计算脉冲在非线性耦合器中演化的Matlab 程序 &Yf",KcL*I b #/i.!:a % This Matlab script file solves the coupled nonlinear Schrodinger equations of
NG" yPn % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\gItZ}+c4} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
A2NF<ZsD % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-f9]v9|l 7)^:8I( %fid=fopen('e21.dat','w');
;wR ' z$8 N = 128; % Number of Fourier modes (Time domain sampling points)
Z19m@vMsIP M1 =3000; % Total number of space steps
cwe1^SJ 6y J =100; % Steps between output of space
.'1SZe7O T =10; % length of time windows:T*T0
|CIC$ 2u T0=0.1; % input pulse width
s]H^wrg& MN1=0; % initial value for the space output location
pjw aL^ dt = T/N; % time step
Y % Ieg.o n = [-N/2:1:N/2-1]'; % Index
\G>Zk gU t = n.*dt;
}"_j0ax u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
u[")*\ CP u20=u10.*0.0; % input to waveguide 2
=X-Tcj?3g u1=u10; u2=u20;
J[@um: U1 = u1;
Dx-KMiQ,"( U2 = u2; % Compute initial condition; save it in U
$*\L4<( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
f<<r TE6 w=2*pi*n./T;
R J~ %0 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
brSi< L=4; % length of evoluation to compare with S. Trillo's paper
=P`~t<ajB dz=L/M1; % space step, make sure nonlinear<0.05
_<zfQZai for m1 = 1:1:M1 % Start space evolution
88lxHoPV u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
S&(^<gwl u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
\NK -L."[ ca1 = fftshift(fft(u1)); % Take Fourier transform
p B p #a ca2 = fftshift(fft(u2));
A&,,9G < c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
J! TBREK c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
C4\,z\Q u2 = ifft(fftshift(c2)); % Return to physical space
bk<FL6z
z u1 = ifft(fftshift(c1));
{G3i0 r if rem(m1,J) == 0 % Save output every J steps.
#yW\5) U1 = [U1 u1]; % put solutions in U array
~@4'HMQ U2=[U2 u2];
&|Np0R MN1=[MN1 m1];
BqH]-'1G z1=dz*MN1'; % output location
%gd(wzco end
v q!uD!lr end
&:5\"b hg=abs(U1').*abs(U1'); % for data write to excel
u~1o(Zn
= ha=[z1 hg]; % for data write to excel
7 &B$HZ t1=[0 t'];
z@Hp,|Vy[ hh=[t1' ha']; % for data write to excel file
|Au ]1 } %dlmwrite('aa',hh,'\t'); % save data in the excel format
zj|WZ=1*Wp figure(1)
x\\~SGd waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+jP~s figure(2)
PdeBDFWD waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
]zf G~^. Sw[{JB;y, 非线性超快脉冲耦合的数值方法的Matlab程序 k2 Q
qZxm! xV\5<7qk5g 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。
9GLb"6+PK 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
<F=9*.@D A,gEM4 k`{7}zxS D y-S98Y % This Matlab script file solves the nonlinear Schrodinger equations
I?Aj.{{$G% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
a
W%5~3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5n lMrK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[I;^^#'P I+( /TP C=1;
^W?Z M1=120, % integer for amplitude
H%F>@(U M3=5000; % integer for length of coupler
EZD y+6b N = 512; % Number of Fourier modes (Time domain sampling points)
od' /% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
sTRJ:fR T =40; % length of time:T*T0.
I5 m][~6.? dt = T/N; % time step
.dMVoG5 n = [-N/2:1:N/2-1]'; % Index
q'Wr[A40j t = n.*dt;
B B$oq' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l fZ04M{2 w=2*pi*n./T;
E#wS_[ g1=-i*ww./2;
I@#;nyAj" g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
p[AO'
xx g3=-i*ww./2;
>slm$~rv P1=0;
rjx6Djo> P2=0;
GB7/x*u P3=1;
8fl Oq"uK^ P=0;
*J|(jdu7 for m1=1:M1
X0(tboj# p=0.032*m1; %input amplitude
vmTs9"ujF, s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
yp .[HMRD s1=s10;
7nq 3S s20=0.*s10; %input in waveguide 2
Iq7}
s30=0.*s10; %input in waveguide 3
2 {Vcb s2=s20;
T:]L/wCj s3=s30;
u"1rF^j6k p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
:#k & \f-Y %energy in waveguide 1
B~
S6R
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Cqi i} %energy in waveguide 2
q#w8wH" p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2 dp>Z", %energy in waveguide 3
YKmsQ(q`N for m3 = 1:1:M3 % Start space evolution
B.r4$:+jb2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
BVsD(
@lX s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
l5xCz=dw s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
$$APgj"|< sca1 = fftshift(fft(s1)); % Take Fourier transform
t VrY3)c sca2 = fftshift(fft(s2));
7\]E~/g sca3 = fftshift(fft(s3));
S"Lx% sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
=@2FX&&E_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
(+ uj1z ^ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
xv{O^Ie+S s3 = ifft(fftshift(sc3));
:cu #V s2 = ifft(fftshift(sc2)); % Return to physical space
k>x&Ip8p s1 = ifft(fftshift(sc1));
WQ yLf;!Lz end
p' 7*6bj1 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
l3Njq^ T p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
DejA4XdW p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
h$e En l} P1=[P1 p1/p10];
(C4fG@n P2=[P2 p2/p10];
jls-@Wl P3=[P3 p3/p10];
X\EVTd)@ P=[P p*p];
Y!iZW end
STZPYeXE figure(1)
Hbv6_ H plot(P,P1, P,P2, P,P3);
WJ<^E"^ `.s({/|[ 转自：
http://blog.163.com/opto_wang/
