计算脉冲在非线性耦合器中演化的Matlab 程序 CxJ 3 u .QZjJ9pvK % This Matlab script file solves the coupled nonlinear Schrodinger equations of
M e ep % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
>$- YNZA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*x]*% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
GbZ~e I`,2 /je
$+ %fid=fopen('e21.dat','w');
JR15y3 F N = 128; % Number of Fourier modes (Time domain sampling points)
Xy!NBh 7I M1 =3000; % Total number of space steps
~ OR^ J =100; % Steps between output of space
3#dz6 + T =10; % length of time windows:T*T0
k0ai#3 iJ T0=0.1; % input pulse width
+ WMXd.iN, MN1=0; % initial value for the space output location
\f(zMP dt = T/N; % time step
-LUZ7,!/>o n = [-N/2:1:N/2-1]'; % Index
i$6rnS&C t = n.*dt;
oA7DhU5n u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
1i~q~ O, u20=u10.*0.0; % input to waveguide 2
pOn &D u1=u10; u2=u20;
_Y]Oloo(' U1 = u1;
_Z 9 d.- U2 = u2; % Compute initial condition; save it in U
*>mjUT}cP ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hi/d%lNZ w=2*pi*n./T;
%*npL Di g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
K?! W9lUq L=4; % length of evoluation to compare with S. Trillo's paper
GK1nGdT] dz=L/M1; % space step, make sure nonlinear<0.05
Q3&D A1b` for m1 = 1:1:M1 % Start space evolution
y {Bajil u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
m;>G]Sbe u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
~| O; Sdo= ca1 = fftshift(fft(u1)); % Take Fourier transform
!uIY , ca2 = fftshift(fft(u2));
Xa#.GrH6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
N"G\ H<n c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
A[7H-1- u2 = ifft(fftshift(c2)); % Return to physical space
!m9hL>5v R u1 = ifft(fftshift(c1));
Bt,'g* Cs if rem(m1,J) == 0 % Save output every J steps.
qpCaW0]7 U1 = [U1 u1]; % put solutions in U array
4 ;AQ12<[1 U2=[U2 u2];
,tg]Gt MN1=[MN1 m1];
rXMc0SPk z1=dz*MN1'; % output location
p_&B+
<z end
*n&Sd~Mg end
phf{b+'#X hg=abs(U1').*abs(U1'); % for data write to excel
0|j44e } ha=[z1 hg]; % for data write to excel
Qb>("j~Z t1=[0 t'];
w6X:39d hh=[t1' ha']; % for data write to excel file
YsVKd h %dlmwrite('aa',hh,'\t'); % save data in the excel format
Xxd D)I figure(1)
4[]*=
waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
{^N,$,Ab. figure(2)
B; NK\5> waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
.$W} $/g`{O I]K 非线性超快脉冲耦合的数值方法的Matlab程序 O-W[^r2e oc K4Nxs 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
LiQH!yHW Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[hg9 0Q6 l emV&$WN| " j?x gV ILH[q> % This Matlab script file solves the nonlinear Schrodinger equations
3gVU#T [[ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
j?]+~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
SC4jKm2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_xi &%F/ uuF~+=.| C=1;
.|07IH/Di{ M1=120, % integer for amplitude
+4T.3Njjn M3=5000; % integer for length of coupler
&K9 RV 4M5 N = 512; % Number of Fourier modes (Time domain sampling points)
Cu24xP` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^q/^.Gf T =40; % length of time:T*T0.
OGJrwl dt = T/N; % time step
G9QvIXRi n = [-N/2:1:N/2-1]'; % Index
BCz4
s{F t = n.*dt;
Et-|[ eL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
*? uUP w=2*pi*n./T;
k{F6 WQ7 g1=-i*ww./2;
Viw,YkC g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>!" Sr3,L g3=-i*ww./2;
rDoMz3[w P1=0;
iiJT%Zq`# P2=0;
8,vP']4r% P3=1;
Oe@w$? P=0;
/c-k{5mH% for m1=1:M1
r1R M7y p=0.032*m1; %input amplitude
A&v Qtd s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
yY49JZ s1=s10;
o_Y?s+~i[/ s20=0.*s10; %input in waveguide 2
+N+117m s30=0.*s10; %input in waveguide 3
Zj ` ;IYFG s2=s20;
g5Io=e@s s3=s30;
<6+B;brh p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
V3VTbgF %energy in waveguide 1
t4: /qy p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
5?
Y(FhnIC %energy in waveguide 2
l,b,U/3R. p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/=9dX;
# %energy in waveguide 3
s % Ph for m3 = 1:1:M3 % Start space evolution
)t-P o'RW s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
r]D>p&4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
BOM0QskLf s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
1)ij*L8k sca1 = fftshift(fft(s1)); % Take Fourier transform
\vV]fX sca2 = fftshift(fft(s2));
9yTkZ`M28 sca3 = fftshift(fft(s3));
3y2L! &'z sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0~W XA=X G sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
BLqK5~ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
>>C
S8 s3 = ifft(fftshift(sc3));
tK *y/S s2 = ifft(fftshift(sc2)); % Return to physical space
P()W\+",n s1 = ifft(fftshift(sc1));
T9r6,yY end
N :+EGmp p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
ls9Y? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3jJV5J'" p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
p*Y V*Arv P1=[P1 p1/p10];
b{-|q6 P2=[P2 p2/p10];
]qq2 VO<b P3=[P3 p3/p10];
MuzQ z.C P=[P p*p];
S-Vxlku] end
Q u8=zI>t figure(1)
~Cyn w( plot(P,P1, P,P2, P,P3);
XA. 1Y) FrLv%tK| 转自：
http://blog.163.com/opto_wang/
