计算脉冲在非线性耦合器中演化的Matlab 程序 A_|X54}w& "!PN + gB % This Matlab script file solves the coupled nonlinear Schrodinger equations of
bN>|4hS % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GbBz;ZV%z, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
wf,w%n % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
VP"C|j^I XchVsA %fid=fopen('e21.dat','w');
aq.Lnbi/X N = 128; % Number of Fourier modes (Time domain sampling points)
C\1x3 M1 =3000; % Total number of space steps
x I(X+d`` J =100; % Steps between output of space
JS(%: T =10; % length of time windows:T*T0
%OT?2-d T0=0.1; % input pulse width
<;zcz[~ MN1=0; % initial value for the space output location
>8w=Vlp dt = T/N; % time step
[xl+/F7 n = [-N/2:1:N/2-1]'; % Index
|OO2>(Fj t = n.*dt;
ko`KAU<T_ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
#Dl=K <I u20=u10.*0.0; % input to waveguide 2
aHSl _[ u1=u10; u2=u20;
N=TDywRI U1 = u1;
|j !U/n.%w U2 = u2; % Compute initial condition; save it in U
t ;bU #THM ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&h;J _Ps w=2*pi*n./T;
hixG/%aO g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ge$ p/ L=4; % length of evoluation to compare with S. Trillo's paper
2NZC,znQ dz=L/M1; % space step, make sure nonlinear<0.05
,<]~/5-f for m1 = 1:1:M1 % Start space evolution
?;CMsO*q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^ <+V[ =X u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}+GIrEDId ca1 = fftshift(fft(u1)); % Take Fourier transform
B x ru7E" ca2 = fftshift(fft(u2));
sf'+; c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
_{y4N0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
_"S1>s)X?j u2 = ifft(fftshift(c2)); % Return to physical space
nb #)$l u1 = ifft(fftshift(c1));
:lp
V if rem(m1,J) == 0 % Save output every J steps.
FYX" q -Z U1 = [U1 u1]; % put solutions in U array
{4HcecT U2=[U2 u2];
XjU/7Q MN1=[MN1 m1];
j @Y'>3 z1=dz*MN1'; % output location
7uxUqM end
\CZD.2p# & end
50NLgu E hg=abs(U1').*abs(U1'); % for data write to excel
d\j[O9W> ha=[z1 hg]; % for data write to excel
Zo T 8 t1=[0 t'];
2#xz,RM. hh=[t1' ha']; % for data write to excel file
iJ!p9E*( %dlmwrite('aa',hh,'\t'); % save data in the excel format
[IPXU9& Q figure(1)
,*d<hBGbh waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
! ^TCe8 figure(2)
6~! l7HqO waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
H.*aVb$ XywsjeI4 非线性超快脉冲耦合的数值方法的Matlab程序 P,={ C6* Y3?)*kz% 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。
7s}E q~ 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
L_Lhmtm}m I9O%/^5^[w -~WDv[ [ (Kb_/ % This Matlab script file solves the nonlinear Schrodinger equations
p{oc}dWin % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
}C<$q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V~"-\@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O("13cU n1;zml:7_ C=1;
WADA p\& M1=120, % integer for amplitude
^H~g7&f9?N M3=5000; % integer for length of coupler
2d JP|T9H N = 512; % Number of Fourier modes (Time domain sampling points)
(u-eL# @ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
l3HfaCP6: T =40; % length of time:T*T0.
NM0s*s42 dt = T/N; % time step
y4j\y
?
T8 n = [-N/2:1:N/2-1]'; % Index
-X_dY>>s t = n.*dt;
<7Ry"z6g; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>h{) 7Hv w=2*pi*n./T;
/<T3^/ ' g1=-i*ww./2;
wL~- k
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
u Xo? g3=-i*ww./2;
j kV 9$W0 P1=0;
{B7${AE P2=0;
>Q[3t79 ^ P3=1;
.njk^,N P=0;
8M8Odz\3 q for m1=1:M1
lkJ"f{4f p=0.032*m1; %input amplitude
i>%A0.9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
yz^4TqJ s1=s10;
kV@?Oj.&I, s20=0.*s10; %input in waveguide 2
XWag+ K s30=0.*s10; %input in waveguide 3
V2 >+s
y s2=s20;
U%rq(`;
s3=s30;
Fuy"JmeR
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=[nuesP' %energy in waveguide 1
c;.jo?RR2 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
m"GgaH3, %energy in waveguide 2
r2T$
;m. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
L'u*WHj|v %energy in waveguide 3
;. Y-e
Q, for m3 = 1:1:M3 % Start space evolution
K8RV=3MBLD s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
i $lp8Y2ih s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
qFN`pe, s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
rVZ l v3 sca1 = fftshift(fft(s1)); % Take Fourier transform
Q PrP3D K sca2 = fftshift(fft(s2));
D-LQQ{!D5 sca3 = fftshift(fft(s3));
` APeS=<
& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
-8:/My sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
m,V"S(A sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Scfe6+\EW s3 = ifft(fftshift(sc3));
{'sp8:$a s2 = ifft(fftshift(sc2)); % Return to physical space
\hI|I!sDWy s1 = ifft(fftshift(sc1));
aRy" _dZ2 end
1|:'jK#gE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
TgA>( HcO p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
){*9$486 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
T'!p{Fbg; P1=[P1 p1/p10];
lQ&J2H<w P2=[P2 p2/p10];
p# JPLCs P3=[P3 p3/p10];
^Q9K] Vo P=[P p*p];
J w0I$W/ end
lof P$ figure(1)
eh}|Wd7J plot(P,P1, P,P2, P,P3);
IO7 cRg'-F ( 'Ha$O72 转自：
http://blog.163.com/opto_wang/
