计算脉冲在非线性耦合器中演化的Matlab 程序 `FwE^_9d 9&{z?* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Bus]OF>hu % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
:!^NjO % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0\ Tp/Ph % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
aQ- SrxmO8 xd\ml
37~ %fid=fopen('e21.dat','w');
<7! "8e N = 128; % Number of Fourier modes (Time domain sampling points)
J50n
E~ M1 =3000; % Total number of space steps
S f6%A J =100; % Steps between output of space
eVd:C8q T =10; % length of time windows:T*T0
bVzJOBe T0=0.1; % input pulse width
NKc<nYdK? MN1=0; % initial value for the space output location
T \#Gc4 dt = T/N; % time step
/|3~LvIt= n = [-N/2:1:N/2-1]'; % Index
(b.4&P"0 t = n.*dt;
J #5V>7G u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
~NB|BwAh u20=u10.*0.0; % input to waveguide 2
x .$cP u1=u10; u2=u20;
qMoo#UX U1 = u1;
{-Gh 62hDg U2 = u2; % Compute initial condition; save it in U
_ gGA/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hAt4+O&P w=2*pi*n./T;
' 6)Yf}I g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
my/KsB L=4; % length of evoluation to compare with S. Trillo's paper
i'.D=o dz=L/M1; % space step, make sure nonlinear<0.05
yo8mfH_, for m1 = 1:1:M1 % Start space evolution
9GsG* $-I u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
>I-rsw2 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
<Mu T7x- ca1 = fftshift(fft(u1)); % Take Fourier transform
KyQTrl.qdl ca2 = fftshift(fft(u2));
fg lN _ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
* 3]2vq c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
e1y#p3 @d u2 = ifft(fftshift(c2)); % Return to physical space
|~#A ?mK- u1 = ifft(fftshift(c1));
l *{Bz5hc if rem(m1,J) == 0 % Save output every J steps.
X,Rl&K\ b" U1 = [U1 u1]; % put solutions in U array
C/QrkTi= U2=[U2 u2];
MPK rr MN1=[MN1 m1];
It<VjN9
z1=dz*MN1'; % output location
\ Rt FF end
^I yYck'y+ end
w~&#:F? hg=abs(U1').*abs(U1'); % for data write to excel
a5aHv/W#P ha=[z1 hg]; % for data write to excel
+SE \c t1=[0 t'];
=qbN?a/?2 hh=[t1' ha']; % for data write to excel file
L8H:, } 2 %dlmwrite('aa',hh,'\t'); % save data in the excel format
FS=LpvOG) figure(1)
n).*= YLN waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
IuA4eDr^Y% figure(2)
~d3@x\I? waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
LwTdmR "shX ~zd5 非线性超快脉冲耦合的数值方法的Matlab程序 $|7=$~y KJv%t_4'F 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。
m 9\"B3sr 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
cr|]\ 3)L#V
. z}B 8&*> Jt #HbAY % This Matlab script file solves the nonlinear Schrodinger equations
gs7_Q % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
j8
`7)^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
C rSBN~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Kv9FqrDj & }0QnO_mj C=1;
uMpuS1 M1=120, % integer for amplitude
^FQn\, M3=5000; % integer for length of coupler
7 h0u7 N N = 512; % Number of Fourier modes (Time domain sampling points)
}s:3_9mE dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
%IE;'aa
} T =40; % length of time:T*T0.
j%D{z5,nKm dt = T/N; % time step
XT*/aa-1' n = [-N/2:1:N/2-1]'; % Index
o3eaNY a t = n.*dt;
.{ZJywE< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7ku=roPoF w=2*pi*n./T;
nP<u. {q
L g1=-i*ww./2;
CE!cZZ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
:475FPy] g3=-i*ww./2;
<RpTk*Yo^= P1=0;
i(.V`G= P2=0;
MM* ~X"A P3=1;
Xit@.:a; P=0;
-ah)/5j for m1=1:M1
S8+l!$7 p=0.032*m1; %input amplitude
Fw {68ggk s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
a(*"r:/lD s1=s10;
~l?c.CS d s20=0.*s10; %input in waveguide 2
%'=2Jy6h s30=0.*s10; %input in waveguide 3
ssS"X@VZ
\ s2=s20;
mPqK k s3=s30;
UZmUYSu; p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#_`p
0wY %energy in waveguide 1
0%%y9;o p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
7=yjd)Iy9m %energy in waveguide 2
`HnZ{PKf p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
WNb2" W %energy in waveguide 3
akPd#mf for m3 = 1:1:M3 % Start space evolution
:8 `$Bb V s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
9I q<*\V 4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
\ltS~E uWU s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
4}t&yu<P> sca1 = fftshift(fft(s1)); % Take Fourier transform
FV7'3fIa sca2 = fftshift(fft(s2));
$T:;Kc W) sca3 = fftshift(fft(s3));
H3vnc\d~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
NS""][# sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
iOCs% J sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
+- SO}P s3 = ifft(fftshift(sc3));
;($xAAR s2 = ifft(fftshift(sc2)); % Return to physical space
PhV/WjCZ s1 = ifft(fftshift(sc1));
S.`hl/ end
;&f(7 Q+T_ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
e6H}L:; p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~%
t'}JDZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
1*$6u5.=F P1=[P1 p1/p10];
0_-o]BY P2=[P2 p2/p10];
*93=}1g N P3=[P3 p3/p10];
w-$iKtb. P=[P p*p];
>?)_, KL end
@$L| figure(1)
r#_0_I1[ plot(P,P1, P,P2, P,P3);
lj8ficANo 6[RTL2&W 转自：
http://blog.163.com/opto_wang/
