计算脉冲在非线性耦合器中演化的Matlab 程序
Vc?=cQ'c UwVc!Lys % This Matlab script file solves the coupled nonlinear Schrodinger equations of
* $v`5rP % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
48"=,IrM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
-/gAb<= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@V7 1%D8{ >Z!H9] f( %fid=fopen('e21.dat','w');
l_ 0 /g^( N = 128; % Number of Fourier modes (Time domain sampling points)
uH=^ILN. M1 =3000; % Total number of space steps
jR@J1IR< J =100; % Steps between output of space
y5$AAas T =10; % length of time windows:T*T0
sq1v._^s T0=0.1; % input pulse width
VY_<c 98v MN1=0; % initial value for the space output location
w5R?9"d@ dt = T/N; % time step
~pve;(e= n = [-N/2:1:N/2-1]'; % Index
;.#l[ t = n.*dt;
X}R Q&k u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
J> %uak< u20=u10.*0.0; % input to waveguide 2
ODE^;:z ! u1=u10; u2=u20;
oC >l|?h, U1 = u1;
Q|i`s=| U2 = u2; % Compute initial condition; save it in U
3iv;4e ; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
bbA J5EqL w=2*pi*n./T;
jp viX#\S_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
}S}9Pm,: L=4; % length of evoluation to compare with S. Trillo's paper
e'L$g-;>4b dz=L/M1; % space step, make sure nonlinear<0.05
k(%h{0' for m1 = 1:1:M1 % Start space evolution
o}VW%G" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
3,$G?auW u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
4 Up \_ ca1 = fftshift(fft(u1)); % Take Fourier transform
XR.Sm<A[ ca2 = fftshift(fft(u2));
z2DjYTm[~ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g*[ DyIm c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
NkL>ru! b9 u2 = ifft(fftshift(c2)); % Return to physical space
rIo)'L$uU u1 = ifft(fftshift(c1));
3*;S%1C^ if rem(m1,J) == 0 % Save output every J steps.
]] Jg%}o U1 = [U1 u1]; % put solutions in U array
GK\`8xWE U2=[U2 u2];
wTK>U`o MN1=[MN1 m1];
3tAX4DnYrq z1=dz*MN1'; % output location
sH `(y)`_ end
}`*DMI;- end
U5pg<xI hg=abs(U1').*abs(U1'); % for data write to excel
kNDN <L ha=[z1 hg]; % for data write to excel
J sc`^a%`' t1=[0 t'];
H;=+ +Dh hh=[t1' ha']; % for data write to excel file
aH+n]J]
=) %dlmwrite('aa',hh,'\t'); % save data in the excel format
`6B jNV figure(1)
``9`Xq waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
b0abl Vk figure(2)
|6y(7Ha waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
+tSfx "Z70
jkW[ 非线性超快脉冲耦合的数值方法的Matlab程序 \V/;i.ng y`Km96 Ui 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Hb|y`O k Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
q>H f2R TOvpv @?- .GH#`j +ZU@MOni % This Matlab script file solves the nonlinear Schrodinger equations
f )K(la^' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
OZed+t= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>UDb:N[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
,a1
1&"xl (TQhO$, C=1;
)mvD2]fK M1=120, % integer for amplitude
Weu%&u- M3=5000; % integer for length of coupler
>+8Kl`2sw; N = 512; % Number of Fourier modes (Time domain sampling points)
Q\ k|pg? dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
!w #x@6yq T =40; % length of time:T*T0.
iZbY@- 3fc dt = T/N; % time step
>;M?f! n = [-N/2:1:N/2-1]'; % Index
BiI}JEp4o t = n.*dt;
^ua 8Ya ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
jUg.Y9 8 w=2*pi*n./T;
#:st>V_h g1=-i*ww./2;
Q@HW`@i g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
;&8 g3=-i*ww./2;
x;L.j7lzA; P1=0;
- D-]tL6w P2=0;
bQelU P3=1;
u iEAi P=0;
Z;4pI@ u for m1=1:M1
bL9EX$P p=0.032*m1; %input amplitude
;S_\-
]m&g s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
lX*IEAc s1=s10;
:*0l*j s20=0.*s10; %input in waveguide 2
0X'2d s30=0.*s10; %input in waveguide 3
M);@XcS s2=s20;
f~{@(g&Gl s3=s30;
z0Bw+&^]} p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<~}# Q,9 %energy in waveguide 1
JZ M: R p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
G<f "_NT %energy in waveguide 2
?.%'[n>P p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
V( A p|I:G %energy in waveguide 3
13v# for m3 = 1:1:M3 % Start space evolution
B[Gl}(E s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
dD{{G :V s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
S+7:fu2?+ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
"spAYk \ sca1 = fftshift(fft(s1)); % Take Fourier transform
\ Rff3$ sca2 = fftshift(fft(s2));
a O'lk sca3 = fftshift(fft(s3));
+_h1JE_}D sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
K9 tuiD+j sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
\vR&-+8dk sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}q~M $ s3 = ifft(fftshift(sc3));
` e~nn s2 = ifft(fftshift(sc2)); % Return to physical space
">V.nao s1 = ifft(fftshift(sc1));
RO10$1IW.2 end
.tny"a& p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
)n&@`>v m p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@C34^\aH+ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
lm
1Mz P1=[P1 p1/p10];
d Lq)Z*r P2=[P2 p2/p10];
Hve' Z,X P3=[P3 p3/p10];
; Fi(zl P=[P p*p];
O%KP,q&}Y end
.2V `sg.! figure(1)
:UrS@W^B plot(P,P1, P,P2, P,P3);
">LX>uYmX- wh~g{(Xvq 转自：
http://blog.163.com/opto_wang/
