计算脉冲在非线性耦合器中演化的Matlab 程序 NP_b~e6O=
~!A*@a C % This Matlab script file solves the coupled nonlinear Schrodinger equations of
O!=ae| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&Y/Myh[P % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~ |t 7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`PVr;& 2^.qKY@g@ %fid=fopen('e21.dat','w');
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\GB:#:X N = 128; % Number of Fourier modes (Time domain sampling points)
% @9pn1, M1 =3000; % Total number of space steps
n 0*a. J =100; % Steps between output of space
yw3E$~ k T =10; % length of time windows:T*T0
~DJ >)pp T0=0.1; % input pulse width
lmjoSINy MN1=0; % initial value for the space output location
5l
ioL) dt = T/N; % time step
eO?.8OM-a n = [-N/2:1:N/2-1]'; % Index
5^W},:3R t = n.*dt;
JDA :)[; u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
`3KXWN`.s u20=u10.*0.0; % input to waveguide 2
qh<h|C ]V u1=u10; u2=u20;
%/r}_V(UN U1 = u1;
'.8E _Jd0E U2 = u2; % Compute initial condition; save it in U
5\6S5JyIL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
( g>>
w=2*pi*n./T;
gBZ1We u-' g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
gfW8s+ L=4; % length of evoluation to compare with S. Trillo's paper
eJv_`#R&Of dz=L/M1; % space step, make sure nonlinear<0.05
5C^oqUZ for m1 = 1:1:M1 % Start space evolution
E)h&<{% u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`*`@r o u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
q=H
dGv ca1 = fftshift(fft(u1)); % Take Fourier transform
W@( EEMhw ca2 = fftshift(fft(u2));
I8RPW:B; B c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
5 u=(zg c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
]*M-8_D u2 = ifft(fftshift(c2)); % Return to physical space
E"|LA[o
u1 = ifft(fftshift(c1));
/ y.+N`_ if rem(m1,J) == 0 % Save output every J steps.
cJ >
#jl& U1 = [U1 u1]; % put solutions in U array
<,S5(pZ U2=[U2 u2];
l( CMP!mY MN1=[MN1 m1];
Q lmZ4fT[r z1=dz*MN1'; % output location
t|ih{0 end
& 1 : _+ end
$aFCe}3b< hg=abs(U1').*abs(U1'); % for data write to excel
:"pA0oB ha=[z1 hg]; % for data write to excel
`- \J/I t1=[0 t'];
E>}(r%B hh=[t1' ha']; % for data write to excel file
! Xzne_V< %dlmwrite('aa',hh,'\t'); % save data in the excel format
?^<
E#2a figure(1)
x=%p~$C waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
#J,?oe=<4 figure(2)
2{sx"/k\A waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
T|{1,wP { vf"`#Q9 非线性超快脉冲耦合的数值方法的Matlab程序 %FDv6peH ^D=1%@l?# 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。
i#lnSJ08 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
s? irT;= % }nNwuJ b,8\i|*!f ~rN:4Q]/ % This Matlab script file solves the nonlinear Schrodinger equations
a->;K+ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
z~S(OM@olJ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Pr%Y!| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
TB GN',, ey~5DY7 C=1;
j<HBzqP%6 M1=120, % integer for amplitude
ds*N1[
* M3=5000; % integer for length of coupler
#'@pL0dj N = 512; % Number of Fourier modes (Time domain sampling points)
t Lz,t&h dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
R@+%~"Z T =40; % length of time:T*T0.
l.
9
i ` dt = T/N; % time step
:?*|D p1 n = [-N/2:1:N/2-1]'; % Index
Ju"* ;/ t = n.*dt;
!m*
YPY31 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1T agQ w=2*pi*n./T;
"
aEk#W g1=-i*ww./2;
Y M <8>d g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
=nQgS.D g3=-i*ww./2;
$E j;CN59 P1=0;
N}j]S{j}' P2=0;
su/!<y P3=1;
jc4#k+sb P=0;
mO6rj=L^ for m1=1:M1
/{[Y l[{"< p=0.032*m1; %input amplitude
3u)NkS= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
[%);N\o2Y s1=s10;
*Va ;ra(V2 s20=0.*s10; %input in waveguide 2
> ;$C@ s30=0.*s10; %input in waveguide 3
k"kGQk4 s2=s20;
x?aNK$A~X s3=s30;
G` _LD+ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
t+ ,' %energy in waveguide 1
GV+K]
KDI p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
e|t@"MxvC %energy in waveguide 2
Q1A_hW2 x p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
m ll-cp %energy in waveguide 3
bc?\lD$ $ for m3 = 1:1:M3 % Start space evolution
J@Qt (rRxi s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
$:7 T s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
al<;*n{/ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
6/%dD DU sca1 = fftshift(fft(s1)); % Take Fourier transform
_V jfH2Y sca2 = fftshift(fft(s2));
VP7g::Ab sca3 = fftshift(fft(s3));
wb#ZRmx} sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
k3HPY}- sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
R;G"LT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
#{m~=1%;Ya s3 = ifft(fftshift(sc3));
K~C6dy
s2 = ifft(fftshift(sc2)); % Return to physical space
h yHeyDO2 s1 = ifft(fftshift(sc1));
<WH u</ end
,esryFRG p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
g+X .8>= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
^Uj\s / p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
*&=sL P1=[P1 p1/p10];
^5MPK@)c,/ P2=[P2 p2/p10];
\6{w#HsP8 P3=[P3 p3/p10];
D?Mj<|| P=[P p*p];
l"{1v ~I end
17
k9h?s* figure(1)
j$<sq plot(P,P1, P,P2, P,P3);
SU,#:s( *N C9S,eSP 转自：
http://blog.163.com/opto_wang/
