计算脉冲在非线性耦合器中演化的Matlab 程序 vPn ( ~d_ yk4Huq&2 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
d+_wN2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&!uN N|W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
DA_ [pR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Q3 M;'m ^gwVh~j %fid=fopen('e21.dat','w');
)2|'` N = 128; % Number of Fourier modes (Time domain sampling points)
`[<j5(T M1 =3000; % Total number of space steps
5h9`lS2 J =100; % Steps between output of space
GB1[`U% T =10; % length of time windows:T*T0
5 JE8/CbH T0=0.1; % input pulse width
{ CM%QMM MN1=0; % initial value for the space output location
=gCv` SFW dt = T/N; % time step
\>8"r,hG| n = [-N/2:1:N/2-1]'; % Index
sglYT!O t = n.*dt;
6OJ`R.DM` u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
f -N: u20=u10.*0.0; % input to waveguide 2
QfuKpcT & u1=u10; u2=u20;
NJG- ~ w U1 = u1;
X&1R6 O U2 = u2; % Compute initial condition; save it in U
l I&%^> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9Z,vpTE w=2*pi*n./T;
#:{Bd8PS g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
p m+_s]s, L=4; % length of evoluation to compare with S. Trillo's paper
b]v.jgD dz=L/M1; % space step, make sure nonlinear<0.05
}|rnyYA for m1 = 1:1:M1 % Start space evolution
fLj#+h-! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
d&: ABI u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Vd 2bG4 *= ca1 = fftshift(fft(u1)); % Take Fourier transform
f?wn;;z` ca2 = fftshift(fft(u2));
c} a. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
>5{Z'UWxh c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Y%v?ROql u2 = ifft(fftshift(c2)); % Return to physical space
#>+O=YO u1 = ifft(fftshift(c1));
Np4'; H if rem(m1,J) == 0 % Save output every J steps.
=,q,W$- U1 = [U1 u1]; % put solutions in U array
-hav/7g U2=[U2 u2];
@B;2z_Y!l MN1=[MN1 m1];
4^T@n$2N z1=dz*MN1'; % output location
#?)g? u%g= end
-iu7/4!j end
acgtXfHR hg=abs(U1').*abs(U1'); % for data write to excel
\IL/?J
5d ha=[z1 hg]; % for data write to excel
xEN" "*Q t1=[0 t'];
qJ=4HlLno hh=[t1' ha']; % for data write to excel file
_T6l*D %dlmwrite('aa',hh,'\t'); % save data in the excel format
C%ibIcm y figure(1)
/3F4t
V waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%./ vh=5) figure(2)
gTE/g'3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
xS%Z
H#IJ&w| 非线性超快脉冲耦合的数值方法的Matlab程序 bmT_tNz 99%oY 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
D9
~jMcX Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
L~_3BX F-?K]t# aZt5/|B }W{rDc kv % This Matlab script file solves the nonlinear Schrodinger equations
ezRhSN? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~|e?@3_G % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V!#+Ti/w4 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.i[rd4MCK i3~"qbU%z[ C=1;
B#RwW, M1=120, % integer for amplitude
okfGd=
& M3=5000; % integer for length of coupler
Tw BwqQ)t N = 512; % Number of Fourier modes (Time domain sampling points)
0 1U/{D6D dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5gnNgt~ T =40; % length of time:T*T0.
cn&\q.!fh dt = T/N; % time step
Wk$ 7< gkr n = [-N/2:1:N/2-1]'; % Index
+uMOT#KjR t = n.*dt;
j4j %r( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
uMl.}t2uYu w=2*pi*n./T;
UR|UGldt_T g1=-i*ww./2;
J-t5kU;L{ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
= h,6/cs g3=-i*ww./2;
fHTqLYd- P1=0;
tZlz0BY! P2=0;
f/t1@d! P3=1;
<11 pk P=0;
w
'?xewx for m1=1:M1
c , a+u p=0.032*m1; %input amplitude
qkB)CY7 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
]O'dwC s1=s10;
{2<A\nW s20=0.*s10; %input in waveguide 2
PZZTRgVc s30=0.*s10; %input in waveguide 3
9 p6QNDp s2=s20;
1"J\iwN3 s3=s30;
N1rBpt p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
'<" eG!O %energy in waveguide 1
s[h& Uv"G p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
("(:w YR% %energy in waveguide 2
Ei!5Qya> p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
r8\"'4B1 %energy in waveguide 3
Lc ,te1 for m3 = 1:1:M3 % Start space evolution
j+0=)Q%I= s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
5~Vra@iab: s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
| k"? I s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
'`g #Zo sca1 = fftshift(fft(s1)); % Take Fourier transform
b|F_]i T sca2 = fftshift(fft(s2));
=Kf V;.& sca3 = fftshift(fft(s3));
19a/E1 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
~~eR,H Yk sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~IvAnwQ' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
z(]1425 0 s3 = ifft(fftshift(sc3));
,H!E :k s2 = ifft(fftshift(sc2)); % Return to physical space
=fmM=@!$< s1 = ifft(fftshift(sc1));
Dohq@+] O end
t}LV[bj1u p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s' \PU1{ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
* B"p:F7J| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
v;.7-9c* P1=[P1 p1/p10];
s)B l1\Q P2=[P2 p2/p10];
jt|e?1:vF P3=[P3 p3/p10];
EVc
E es P=[P p*p];
gf/$M[H! end
/mLOh2 T figure(1)
c>+l3&` plot(P,P1, P,P2, P,P3);
uM"G)$I\ y/t{*a
转自：
http://blog.163.com/opto_wang/
