time step ?CcX>R-/  
n = [-N/2:1:N/2-1]';           % Index COmu.'%*  
t = n.*dt;   34nfL: y  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 bW=3X-)  
u20=u10.*0.0;                  % input to waveguide 2 dczSW]%  
u1=u10; u2=u20;                 %5nEyZOq  
U1 = u1;   p(K^Zc  
U2 = u2;                       % Compute initial condition; save it in U )d2:r 07a  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 1}+b4"7]  
w=2*pi*n./T; M^>l>?#rl  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T &0fV;%N  
L=4;                           % length of evoluation to compare with S. Trillo's paper XODp[+xEEt  
dz=L/M1;                       % space step, make sure nonlinear<0.05 S4-jFD)U  
for m1 = 1:1:M1                                    % Start space evolution
H4j1yD(d  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS *'\HG  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ZX8@/8sv  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 5HE5$S  
   ca2 = fftshift(fft(u2)); 69apTx  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation radP%W-U  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ~tZB1+%)  
   u2 = ifft(fftshift(c2));                        % Return to physical space "fUNrhCx  
   u1 = ifft(fftshift(c1)); 6a_U[-a9;  
if rem(m1,J) == 0                                 % Save output every J steps. MUGoW;}v)  
    U1 = [U1 u1];                                  % put solutions in U array }[h]z7e2S  
    U2=[U2 u2]; g1.u1}  
    MN1=[MN1 m1]; J@}PySq  
    z1=dz*MN1';                                    % output location G6G-qqXy6  
  end (:?bQA'Td  
end +{C)^!zBK  
hg=abs(U1').*abs(U1');                             % for data write to excel rK`^A  
ha=[z1 hg];                                        % for data write to excel Q w - z  
t1=[0 t']; {9.UeVz  
hh=[t1' ha'];                                      % for data write to excel file o4Cq  /K  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format h.KgHMV`  
figure(1) ;Krb/qr4_  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn  + #E?)  
figure(2) dUl"w`3  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn )Q>Ao.  
B& R?{y*  
非线性超快脉冲耦合的数值方法的Matlab程序 wu`+KUx  
>]C/ Q6  
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。   11kyrv  
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 ('$*QC.M  
V\opC6*L_e  
!H{>c@i  
O:pg+o&  
%  This Matlab script file solves the nonlinear Schrodinger equations DT)][V^w  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of k;2.g$)W[c  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear =&qH%S
6  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 YRr,{[e  
$xq04ejJ  
C=1;                           d_0(;'
 
M1=120,                       % integer for amplitude UK1)U)*+  
M3=5000;                      % integer for length of coupler .:B>xg~2  
N = 512;                      % Number of Fourier modes (Time domain sampling points) DHx&%]r;D  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. P8|ANe1 v  
T =40;                        % length of time:T*T0. AI#.+PrC{/  
dt = T/N;                     % time step m%>}T75C^  
n = [-N/2:1:N/2-1]';          % Index O8_!!Qd  
t = n.*dt;   l^B4.1rT  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. vyB{35p$  
w=2*pi*n./T; @:#J^CsM+'  
g1=-i*ww./2; aNNRw(0/  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; (_CvN=A  
g3=-i*ww./2; 3 H5  
P1=0; &=$f\O1Ty  
P2=0;
b6sf1E  
P3=1; e84%Y8,0  
P=0; dv3u<XM~  
for m1=1:M1                 6w{_+=T  
p=0.032*m1;                %input amplitude jw{B8<@s  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 }1~9i'o%Z  
s1=s10; js"5{w&  
s20=0.*s10;                %input in waveguide 2 >/Q^.hzd  
s30=0.*s10;                %input in waveguide 3 6sQ;Z|!Pz  
s2=s20; Ql l{;A  
s3=s30; <)T~_s  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   $x]/|u/9  
%energy in waveguide 1 "J2q|@.  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ]?wz.  
%energy in waveguide 2 CI$z+zN  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   yt="kZ  
%energy in waveguide 3 knph549  
for m3 = 1:1:M3                                    % Start space evolution ~u2f`67
{  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS alHA&YC{K  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; -T{2R:\{  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; j>:N0:  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform 
5;p
|iT  
   sca2 = fftshift(fft(s2)); |3!)  
   sca3 = fftshift(fft(s3)); Pmd[2/][  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Yk|.UuXT  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 1Q? RD%lkf  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); " M?dU^U^  
   s3 = ifft(fftshift(sc3)); aGi`(|shW  
   s2 = ifft(fftshift(sc2));                       % Return to physical space lN,a+S/'  
   s1 = ifft(fftshift(sc1)); ~wv$uL8y  
end q{f\_2[  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); %X %zK1  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Cb+$|Kg/"b  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); {cIk-nG-_  
   P1=[P1 p1/p10]; h4|}BGO  
   P2=[P2 p2/p10]; g
0U
?`;n$  
   P3=[P3 p3/p10]; Rk#'^}  
   P=[P p*p]; O_4B> )zd  
end 43M.Hj]  
figure(1) c!7WRHJE_a  
plot(P,P1, P,P2, P,P3); 1 Ga3[g  
}8aqSD<:  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~