计算脉冲在非线性耦合器中演化的Matlab 程序 >9+h2B
0..]c-V(G % This Matlab script file solves the coupled nonlinear Schrodinger equations of
F T$x#> % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
w{"ro~9o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
d",VOhW7)S % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Vv_lBYV {' UK> S %fid=fopen('e21.dat','w');
8zrLl :{ N = 128; % Number of Fourier modes (Time domain sampling points)
y[DS$>E M1 =3000; % Total number of space steps
% pQi}x J =100; % Steps between output of space
W690N&Wz T =10; % length of time windows:T*T0
~[Z,:=z T0=0.1; % input pulse width
DR(/|?k+ MN1=0; % initial value for the space output location
pn p)- a*7 dt = T/N; % time step
h#}'9oA n = [-N/2:1:N/2-1]'; % Index
/2x@Z> t = n.*dt;
1xDh[:6 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
#By~gcN u20=u10.*0.0; % input to waveguide 2
sEHA?UP$<F u1=u10; u2=u20;
sI5S)^'IQ U1 = u1;
|.?X ov] U2 = u2; % Compute initial condition; save it in U
YZZog 6% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kL e{3>}j w=2*pi*n./T;
6){nu rDBG g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
c+ukVn`r L=4; % length of evoluation to compare with S. Trillo's paper
& R,QJ4L dz=L/M1; % space step, make sure nonlinear<0.05
PB;j4 for m1 = 1:1:M1 % Start space evolution
c@x6<S%* u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
H+5S )r u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
)S^[b2P]y_ ca1 = fftshift(fft(u1)); % Take Fourier transform
"]}?{ 2i;
ca2 = fftshift(fft(u2));
i}/Het+( c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
T-y5U}, c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
`4 -m$ab u2 = ifft(fftshift(c2)); % Return to physical space
o]aMhSol u1 = ifft(fftshift(c1));
ke19(r Ch if rem(m1,J) == 0 % Save output every J steps.
@e2P3K gg U1 = [U1 u1]; % put solutions in U array
d Z}|G-: U2=[U2 u2];
U"535<mR MN1=[MN1 m1];
5Bp>*MR/". z1=dz*MN1'; % output location
|& _(I end
d 0 mfqP= end
7`SrqI& hg=abs(U1').*abs(U1'); % for data write to excel
.RpWE.C ha=[z1 hg]; % for data write to excel
nq:'jdY5| t1=[0 t'];
XBm ^7' hh=[t1' ha']; % for data write to excel file
;umbld0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
oA+'9/UY figure(1)
W?yGV{#V(= waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
-Yg?@yt figure(2)
0QY9vuhL< waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
5Un)d<!7&u +wcif - 非线性超快脉冲耦合的数值方法的Matlab程序 wPvYnhr|G- +@d gHDJ 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。
$pajE^d4V Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
p7Z/%~0v: CcZM0 +8.1cDEH\ Pv\-D<&@m % This Matlab script file solves the nonlinear Schrodinger equations
SN;_.46k % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
h]W W?. % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
P,)\#([vc % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|XJ|vQGU |N0RBa4% C=1;
x{3q'2 M1=120, % integer for amplitude
(^$SM uC M3=5000; % integer for length of coupler
MPMAFs N = 512; % Number of Fourier modes (Time domain sampling points)
/\U:F dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
fJ;1ii~ T =40; % length of time:T*T0.
|u.3Tp|3W dt = T/N; % time step
(H-kWT n = [-N/2:1:N/2-1]'; % Index
O )INM t = n.*dt;
WfYC`e7q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
z
q@"qnr w=2*pi*n./T;
%t%D|cf g1=-i*ww./2;
toel!+ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~8Ez K_c g3=-i*ww./2;
P9M. J^< P1=0;
Ph17(APt,Q P2=0;
9-E dT4=r, P3=1;
5>>JQ2'W P=0;
c3J12+~; for m1=1:M1
q{pa _ p=0.032*m1; %input amplitude
i!+0''i{# s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
|H;+9( s1=s10;
LzD,]{CC5 s20=0.*s10; %input in waveguide 2
Q1P=A:*]9 s30=0.*s10; %input in waveguide 3
@"n]v)[4 s2=s20;
I[P_j`aE s3=s30;
RP%FMb}nt p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]%+T+ zg(Y %energy in waveguide 1
/|8/C40aY p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
bdHHOpXM %energy in waveguide 2
8b< ' jft p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Ie/dMB=t %energy in waveguide 3
V(0V$&qipc for m3 = 1:1:M3 % Start space evolution
KVPWJHGr s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
T=VBKaSbU s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
lMe+.P| s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
S&NWZ:E3[ sca1 = fftshift(fft(s1)); % Take Fourier transform
`I t3X.^} sca2 = fftshift(fft(s2));
VJgYXPE
` sca3 = fftshift(fft(s3));
_z53r+A sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
98lz2d/Fcq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ag eTv/ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
N;*
wd< s3 = ifft(fftshift(sc3));
F_~A8 y s2 = ifft(fftshift(sc2)); % Return to physical space
.DHQJ|J-1 s1 = ifft(fftshift(sc1));
$J*lD -h- end
[n&SA]a p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
, nW)A/?} p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
9S8V`aC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
yw*|
H T P1=[P1 p1/p10];
af|x(:!H P2=[P2 p2/p10];
FMz>p1s|dK P3=[P3 p3/p10];
t"X^|!hKIF P=[P p*p];
c N~F32< end
I.ku Y D62 figure(1)
13f 'zx(AO plot(P,P1, P,P2, P,P3);
+Os9}uKf ))E| SAr 转自：
http://blog.163.com/opto_wang/
