计算脉冲在非线性耦合器中演化的Matlab 程序 .y lvJ$ ;]@Pm<f % This Matlab script file solves the coupled nonlinear Schrodinger equations of
i! gS]?*DH % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
RT${7= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Wb[k2V % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
L|B! ]} lB.n5G %fid=fopen('e21.dat','w');
"Q{ l])N N = 128; % Number of Fourier modes (Time domain sampling points)
3gnO)"$ M1 =3000; % Total number of space steps
J57; X=M J =100; % Steps between output of space
nLCaik_,m T =10; % length of time windows:T*T0
<@Vf:`a!P> T0=0.1; % input pulse width
nxNHf3
MN1=0; % initial value for the space output location
=3!o _ dt = T/N; % time step
=T\=,B n = [-N/2:1:N/2-1]'; % Index
_EJP I t = n.*dt;
M8/: PmR< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@C^wV u20=u10.*0.0; % input to waveguide 2
G4&?O_\; u1=u10; u2=u20;
Cy)N hgz U1 = u1;
,HI% ym U2 = u2; % Compute initial condition; save it in U
*+nw%gZG ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.rS.
>d^n w=2*pi*n./T;
:wG
) g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
:(wFNK/0{ L=4; % length of evoluation to compare with S. Trillo's paper
t=9f:,I$ dz=L/M1; % space step, make sure nonlinear<0.05
tY:
Nq*@
for m1 = 1:1:M1 % Start space evolution
\j5`6}zm u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
K: GEC- u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
lQ BE q"7$ ca1 = fftshift(fft(u1)); % Take Fourier transform
'#=0q ca2 = fftshift(fft(u2));
`oH4"9&]k3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
QZIzddwp c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
r)OiiD" u2 = ifft(fftshift(c2)); % Return to physical space
<XQwu*_\ u1 = ifft(fftshift(c1));
)W InPW if rem(m1,J) == 0 % Save output every J steps.
.FC+ U1 = [U1 u1]; % put solutions in U array
Z4rk$K'=1w U2=[U2 u2];
*ra>Kl0
MN1=[MN1 m1];
+I3O/=) z1=dz*MN1'; % output location
^9 ]iUx end
=,h'}(z_ end
4 Yv:\c hg=abs(U1').*abs(U1'); % for data write to excel
T\g+w\N ha=[z1 hg]; % for data write to excel
841 y"@*BY t1=[0 t'];
XH@(V4J(. hh=[t1' ha']; % for data write to excel file
|xg _z&dX %dlmwrite('aa',hh,'\t'); % save data in the excel format
9 [;da figure(1)
RV);^, b waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
,B_c figure(2)
YB<nz<;JR waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
tfZ@4%' P/.<s r=2 非线性超快脉冲耦合的数值方法的Matlab程序 t$wb wP `-Ozjb M 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。
^L)TfI_n 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
+L`}(yLJ)9 {-8Nq`w E #B$.K #QIY+muN % This Matlab script file solves the nonlinear Schrodinger equations
C\~}ySQc.e % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
6h2keyod % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J?yasjjgP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{it}\[3 rq4g~e!S C=1;
AvB=/p@] M1=120, % integer for amplitude
jC4>%!{m M3=5000; % integer for length of coupler
Nw$OJ9$L>
N = 512; % Number of Fourier modes (Time domain sampling points)
..X _nF dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
7 QNx*8 p T =40; % length of time:T*T0.
=CJ`0yDQ> dt = T/N; % time step
CuvY^[" n = [-N/2:1:N/2-1]'; % Index
ZTV)D t = n.*dt;
|Z{#DOT ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
HY
FMf3 w=2*pi*n./T;
yn_f%^!G g1=-i*ww./2;
#qY gQ<TM! g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
vI0,6fOd6 g3=-i*ww./2;
&1yJr j9y P1=0;
G<D8a2q P2=0;
GIH{tr1:< P3=1;
+pwTM]bV P=0;
tWTHy L for m1=1:M1
$rmxwxz&W: p=0.032*m1; %input amplitude
WA~[) S0 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ye9GBAj
/ s1=s10;
C@eL9R;N1 s20=0.*s10; %input in waveguide 2
t;6 < k7h s30=0.*s10; %input in waveguide 3
b4-gNF]Yt s2=s20;
#e-K It s3=s30;
O-
QT+] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
?'+]d;U O& %energy in waveguide 1
">CRFee0 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
&qG/\ %energy in waveguide 2
T`":Q1n p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
F: T(-, %energy in waveguide 3
g:ky;-G8b for m3 = 1:1:M3 % Start space evolution
j \jMN*dmV s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1F,U^O s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
c-(RjQ~M5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
:_6o|9J\t sca1 = fftshift(fft(s1)); % Take Fourier transform
Os'E 7;:1h sca2 = fftshift(fft(s2));
iYgVSV Ng sca3 = fftshift(fft(s3));
cM' MgX9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
hdx_Tduue sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
t3Gy *B sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
hS8M|_ s3 = ifft(fftshift(sc3));
&uRT/+18W3 s2 = ifft(fftshift(sc2)); % Return to physical space
<q!HY~"V s1 = ifft(fftshift(sc1));
7HH@7vpJ^ end
@ i! +Z p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
syW[uXNLZ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
N^$ q;% p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
v77UE"4|c P1=[P1 p1/p10];
yO7y`;Q(sF P2=[P2 p2/p10];
"h_f- vP P3=[P3 p3/p10];
]pBEoktp P=[P p*p];
k-
9i end
IC'+{3.m8 figure(1)
3WF]%P%
plot(P,P1, P,P2, P,P3);
4;J.$ \#]%S/_ A 转自：
http://blog.163.com/opto_wang/
