计算脉冲在非线性耦合器中演化的Matlab 程序 f\rE{% d5>EvK U % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ih|;H:"^ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
R XCj Yzt % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3ey.r%n % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q@G}Hjn i[?VF\Y( %fid=fopen('e21.dat','w');
1V wcJd N = 128; % Number of Fourier modes (Time domain sampling points)
.Y|wG<E M1 =3000; % Total number of space steps
U(PW$\l J =100; % Steps between output of space
nQOzKw<j% T =10; % length of time windows:T*T0
v, CWE T0=0.1; % input pulse width
c1q; MN1=0; % initial value for the space output location
,(RpBTV dt = T/N; % time step
(q0vql n = [-N/2:1:N/2-1]'; % Index
E/hT/BOPK t = n.*dt;
%Z+ **>1J u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
T, +=ka$ u20=u10.*0.0; % input to waveguide 2
,1g_{dMx u1=u10; u2=u20;
>=d 5Scix U1 = u1;
0x,**6 U2 = u2; % Compute initial condition; save it in U
7|o!v);uR ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mrq,kwM w=2*pi*n./T;
HOx+umjxW g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Qqi?DW1)- L=4; % length of evoluation to compare with S. Trillo's paper
2cO6' ?b dz=L/M1; % space step, make sure nonlinear<0.05
bSz@@s. for m1 = 1:1:M1 % Start space evolution
NiFe#SLA u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
+J85Re ` u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
0~EGrEt ca1 = fftshift(fft(u1)); % Take Fourier transform
[K@(,/$ ca2 = fftshift(fft(u2));
ie11syhV" c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
qDTdYf c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
v
k= |TE u2 = ifft(fftshift(c2)); % Return to physical space
d&+ 0JI< u1 = ifft(fftshift(c1));
hj& ~Dn( if rem(m1,J) == 0 % Save output every J steps.
t`'jr=e,~ U1 = [U1 u1]; % put solutions in U array
W
mbIz[un U2=[U2 u2];
f`KO#Wc MN1=[MN1 m1];
(t\U5-w z1=dz*MN1'; % output location
fdW qc_ end
-$k IVh end
?E_;[(Mcr hg=abs(U1').*abs(U1'); % for data write to excel
Z wz co ha=[z1 hg]; % for data write to excel
+I-BqA9 t1=[0 t'];
7AS_Aw1L hh=[t1' ha']; % for data write to excel file
z@ J>A![m %dlmwrite('aa',hh,'\t'); % save data in the excel format
K@JaN/OM figure(1)
[KFCc_: waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ByuBZ!m figure(2)
RJU IB waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
D)pTE?@W' } zS5o
[OE 非线性超快脉冲耦合的数值方法的Matlab程序 g1?9ge 1 uO-|? {29 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。
sa &`CEa 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
WF-jy7+ $=Ns7Sbup tHo|8c~ [ @D !*@M6 % This Matlab script file solves the nonlinear Schrodinger equations
n ((A:b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Xz)qtDN|( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}vh4ix % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%LzARTX !V(r
p 80 C=1;
f1v4h[)- M1=120, % integer for amplitude
]j>`BK>FE M3=5000; % integer for length of coupler
Cc*R3vHM6 N = 512; % Number of Fourier modes (Time domain sampling points)
3^nH>f-Y dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
dCS f$5 T =40; % length of time:T*T0.
j}B86oX dt = T/N; % time step
}IZ w6KiN n = [-N/2:1:N/2-1]'; % Index
-|^)8 t = n.*dt;
\v6 lcAL- ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+t%2V? w=2*pi*n./T;
$/|) ,n g1=-i*ww./2;
A6 .wXv, g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
,Pcg+^A g3=-i*ww./2;
.4 U*.Rf
P1=0;
*!JB^5(H P2=0;
In?#?:Q@& P3=1;
Z]R#F0 "U P=0;
'2i !RT- for m1=1:M1
@tY]=pqn_ p=0.032*m1; %input amplitude
oSmETk\ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
"OK [uug s1=s10;
:U P8nq s20=0.*s10; %input in waveguide 2
~Gz9pBv1 s30=0.*s10; %input in waveguide 3
#T2J + s2=s20;
z'$1$ ~I s3=s30;
=EMB~i p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
}mK,Bi ?bj %energy in waveguide 1
"O0xh_Nr p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
}.&;NgZS %energy in waveguide 2
&mmaoWR p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
d)bsyZ;U %energy in waveguide 3
|% F,n2 for m3 = 1:1:M3 % Start space evolution
mICEJ\`x s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
.?Y"o3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%b<W]HwA s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
+x}9a~QG# sca1 = fftshift(fft(s1)); % Take Fourier transform
d?J&mLQ6 sca2 = fftshift(fft(s2));
72"H#dy%U sca3 = fftshift(fft(s3));
Q2- lHn^L: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
L;$>SLl, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ltDohm? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
:&TM0O s3 = ifft(fftshift(sc3));
Z:7eroZP s2 = ifft(fftshift(sc2)); % Return to physical space
rvy%8%e? s1 = ifft(fftshift(sc1));
tkcs6uy end
1u7D:h># p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
V0_tk" p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@WS77d~S p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
< A8>To< P1=[P1 p1/p10];
IF0!@f P2=[P2 p2/p10];
[V:~j1{3 P3=[P3 p3/p10];
&xN+a{& P=[P p*p];
I2}eFz&FE end
"QNQ00[T`> figure(1)
g ,EDE6`8 plot(P,P1, P,P2, P,P3);
N;'c4=M~( bA#9'Qu^j
转自：
http://blog.163.com/opto_wang/
