计算脉冲在非线性耦合器中演化的Matlab 程序 J
s<MJ4r>/ sQ:VrX wP % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ws2 j:B % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&iiK ZZ`_o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
zg Y*|{4Sl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0 /P-> n~ bC4* w
O %fid=fopen('e21.dat','w');
f93rY < N = 128; % Number of Fourier modes (Time domain sampling points)
0tm_}L$g=b M1 =3000; % Total number of space steps
.cT$h?+jyl J =100; % Steps between output of space
y~c4:*L3 T =10; % length of time windows:T*T0
k3 /JQ]'D T0=0.1; % input pulse width
0?Tk* X MN1=0; % initial value for the space output location
q8 xc70: R dt = T/N; % time step
aRO_,n9 n = [-N/2:1:N/2-1]'; % Index
)-?uX.E{ t = n.*dt;
zNr_W[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
=PKt0 9b^ u20=u10.*0.0; % input to waveguide 2
,gL)~6!A u1=u10; u2=u20;
E}b> 7L&w U1 = u1;
&>zy_) U2 = u2; % Compute initial condition; save it in U
qe6C|W~n ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
E0)mI)RW. w=2*pi*n./T;
`k{ ff g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
FQ|LA[~ L=4; % length of evoluation to compare with S. Trillo's paper
Hu9-<upc& dz=L/M1; % space step, make sure nonlinear<0.05
kk_9G -M for m1 = 1:1:M1 % Start space evolution
K jn& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
&pMlt7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
kL PO+lg+ ca1 = fftshift(fft(u1)); % Take Fourier transform
AY/-j$5+? ca2 = fftshift(fft(u2));
Ro'4/{}+ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
\p@nH%@v c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
V:G }=~+= u2 = ifft(fftshift(c2)); % Return to physical space
HDSA]{:sl u1 = ifft(fftshift(c1));
]IHD:!Z-= if rem(m1,J) == 0 % Save output every J steps.
^= izqh5S U1 = [U1 u1]; % put solutions in U array
$O~F>.* U2=[U2 u2];
;!0.Kk
4 MN1=[MN1 m1];
APQQ:'>N4~ z1=dz*MN1'; % output location
_]=TFz2O end
!|Xl 8lV` end
<^*+8{* hg=abs(U1').*abs(U1'); % for data write to excel
C;)Xwm>e ha=[z1 hg]; % for data write to excel
>xU72l#5 t1=[0 t'];
k{}[>))Q hh=[t1' ha']; % for data write to excel file
VO @
4A6 %dlmwrite('aa',hh,'\t'); % save data in the excel format
xu"94y+ figure(1)
`hK>bHj waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ek(kY6x: figure(2)
D,GPn%Wqi waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
h$aew63 ]U#[\ Z 非线性超快脉冲耦合的数值方法的Matlab程序 ?HEtr X,q i^yH?bH @~ 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。
&3 XFg Ho 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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5o<Q'( ^:cb
$9F % This Matlab script file solves the nonlinear Schrodinger equations
`uNvFlP % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
y?*[}S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_>jrlIfc % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
A"\P&kqMV t-eKr uj+ C=1;
U!a!|s> M1=120, % integer for amplitude
c#\ah}]Vo M3=5000; % integer for length of coupler
1IOo?e=/bM N = 512; % Number of Fourier modes (Time domain sampling points)
H IPcZ!p dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
e8XM=$@ T =40; % length of time:T*T0.
kO..~@ aY dt = T/N; % time step
)tN?: l n = [-N/2:1:N/2-1]'; % Index
'B:Z=0{>N t = n.*dt;
y"|K
|QT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#uD)0zdw w=2*pi*n./T;
]HJ{dcF g1=-i*ww./2;
;1 *m} uNz g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
B&4fYpn g3=-i*ww./2;
Xb(CH#*{z P1=0;
P S _3Oq) P2=0;
%jbJ6c P3=1;
;PfeP ;z P=0;
"4Lg8q m for m1=1:M1
Wz6]*P`qv p=0.032*m1; %input amplitude
;xW8Z<\- s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
! F0r d9 s1=s10;
mHK@(D7X s20=0.*s10; %input in waveguide 2
0v_6cYA s30=0.*s10; %input in waveguide 3
njy~ s2=s20;
ot|N;=ZKo s3=s30;
Xk {!' 0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
y'J:?!S,Yu %energy in waveguide 1
iX8h2l p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
L\/u}]dPQ %energy in waveguide 2
u #a%( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b lRY7 %energy in waveguide 3
{f`lSu for m3 = 1:1:M3 % Start space evolution
olD@W
UB s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Y=P9:unG s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Ph(]?MG\_ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
T7>4 8eH sca1 = fftshift(fft(s1)); % Take Fourier transform
.Dgo Oo%?" sca2 = fftshift(fft(s2));
V;>9&'Z3 sca3 = fftshift(fft(s3));
pchQ#GU sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
2x7(}+eD sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
\]Y\P~n sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4)3g!o ? s3 = ifft(fftshift(sc3));
o/tVcv s2 = ifft(fftshift(sc2)); % Return to physical space
h|J;6Sm@ s1 = ifft(fftshift(sc1));
{ c v;w end
K(-G: | p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
%/{IssCR7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@Ufa -h5"( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
VKq0 <+M P1=[P1 p1/p10];
07.nq;/R P2=[P2 p2/p10];
:wQC_; P3=[P3 p3/p10];
. o-0aBG P=[P p*p];
X4d Xm>*?= end
Nc
G ,0K figure(1)
AC 9{*K[ plot(P,P1, P,P2, P,P3);
fC=fJZU7$ E)KB@f<g* 转自：
http://blog.163.com/opto_wang/
