计算脉冲在非线性耦合器中演化的Matlab 程序 .oM;D~(=9 / hg)=p % This Matlab script file solves the coupled nonlinear Schrodinger equations of
JmC2buO % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Z.`0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;OC{B}.vH % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
E~c>j<'-"< wo a|h"T %fid=fopen('e21.dat','w');
:w]NN \ N = 128; % Number of Fourier modes (Time domain sampling points)
=om<* \vsO M1 =3000; % Total number of space steps
9a#Y
D;-p J =100; % Steps between output of space
@=OX7zq\h- T =10; % length of time windows:T*T0
:Wihb#TO) T0=0.1; % input pulse width
~l('ly MN1=0; % initial value for the space output location
(coaGQ@d dt = T/N; % time step
Wcbm,O4u n = [-N/2:1:N/2-1]'; % Index
'U,\5jj'Y t = n.*dt;
kzVK%[/ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
^fV-m&F)K* u20=u10.*0.0; % input to waveguide 2
qOAP_\@T u1=u10; u2=u20;
c qaq~ U1 = u1;
7pN&fAtj/ U2 = u2; % Compute initial condition; save it in U
3L-$+j~u ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
X/bu z w=2*pi*n./T;
V/xjI< , g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
)Fw#]~Z L=4; % length of evoluation to compare with S. Trillo's paper
+i[@+`
dz=L/M1; % space step, make sure nonlinear<0.05
/8 y v8 for m1 = 1:1:M1 % Start space evolution
ZFtJoGaR u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
'!`| H 3 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
7X8*7'.2 ca1 = fftshift(fft(u1)); % Take Fourier transform
|tC= j. ca2 = fftshift(fft(u2));
_0y]U];ce c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Uu|2!}^T c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
)LsUO#%DO u2 = ifft(fftshift(c2)); % Return to physical space
|n;5D,r0C u1 = ifft(fftshift(c1));
`QZK W if rem(m1,J) == 0 % Save output every J steps.
K+d{R=s^ U1 = [U1 u1]; % put solutions in U array
`4e| I.`^r U2=[U2 u2];
Rp!"c MN1=[MN1 m1];
4&%E?_M z1=dz*MN1'; % output location
zCv)%y end
KpIY>k end
|"[;0)dw^ hg=abs(U1').*abs(U1'); % for data write to excel
(w`_{%T ha=[z1 hg]; % for data write to excel
R2Lq??XA= t1=[0 t'];
1d$wP$ hh=[t1' ha']; % for data write to excel file
S~W;Ld<>fB %dlmwrite('aa',hh,'\t'); % save data in the excel format
%q.5; L figure(1)
*,)1Dcv( waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
P
F); K Q figure(2)
IpM"k)HR waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
WR u/7$8 C~^T=IP 非线性超快脉冲耦合的数值方法的Matlab程序 )` S5>[6 (=j/"Mb 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
%L$ ?Mey 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
.J=QWfqt Bc`L ]< Ur ol)_3X n<F3&2w % This Matlab script file solves the nonlinear Schrodinger equations
HG)$ W % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
n'?]_ z< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WEoD ?GLS8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4sfq,shRq >[~`rOU*|Y C=1;
#Zi6N M1=120, % integer for amplitude
Nfv`
)n@ M3=5000; % integer for length of coupler
t3*.Bm:^ N = 512; % Number of Fourier modes (Time domain sampling points)
p@h<u!rL8 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
bM }zGFt T =40; % length of time:T*T0.
Ft}nG&D dt = T/N; % time step
?X\ uzu n = [-N/2:1:N/2-1]'; % Index
U lCw{:#F t = n.*dt;
F& Rr&m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
y-S23B( w=2*pi*n./T;
r oBb o g1=-i*ww./2;
v P_mS 4X g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~mZ[@ Z g3=-i*ww./2;
Ir(U7 D P1=0;
_,? xc" P2=0;
b?<@ P3=1;
sxdDI?W4 P=0;
L>lx kq8!Q for m1=1:M1
> .H} (! p=0.032*m1; %input amplitude
4F<wa s/ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
J3/e;5w2Z s1=s10;
iG"1~/U s20=0.*s10; %input in waveguide 2
W}|k!_/ s30=0.*s10; %input in waveguide 3
b?2 \j} s2=s20;
p9 !jM\( s3=s30;
G7KOJZb+D p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
l\2"u M#7 %energy in waveguide 1
<e wcW r p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
dz/3=0
%energy in waveguide 2
jF(R;?, p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
P,#l~ \ %energy in waveguide 3
u Tdz$Nh for m3 = 1:1:M3 % Start space evolution
-zZb]8\E s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
z~i>GN_ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
cV7a, * s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
tVNFulcz$ sca1 = fftshift(fft(s1)); % Take Fourier transform
HcV,r,>e sca2 = fftshift(fft(s2));
0d89>UB-8q sca3 = fftshift(fft(s3));
,>nf/c0. sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!
GtF%V sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
M o i>Dp sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
};'~@%U]/ s3 = ifft(fftshift(sc3));
]4'V59\ s2 = ifft(fftshift(sc2)); % Return to physical space
y>cT{ )E$ s1 = ifft(fftshift(sc1));
B->oTC`5 end
,,g: x p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
cnDF`7xrT p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
BFqM6_/J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
@udc/J$ P1=[P1 p1/p10];
YllW2g: P2=[P2 p2/p10];
?\<Kb|Q P3=[P3 p3/p10];
9U@>& 3[v P=[P p*p];
j*~z.Q | end
O7J V{ '? figure(1)
w;kiH+& plot(P,P1, P,P2, P,P3);
|-%dN }O YWDd[\4 转自：
http://blog.163.com/opto_wang/
