计算脉冲在非线性耦合器中演化的Matlab 程序 7D5;lM[_ EBF608nWfW % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\5g7_3,3W % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
I%dFVt@ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
V*an0@ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*.g0;\HF WJH)>4M# %fid=fopen('e21.dat','w');
gQ]WNJ~> N = 128; % Number of Fourier modes (Time domain sampling points)
JzhbuWwF- M1 =3000; % Total number of space steps
[X >sG)0S~ J =100; % Steps between output of space
YS$? Wz T =10; % length of time windows:T*T0
:H}a/ x*ur T0=0.1; % input pulse width
4]\ f} MN1=0; % initial value for the space output location
+AP f[ZpU dt = T/N; % time step
3hzI6otKS n = [-N/2:1:N/2-1]'; % Index
jY.iQBhjEB t = n.*dt;
)ZkQWiP- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
FcR(uv< u20=u10.*0.0; % input to waveguide 2
gHU/yi!T u1=u10; u2=u20;
Kv**(~FNnH U1 = u1;
oBVYgv) U2 = u2; % Compute initial condition; save it in U
EH;w
<LvT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
E_VLI'Hn? w=2*pi*n./T;
SoS GQ& k g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
YuO-a$BP L=4; % length of evoluation to compare with S. Trillo's paper
6>I{I k@> dz=L/M1; % space step, make sure nonlinear<0.05
99T_y `df for m1 = 1:1:M1 % Start space evolution
_O!) aD u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
m @K5eh u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
f< A@D"m/ ca1 = fftshift(fft(u1)); % Take Fourier transform
?sb
Ob ca2 = fftshift(fft(u2));
idL6 *%M c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[K2\e N~g c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
]6wo] nV[P u2 = ifft(fftshift(c2)); % Return to physical space
}m6zu'CV u1 = ifft(fftshift(c1));
aL6 3=y if rem(m1,J) == 0 % Save output every J steps.
IvLo&6swW U1 = [U1 u1]; % put solutions in U array
*W()|-[V 3 U2=[U2 u2];
z6B(}(D MN1=[MN1 m1];
"^A4 !. z1=dz*MN1'; % output location
&<</[h/B/F end
vB0O3] end
MPt:bf# hg=abs(U1').*abs(U1'); % for data write to excel
INQ0h `T ha=[z1 hg]; % for data write to excel
} $:uN t1=[0 t'];
sS$"6 hh=[t1' ha']; % for data write to excel file
; aA,H& %dlmwrite('aa',hh,'\t'); % save data in the excel format
Yh%a7K figure(1)
79:Wo>C3- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
x,W)qv figure(2)
_C ` cO waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
k(n{$ #bX~.jKW 非线性超快脉冲耦合的数值方法的Matlab程序 aL\vQ(1zO d/>owCwQ 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。
# *^vd{fl 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
+dWx?$ n <{rRcFR lSw9e<jYO L(tA~Z"k % This Matlab script file solves the nonlinear Schrodinger equations
2mVcT3 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
74*1|S < % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Vl;GQe % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K-Bf=7F, >*ey 7g C=1;
SJY<#_b M1=120, % integer for amplitude
HJl$v#]#+ M3=5000; % integer for length of coupler
(1 7%/80-J N = 512; % Number of Fourier modes (Time domain sampling points)
$~UQKv> dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
e %VJ:Dj T =40; % length of time:T*T0.
MS{pur D dt = T/N; % time step
\VmqK&9 n = [-N/2:1:N/2-1]'; % Index
HJ pkR<h t = n.*dt;
]^,<Ez ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@=o1q=5@8 w=2*pi*n./T;
b-e3i;T!}~ g1=-i*ww./2;
G)28#aH g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
_RG!lmJV g3=-i*ww./2;
+5pK[%k P1=0;
y(&JE^GfX P2=0;
= |IB= P3=1;
^p#f B4z P=0;
f$a%&X6"- for m1=1:M1
td^2gjr^5 p=0.032*m1; %input amplitude
Q+/:5Z
C s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
%)[m bb s1=s10;
QF/A-[V s20=0.*s10; %input in waveguide 2
h4C DZ s30=0.*s10; %input in waveguide 3
2XJn3wPi s2=s20;
w[w{~`([", s3=s30;
;2"#X2B p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
YH33E~f %energy in waveguide 1
m%ZJp7C p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8%s ^>.rG %energy in waveguide 2
WN9 < p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
u9>zC QRO %energy in waveguide 3
iTgGf for m3 = 1:1:M3 % Start space evolution
ZbTU1Y/'
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
@/}{Trmg/ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
M0 `nr}g s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
}^uUw& sca1 = fftshift(fft(s1)); % Take Fourier transform
E@\e37e sca2 = fftshift(fft(s2));
@xR7>-$0p sca3 = fftshift(fft(s3));
Wr h C
q6 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6'y+Ev$9 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
zAEq)9Y"l' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%Kd&A * s3 = ifft(fftshift(sc3));
dzDh V{ s2 = ifft(fftshift(sc2)); % Return to physical space
i:`ur s1 = ifft(fftshift(sc1));
lcgT9 m# end
MdK!Y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
.+3= H@8h p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
GSg|Gz""J0 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Z qX U P1=[P1 p1/p10];
[^ r0red P2=[P2 p2/p10];
jR7 , b5 P3=[P3 p3/p10];
Izq]n R P=[P p*p];
rDkAeX0 end
vlCjh! x figure(1)
HM%n`1ZU plot(P,P1, P,P2, P,P3);
$2E n^ DX.u"&Mm 转自：
http://blog.163.com/opto_wang/
