计算脉冲在非线性耦合器中演化的Matlab 程序 s/"bH3Ob9v R:~ aX,qR % This Matlab script file solves the coupled nonlinear Schrodinger equations of
& &}_[{fc % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
9lYKG ^#D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
k)b{ UFRW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k k=n&M <<
6 GE %fid=fopen('e21.dat','w');
ly%^\jW N = 128; % Number of Fourier modes (Time domain sampling points)
Z@Rm^g]o M1 =3000; % Total number of space steps
5T;LWS J =100; % Steps between output of space
{xTq5`&gT T =10; % length of time windows:T*T0
^N={4'G) T0=0.1; % input pulse width
c-$r B_t+ MN1=0; % initial value for the space output location
=0cTct6\ dt = T/N; % time step
*?m)VvR> | n = [-N/2:1:N/2-1]'; % Index
#kW=|8X t = n.*dt;
JG!B3^qB u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
%ztZ#h~g u20=u10.*0.0; % input to waveguide 2
e/D{^ *~S u1=u10; u2=u20;
7:UeE~ uB: U1 = u1;
y<Koc>8 U2 = u2; % Compute initial condition; save it in U
^OY$
W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:4{
`c.S w=2*pi*n./T;
HJl?@& l/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[edF'7La L=4; % length of evoluation to compare with S. Trillo's paper
)O[8 D dz=L/M1; % space step, make sure nonlinear<0.05
@8W@I| for m1 = 1:1:M1 % Start space evolution
6Ryc&z5 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
']nIa7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
.V;,6Vq ca1 = fftshift(fft(u1)); % Take Fourier transform
e1Db
+ QBV ca2 = fftshift(fft(u2));
a OmG, +o c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
JT
7WZc) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
? $B4' wc5 u2 = ifft(fftshift(c2)); % Return to physical space
0C<\m\|~k u1 = ifft(fftshift(c1));
_`?0w#> 0 if rem(m1,J) == 0 % Save output every J steps.
ko} & X= U1 = [U1 u1]; % put solutions in U array
Z 8w\[AF{$ U2=[U2 u2];
q2%cLbI
F MN1=[MN1 m1];
q-z1ElrN7u z1=dz*MN1'; % output location
V>Jr4z end
IUOf/m M5 end
2* g2UP hg=abs(U1').*abs(U1'); % for data write to excel
S|=)^$: ha=[z1 hg]; % for data write to excel
b~^'P t1=[0 t'];
.BP d06y hh=[t1' ha']; % for data write to excel file
K28L(4 ) %dlmwrite('aa',hh,'\t'); % save data in the excel format
o CC tjr figure(1)
* B&P[n waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
"(mJupI figure(2)
.<t {saToU waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
q[A i^79 iF`_-t/k 非线性超快脉冲耦合的数值方法的Matlab程序 \6
\bD< Szz j9K 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
["nWIs[h Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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B Y j([b)k= I!/EQO| M{L<aYe % This Matlab script file solves the nonlinear Schrodinger equations
[],[ LkS % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
0Jv6?7]LKa % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
dg|+?M^9` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>)K3 P"7` : a C=1;
| co#X8J M1=120, % integer for amplitude
8J,^O04< M3=5000; % integer for length of coupler
B>i%:[-e N = 512; % Number of Fourier modes (Time domain sampling points)
g Nr4oOR{ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^ ?e[$} T =40; % length of time:T*T0.
\ gP?uJ dt = T/N; % time step
pqg2#@F. n = [-N/2:1:N/2-1]'; % Index
cEHpa%_5 t = n.*dt;
_L8&.=4]i ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[
&Wy $ w=2*pi*n./T;
Z*Ffdh>*:& g1=-i*ww./2;
\B' )2phE g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
g(P7CX+y g3=-i*ww./2;
*l d)nH{ P1=0;
W<<G
'Km P2=0;
|e8A)xM]wC P3=1;
n WelM2 P=0;
Z( :\Vj" for m1=1:M1
z \v p=0.032*m1; %input amplitude
-F`gRAr- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
,U9j7E< 4 s1=s10;
y6am(ugE s20=0.*s10; %input in waveguide 2
v_5O*F7) s30=0.*s10; %input in waveguide 3
A#$l;M.3R s2=s20;
QY+{ OCB s3=s30;
9@t&jznt< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
${ Lrj}93 %energy in waveguide 1
,pcyU\6 8v p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Fz8& Jn! %energy in waveguide 2
jGLmgJG-P p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Rq1 5AR %energy in waveguide 3
~a=]w#-KD for m3 = 1:1:M3 % Start space evolution
tDAX
pi( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
[]\-*{^r s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
pe[ huYE s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
6+sz4 sca1 = fftshift(fft(s1)); % Take Fourier transform
V,ZRX}O sca2 = fftshift(fft(s2));
:TrP3wV _ sca3 = fftshift(fft(s3));
4-O.i\1q sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
P3bRv^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
:SF f} sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
U;&s=M0 [ s3 = ifft(fftshift(sc3));
(O ;R~Io s2 = ifft(fftshift(sc2)); % Return to physical space
}0R"ZPU1Rw s1 = ifft(fftshift(sc1));
,9|7{j|u end
j; /@A
lZl p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
QdZH Igh`i p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2aivc,m{r p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[9EL[} P1=[P1 p1/p10];
$xvwnbq#y P2=[P2 p2/p10];
BI2'NN\ P3=[P3 p3/p10];
un6W|{4] P=[P p*p];
K0*er end
-b%' K}.C figure(1)
U&kdR+dB plot(P,P1, P,P2, P,P3);
*[nS*D\: :@~3wD[y 转自：
http://blog.163.com/opto_wang/
