计算脉冲在非线性耦合器中演化的Matlab 程序 n.0fVV-A
M/K5#8Arj % This Matlab script file solves the coupled nonlinear Schrodinger equations of
8X|-rM{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
D,FkB"ZZE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
XOS[No~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
C 3YT1tK o`*,|Nsq %fid=fopen('e21.dat','w');
C~iL3C b N = 128; % Number of Fourier modes (Time domain sampling points)
S^ \Vgi( M1 =3000; % Total number of space steps
kPLxEwl J =100; % Steps between output of space
<e</m)j T =10; % length of time windows:T*T0
pIX`MlBdF T0=0.1; % input pulse width
p.?rey<% MN1=0; % initial value for the space output location
3/n5#&c\4 dt = T/N; % time step
N<injx n = [-N/2:1:N/2-1]'; % Index
)I.$=s t = n.*dt;
omBoo5e u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
&KRX[2 u20=u10.*0.0; % input to waveguide 2
/ s}} &u/ u1=u10; u2=u20;
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R U1 = u1;
Q$@I"V&G. U2 = u2; % Compute initial condition; save it in U
y_lU=(%Jd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
YcpoL@ab w=2*pi*n./T;
9mTJ|sN:e g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|8tilOqI L=4; % length of evoluation to compare with S. Trillo's paper
D!IY&H,wo dz=L/M1; % space step, make sure nonlinear<0.05
QB'aON\S for m1 = 1:1:M1 % Start space evolution
A2jUmK.& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*CI#+P u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
G*P#]eO ca1 = fftshift(fft(u1)); % Take Fourier transform
81
sG ca2 = fftshift(fft(u2));
YteO 6A;
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
IB] l1< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
DN5 7p!z u2 = ifft(fftshift(c2)); % Return to physical space
wcY? rE9 u1 = ifft(fftshift(c1));
}?Ai87-{ if rem(m1,J) == 0 % Save output every J steps.
wEvVL U1 = [U1 u1]; % put solutions in U array
( 0_2sfS U2=[U2 u2];
XuM'_FN`A< MN1=[MN1 m1];
:^B1~p(?sK z1=dz*MN1'; % output location
RdR p.pb8 end
*wB 1 ,U{ end
%/ #NK1&M hg=abs(U1').*abs(U1'); % for data write to excel
_^%,x ha=[z1 hg]; % for data write to excel
ExL0?FemWV t1=[0 t'];
N U` hh=[t1' ha']; % for data write to excel file
VQ9/Gxdeo %dlmwrite('aa',hh,'\t'); % save data in the excel format
lp%pbx43s figure(1)
C1 GKLl~ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
^yN&ZI3P& figure(2)
t=W}SH waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
57']#j#"hj [j/9neay e 非线性超快脉冲耦合的数值方法的Matlab程序 hy"\RW UJ')I`zuI 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。
K/yxE|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
:(* V?WI 9 X`Sm}i jLHkOk5{: @>Km_A x % This Matlab script file solves the nonlinear Schrodinger equations
x\G'kEd % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
5f K_Aq{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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y= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
A0 C,tVd 4yA+ h2 C=1;
O`t&ldU M1=120, % integer for amplitude
9gK` E M3=5000; % integer for length of coupler
Sp]0c[37R N = 512; % Number of Fourier modes (Time domain sampling points)
!9VY|&fHe dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
#yF&X(% T =40; % length of time:T*T0.
<
!C)x dt = T/N; % time step
m'=Cr ei n = [-N/2:1:N/2-1]'; % Index
nV /G8SeI t = n.*dt;
}-2 2XYh ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
h_,i&d@( w=2*pi*n./T;
0gP}zM73 g1=-i*ww./2;
'/p/8V.O. g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~H<6gN<j(. g3=-i*ww./2;
oDA XiY$u P1=0;
6wjw ^m0 P2=0;
#rQ2gx4 P3=1;
A d9 }9!< P=0;
~t~k2^)|" for m1=1:M1
fW1CFRHH p=0.032*m1; %input amplitude
%axh`xK# s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
}?_?V&K| s1=s10;
,77d(bR < s20=0.*s10; %input in waveguide 2
` *N [jm" s30=0.*s10; %input in waveguide 3
SBk4_J/_ s2=s20;
k1 Y ? s3=s30;
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gt p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)e=D(qd %energy in waveguide 1
Gd xnpE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
E`usknf>l %energy in waveguide 2
pG^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
_P 3G %energy in waveguide 3
e>7>j@(K] for m3 = 1:1:M3 % Start space evolution
qUW!
G&R s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}9# r0Vja s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
!v_|zoCEj s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
oC: {aK6\ sca1 = fftshift(fft(s1)); % Take Fourier transform
g- </ua(j sca2 = fftshift(fft(s2));
g<; q.ZylT sca3 = fftshift(fft(s3));
U!?_W=? sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
iDz++VNV sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
%XoiVlT@: sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{
Vf XsI s3 = ifft(fftshift(sc3));
r Iu$ pZO s2 = ifft(fftshift(sc2)); % Return to physical space
GxI!{oi2 s1 = ifft(fftshift(sc1));
y@: h4u"3 end
#64-~NVL_ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
lH x^D;m6 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
):6 8%, p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Q4!_>YZ P1=[P1 p1/p10];
n&;85IF1 P2=[P2 p2/p10];
fo#fg8zX% P3=[P3 p3/p10];
6azGhxh P=[P p*p];
i$:*Pb3mV end
'qb E= figure(1)
F^ t DL: plot(P,P1, P,P2, P,P3);
L~rBAIdD HV!m8k=6 转自：
http://blog.163.com/opto_wang/
