计算脉冲在非线性耦合器中演化的Matlab 程序 %Jn5M(myC ?#_ _# % This Matlab script file solves the coupled nonlinear Schrodinger equations of
}J= z O8OL % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
7.C]ZcU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5a* Awv} % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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kvVE &HJ~\6r\ %fid=fopen('e21.dat','w');
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%{ N = 128; % Number of Fourier modes (Time domain sampling points)
*oIKddZh M1 =3000; % Total number of space steps
#elaz8 5 J =100; % Steps between output of space
s3M#ua#mX T =10; % length of time windows:T*T0
dRTpGz T0=0.1; % input pulse width
U9AtC.IG! MN1=0; % initial value for the space output location
(7v`5|'0 dt = T/N; % time step
\g|;7&%l3 n = [-N/2:1:N/2-1]'; % Index
#p=Wt &2 t = n.*dt;
c:}K(yAdd u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-A Nq!$E u20=u10.*0.0; % input to waveguide 2
wD[ qE u1=u10; u2=u20;
EtB56FU\ U1 = u1;
<JJi U2 = u2; % Compute initial condition; save it in U
& l~=c2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
OZh+x`' # w=2*pi*n./T;
dGc>EZSdj g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$w<~ W1\: L=4; % length of evoluation to compare with S. Trillo's paper
JDC,] dz=L/M1; % space step, make sure nonlinear<0.05
14\!FCe)! for m1 = 1:1:M1 % Start space evolution
WTh|7& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
q}5&B =2pM u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
II_MY#0X ca1 = fftshift(fft(u1)); % Take Fourier transform
Xgm9>/y ca2 = fftshift(fft(u2));
o6;VrpaNi c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&nZ.$UK< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
,#-^ u2 = ifft(fftshift(c2)); % Return to physical space
z9KsSlS ^ u1 = ifft(fftshift(c1));
0 .p $q if rem(m1,J) == 0 % Save output every J steps.
iAW oKW U1 = [U1 u1]; % put solutions in U array
%n #^#: U2=[U2 u2];
6_a.`ehtj< MN1=[MN1 m1];
O~&l.>?? z1=dz*MN1'; % output location
';7|H|,F end
({x<!5XL end
B F 6H_g hg=abs(U1').*abs(U1'); % for data write to excel
Web8"8eD ha=[z1 hg]; % for data write to excel
? 5
V-D8k t1=[0 t'];
l@YpgyqaL hh=[t1' ha']; % for data write to excel file
]t3
NA*mM %dlmwrite('aa',hh,'\t'); % save data in the excel format
'lNl><e- figure(1)
J XnPKAN waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
gf2w@CVF>= figure(2)
,@ Cru= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
u]c nbm G8?<(.pi@ 非线性超快脉冲耦合的数值方法的Matlab程序 f1>^kl3@P `0Q:d' 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
i&FC-{|Z Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^ihXM]1{G i]L K ,' ?8 C+wW tg5jS]O % This Matlab script file solves the nonlinear Schrodinger equations
LGCL*Qbsg % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.< vg[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
T }] Ao % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^NLKX5Q h?YjG^'9 C=1;
o-Idr{ M1=120, % integer for amplitude
{nOK*7+ " M3=5000; % integer for length of coupler
NI s4v(! N = 512; % Number of Fourier modes (Time domain sampling points)
cCV"(Oo[H| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
)3B5"b , T =40; % length of time:T*T0.
UmgLH Cz dt = T/N; % time step
NV-9C$<n2! n = [-N/2:1:N/2-1]'; % Index
Tz L40="F t = n.*dt;
::T<de 7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
=3SL&
:8 w=2*pi*n./T;
0XYO2 k g1=-i*ww./2;
r rwsj` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3Ob"r` g3=-i*ww./2;
j*:pW;)^ P1=0;
kdYl>M P2=0;
$=m17G D P3=1;
JN KZ' 9 P=0;
kyo ,yD for m1=1:M1
dju&Ku
p=0.032*m1; %input amplitude
NxX1 _d s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
/l$noaskX s1=s10;
xf]4!zE s20=0.*s10; %input in waveguide 2
-X}R(.}x s30=0.*s10; %input in waveguide 3
] VYl Eqe s2=s20;
ToJru s3=s30;
I3 x}F$^ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
M7> \Qk %energy in waveguide 1
Csc2 yI%3 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
,6buo~?W: %energy in waveguide 2
GKd>AP_ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
`( a^=e5 %energy in waveguide 3
^ KjqS\< for m3 = 1:1:M3 % Start space evolution
#129 i2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
er#=xqUY s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
(_08? cN s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+{w& ksk sca1 = fftshift(fft(s1)); % Take Fourier transform
L
wu;y@[ sca2 = fftshift(fft(s2));
,`7GI*Vq sca3 = fftshift(fft(s3));
/&dt! .WY^ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
si;]C~X* sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
68!f cK sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
tj&A@\/ s3 = ifft(fftshift(sc3));
5nn*)vK { s2 = ifft(fftshift(sc2)); % Return to physical space
]1[;A$7 s1 = ifft(fftshift(sc1));
;i#gk%-
2 end
`3:%F> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
%% >?<4t p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
F3' X p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
yEny2q} P1=[P1 p1/p10];
fytx({I
.a P2=[P2 p2/p10];
,'673PR P3=[P3 p3/p10];
h5gXYmk P=[P p*p];
W*m[t&; end
>dl!Ep figure(1)
K]oPh:E plot(P,P1, P,P2, P,P3);
HlSuhbi'@ Wd}mC <rv1 转自：
http://blog.163.com/opto_wang/
