计算脉冲在非线性耦合器中演化的Matlab 程序 YF} 9k paW'R +Rck % This Matlab script file solves the coupled nonlinear Schrodinger equations of
9v~1We;{$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
pO"m~ mpA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h zaLx8L % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
UhsO\ 9}qH z *6$&sS\> %fid=fopen('e21.dat','w');
fd4;mc1T N = 128; % Number of Fourier modes (Time domain sampling points)
MWM
+hk1fs M1 =3000; % Total number of space steps
n}19?K]g J =100; % Steps between output of space
Dba+z-3Nzy T =10; % length of time windows:T*T0
QT#b>xV)1 T0=0.1; % input pulse width
XjX 2[*l MN1=0; % initial value for the space output location
c
Qld$ dt = T/N; % time step
k_]\(myq n = [-N/2:1:N/2-1]'; % Index
F?7u~b|@{ t = n.*dt;
P,(9c yS{ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
%fHH {60 u20=u10.*0.0; % input to waveguide 2
!0` lu_ZN u1=u10; u2=u20;
GF&_~48GD U1 = u1;
SijtTY#r U2 = u2; % Compute initial condition; save it in U
&a.']!$^" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ZQ|5W6c w=2*pi*n./T;
a;%I\w;2 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
;:P7}v fz! L=4; % length of evoluation to compare with S. Trillo's paper
8Bq- 0=E dz=L/M1; % space step, make sure nonlinear<0.05
iBucT"d] for m1 = 1:1:M1 % Start space evolution
^D >fis u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
d$}&nV/A) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
UanEzx% ca1 = fftshift(fft(u1)); % Take Fourier transform
2zhn`m ca2 = fftshift(fft(u2));
j(sLK
& c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Z%#^xCz;w> c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
F "I*-!o u2 = ifft(fftshift(c2)); % Return to physical space
22z1g(; @ u1 = ifft(fftshift(c1));
:W VSJ,. ! if rem(m1,J) == 0 % Save output every J steps.
p+$+MeBz U1 = [U1 u1]; % put solutions in U array
#*^e,FF< U2=[U2 u2];
wZQ)jo7*g MN1=[MN1 m1];
d , UCH z1=dz*MN1'; % output location
M_Bu,<q^ end
)AI?x@ end
c+8V| '4 hg=abs(U1').*abs(U1'); % for data write to excel
ZNi
+Aw$u ha=[z1 hg]; % for data write to excel
})P O7: t1=[0 t'];
Y3k[~A7X hh=[t1' ha']; % for data write to excel file
Hte[TRb M %dlmwrite('aa',hh,'\t'); % save data in the excel format
`%Q&</X figure(1)
:5jexz."M waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
T Ko<~? figure(2)
/[%w*v*' waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9mDn KW NEw $q4 非线性超快脉冲耦合的数值方法的Matlab程序 q4/909x= `Ug t vo 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。
o,1Dqg4P3 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
gX^ PSsp J:AMnUOcDi wN(&5rfS OM)3Y6rK % This Matlab script file solves the nonlinear Schrodinger equations
{rDq_^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
W qE
'( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
e\D|
o?v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}RIU8=P RU|X*3";T C=1;
et` 0Je M1=120, % integer for amplitude
aBxiK[[` M3=5000; % integer for length of coupler
%m`zWg- N = 512; % Number of Fourier modes (Time domain sampling points)
$Asr`Q1i
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
WI&lj<* T =40; % length of time:T*T0.
xzr<k Sp dt = T/N; % time step
LTXz$Z] n = [-N/2:1:N/2-1]'; % Index
w#9_eq|3 t = n.*dt;
|c gui ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ys3uPs w=2*pi*n./T;
ezUQ>
e g1=-i*ww./2;
DW>ES/B8$( g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
f@d9Hqr+l; g3=-i*ww./2;
,EI:gLH P1=0;
wXbsS)#/ P2=0;
I3(d<+M P3=1;
gi$XB}L+X P=0;
"}zt`3 for m1=1:M1
nZ
E )_ p=0.032*m1; %input amplitude
2khh4?| \ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
? :uNN s1=s10;
$(rc/h0/E s20=0.*s10; %input in waveguide 2
v@n_F s30=0.*s10; %input in waveguide 3
t7* #[x)a s2=s20;
50$W0L$ s3=s30;
I2[]A,f , p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=wrP:wYF %energy in waveguide 1
>;9NtoE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
l'"'o~MC %energy in waveguide 2
Wekqn !h p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
:FHA]o ec1 %energy in waveguide 3
:kG)sw7 for m3 = 1:1:M3 % Start space evolution
%u!b& 5]e s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|`0 n" x7 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
B<,YPS8w s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
FFvCi@oT sca1 = fftshift(fft(s1)); % Take Fourier transform
JvL{| KtyU sca2 = fftshift(fft(s2));
Ch5+N6c^ sca3 = fftshift(fft(s3));
O|'1B>X sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;gB `YNL sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
+}JM&bfK sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
76@qHTh } s3 = ifft(fftshift(sc3));
GBQn_(b9I s2 = ifft(fftshift(sc2)); % Return to physical space
rL v;Y s1 = ifft(fftshift(sc1));
s&Y i 6:J end
z 7T0u.4Ss p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
r\qz5G *6 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
N$#\Xdo p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Dl,`\b@Fw3 P1=[P1 p1/p10];
N+g@8Q2s;5 P2=[P2 p2/p10];
[po " To P3=[P3 p3/p10];
fY W|p<Q0 P=[P p*p];
."6[:MF end
5o 0Ch figure(1)
SSA W5 2xC plot(P,P1, P,P2, P,P3);
z]@6fM[ Vw~\H Gs/~ 转自：
http://blog.163.com/opto_wang/
