计算脉冲在非线性耦合器中演化的Matlab 程序 f`8mES'gc8 1IV
R4:a % This Matlab script file solves the coupled nonlinear Schrodinger equations of
6O'6,%# % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
2V = bE- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
R%^ AW2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[;hCwj# FK.Qj P: %fid=fopen('e21.dat','w');
y7Sj^muBY N = 128; % Number of Fourier modes (Time domain sampling points)
^ _pJEX M1 =3000; % Total number of space steps
S*?x|& a J =100; % Steps between output of space
Q1?0 ]5 T =10; % length of time windows:T*T0
wv_<be[?* T0=0.1; % input pulse width
Shb"Jc_i MN1=0; % initial value for the space output location
,N`D{H"F dt = T/N; % time step
9>HCt*|_8 n = [-N/2:1:N/2-1]'; % Index
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p5D6 t = n.*dt;
cp<jwcc! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
9EKc{1
z u20=u10.*0.0; % input to waveguide 2
L\(" u1=u10; u2=u20;
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U1 = u1;
mY,t]#^m7 U2 = u2; % Compute initial condition; save it in U
h5.AM?*TNd ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l T ~A~O w=2*pi*n./T;
~Y'j8W g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
rLOdQN L=4; % length of evoluation to compare with S. Trillo's paper
R3Ka^l8R| dz=L/M1; % space step, make sure nonlinear<0.05
?br 4 wl for m1 = 1:1:M1 % Start space evolution
R
SqO$~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
zV"oB9\9O u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
UV8K$n < ca1 = fftshift(fft(u1)); % Take Fourier transform
'ai!6[|SD ca2 = fftshift(fft(u2));
om}jQJ]KH c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~ 6-6aYhe c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
_4#&!b6 u2 = ifft(fftshift(c2)); % Return to physical space
Tx\g5rk u1 = ifft(fftshift(c1));
, 1` -u$ if rem(m1,J) == 0 % Save output every J steps.
>*cg
K}!@ U1 = [U1 u1]; % put solutions in U array
Jd p@3mP
U2=[U2 u2];
JypXQC}~ MN1=[MN1 m1];
m5rJY/ z1=dz*MN1'; % output location
J}J7A5P end
dw]wQ\4B end
*QT|J 6ng hg=abs(U1').*abs(U1'); % for data write to excel
,3E9H &@ j ha=[z1 hg]; % for data write to excel
J=C63YB t1=[0 t'];
[.`%]Z( hh=[t1' ha']; % for data write to excel file
s/J/kKj*s %dlmwrite('aa',hh,'\t'); % save data in the excel format
e<[0H 8 figure(1)
K{x FhdW waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
[Y=X^"PF figure(2)
F_&bE @k waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
- *r]9f6 x ]J* y `jn 非线性超快脉冲耦合的数值方法的Matlab程序 &9F(uk=X 4%L-3Ij 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。
Om=*b#k 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
lYMNx|PF ,dO$R.h X ?l F,p 1_z6O!rx % This Matlab script file solves the nonlinear Schrodinger equations
Qo;#}%}^^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
oK3aW6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3Ta<7tEM f8' $Mn, C=1;
HAr_z@#E M1=120, % integer for amplitude
oz- k_9% M3=5000; % integer for length of coupler
(ATCP#lF N = 512; % Number of Fourier modes (Time domain sampling points)
:xP$iEA`G dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
11Hf)]M
T =40; % length of time:T*T0.
" Nn+Zw43 dt = T/N; % time step
e;/C}sK: n = [-N/2:1:N/2-1]'; % Index
p!~{<s] t = n.*dt;
T|& 2!Sh ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+#d}3^_] w=2*pi*n./T;
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C g1=-i*ww./2;
U~w g' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
4 Dd7 I g3=-i*ww./2;
VI (;8 P1=0;
K{s% h0 P2=0;
Iu -CXc P3=1;
?$T39U^ P=0;
khW9n* for m1=1:M1
9C{\=?e; p=0.032*m1; %input amplitude
Fc"&lk4e s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
F}lgy;= h s1=s10;
]U,K]y[Bj s20=0.*s10; %input in waveguide 2
l^IPN 'O@ s30=0.*s10; %input in waveguide 3
XI*_t i s2=s20;
gAY%VFBP0 s3=s30;
K~# wvUb p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
G{cTQH| %energy in waveguide 1
weOzs]uc p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
z]YP %energy in waveguide 2
Gkr^uXNg# p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Q l$t %energy in waveguide 3
s\`Vr;R:| for m3 = 1:1:M3 % Start space evolution
4P>tGO&*x s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
u%7a&1c s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
2 8j=q-9Z s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Bn"r;pqWiT sca1 = fftshift(fft(s1)); % Take Fourier transform
i~IQlyGr. sca2 = fftshift(fft(s2));
lK?
Z38 sca3 = fftshift(fft(s3));
/Jc?;@{ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
LxGE<xj|V% sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
D k'EKT- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
0)8 Q OTeT s3 = ifft(fftshift(sc3));
x Qh ? s2 = ifft(fftshift(sc2)); % Return to physical space
=oF6|\]{ ; s1 = ifft(fftshift(sc1));
4pF U` g= end
@HfWA FT p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
I~R<}volu p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
RTSR-<{z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
-%=StWdb
P1=[P1 p1/p10];
fxDY:l P2=[P2 p2/p10];
t#y P3=[P3 p3/p10];
afEp4(X~ P=[P p*p];
xrT_r o8 end
+fhyw{ figure(1)
L-d8bA plot(P,P1, P,P2, P,P3);
wYf=(w \c >5Zp x8W 转自：
http://blog.163.com/opto_wang/
