计算脉冲在非线性耦合器中演化的Matlab 程序 )Dk0V!%N 0j
a % This Matlab script file solves the coupled nonlinear Schrodinger equations of
b *'=W"%\ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_V_8p) % % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5UrXVdP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fG8}= xH_& 4pfix1F g %fid=fopen('e21.dat','w');
5C Y@R N = 128; % Number of Fourier modes (Time domain sampling points)
X%4uShM M1 =3000; % Total number of space steps
c :?#zX J =100; % Steps between output of space
IS0HV$OI T =10; % length of time windows:T*T0
@n~>j&Kp T0=0.1; % input pulse width
wZ]BY; MN1=0; % initial value for the space output location
Oi
kU$~| dt = T/N; % time step
L#7)X5a__ n = [-N/2:1:N/2-1]'; % Index
Ww'TCWk@ t = n.*dt;
V 9QvQA
r u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
eZR8<Z % u20=u10.*0.0; % input to waveguide 2
)MD* )O u1=u10; u2=u20;
ctc`^#q U1 = u1;
E1l\~%A U2 = u2; % Compute initial condition; save it in U
DK@w^ZW6JA ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m]-v IUpb w=2*pi*n./T;
;G4HMtL g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
gq/ePSa L=4; % length of evoluation to compare with S. Trillo's paper
AjL?Qh4 dz=L/M1; % space step, make sure nonlinear<0.05
aiR|.opIb for m1 = 1:1:M1 % Start space evolution
r7Q:l ?F2 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
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u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
A<YZ BR_ ca1 = fftshift(fft(u1)); % Take Fourier transform
h87L8qh9 ca2 = fftshift(fft(u2));
Zeme`/aBb c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
l# !@{ < c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
{x&jh|f`g u2 = ifft(fftshift(c2)); % Return to physical space
!d bA ( u1 = ifft(fftshift(c1));
{0)WS}& if rem(m1,J) == 0 % Save output every J steps.
qa0JQ _?o] U1 = [U1 u1]; % put solutions in U array
HjUw[Yz+6 U2=[U2 u2];
j;AzkReb MN1=[MN1 m1];
<PfPh~ z1=dz*MN1'; % output location
nIT ^' end
FQ9csUjpB end
e&H<lT hg=abs(U1').*abs(U1'); % for data write to excel
- ;@5Ua1uf ha=[z1 hg]; % for data write to excel
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t1=[0 t'];
N}l]Ilm$34 hh=[t1' ha']; % for data write to excel file
xPfnyAo?%z %dlmwrite('aa',hh,'\t'); % save data in the excel format
+3o)L?: g figure(1)
St3(1mApl waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*(\;}JF - figure(2)
. ~A"Wyu\ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
*nsnX/e(- ZB^4 (F')H 非线性超快脉冲耦合的数值方法的Matlab程序
wWOT*R_ n7, 6a 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。
~\)&{ ' 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
u6qi uu@'02G8 (;2J(GZ:$U soqNzdTB2 % This Matlab script file solves the nonlinear Schrodinger equations
T 24#gF~ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
2;?wN`}5g= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
WW\)B -}T % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$p6Xa;j$ 9 X,!OWz:[ C=1;
H8t{ >C)] M1=120, % integer for amplitude
Sj{rvW M3=5000; % integer for length of coupler
vn%U;} N = 512; % Number of Fourier modes (Time domain sampling points)
a5U2[Ko80 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
U70@}5! T =40; % length of time:T*T0.
[>J~M!yu:r dt = T/N; % time step
bhm~Ii n = [-N/2:1:N/2-1]'; % Index
,Y\4xg*` t = n.*dt;
6B;_uIq5 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
j=jrzG+` w=2*pi*n./T;
B> " r -O g1=-i*ww./2;
E-U;8cOMv g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
dW^_tzfF7 g3=-i*ww./2;
!DX/^b P1=0;
c7nk~K[6 P2=0;
fkv{\zN P3=1;
Lq
$4.l[j P=0;
hA,rSq for m1=1:M1
S E}RP3dF! p=0.032*m1; %input amplitude
\I,Dje/:w s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
^SSOh# s1=s10;
k89gJ5B$ s20=0.*s10; %input in waveguide 2
p4t!T=o/ s30=0.*s10; %input in waveguide 3
hzPB~obC s2=s20;
K<7T}XzU$ s3=s30;
VF!kr1 n! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Lc: SqF %energy in waveguide 1
%qjyk=z+Z p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
$:gSc &mx %energy in waveguide 2
sv{0XVn+^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
:Ye#NPOI %energy in waveguide 3
io? {ew for m3 = 1:1:M3 % Start space evolution
* sIG& s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
\PMKmJ X0O s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Y %D*O s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
v^18o$=K", sca1 = fftshift(fft(s1)); % Take Fourier transform
}Keon.N? sca2 = fftshift(fft(s2));
}Ka.bZS sca3 = fftshift(fft(s3));
x< y [na sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
/2\= sTd sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
KjfKo;T sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
pQMpkAX s3 = ifft(fftshift(sc3));
10I` AjF0 s2 = ifft(fftshift(sc2)); % Return to physical space
OTHd1PSOu s1 = ifft(fftshift(sc1));
>5vl{{,$K end
yJ`1},^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
k$x
'v# p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"T1#*"{j p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
N9h@1'> P1=[P1 p1/p10];
a~eLkWnh<k P2=[P2 p2/p10];
Qbt>}?- P3=[P3 p3/p10];
,bwopRcA P=[P p*p];
"`gZ y)E end
)%@WoBRj figure(1)
|VR5Q(d plot(P,P1, P,P2, P,P3);
GGQ(| ? w ^]!1 'xg 转自：
http://blog.163.com/opto_wang/
