计算脉冲在非线性耦合器中演化的Matlab 程序 &oK/ ]lub 37M[9m|D* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\ /X!tlwxh % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
!\D] \|Bo % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Pi]s<3PL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{$QF*j IG3K Pmu %fid=fopen('e21.dat','w');
% &Q7;? N = 128; % Number of Fourier modes (Time domain sampling points)
2M( PH]D M1 =3000; % Total number of space steps
VkP:%-*#v J =100; % Steps between output of space
C6=;(=?C T =10; % length of time windows:T*T0
krnk%ug T0=0.1; % input pulse width
oe_[h] Hgl MN1=0; % initial value for the space output location
z&HN>7 dt = T/N; % time step
tU~ H@' n = [-N/2:1:N/2-1]'; % Index
W0?Y%Da(4m t = n.*dt;
*mhw5Z=!
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
RT+30Q ? u20=u10.*0.0; % input to waveguide 2
f6_|dvY3 u1=u10; u2=u20;
lt(-,md U1 = u1;
J/&*OC U2 = u2; % Compute initial condition; save it in U
]2s Zu7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Q j~W-^/ - w=2*pi*n./T;
,;ruH^ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'8pPGh9D L=4; % length of evoluation to compare with S. Trillo's paper
u {lDof> dz=L/M1; % space step, make sure nonlinear<0.05
fOjt` ~ToI for m1 = 1:1:M1 % Start space evolution
D(ntVR u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,DUQto u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
yW=hnV{ ca1 = fftshift(fft(u1)); % Take Fourier transform
6_}){ZR ca2 = fftshift(fft(u2));
~aq?Kk c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ujHzG}2z c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
)+{omQ7v u2 = ifft(fftshift(c2)); % Return to physical space
; dHOH\,: u1 = ifft(fftshift(c1));
"E[*rnsLN if rem(m1,J) == 0 % Save output every J steps.
Cq;K, B9 U1 = [U1 u1]; % put solutions in U array
QO`Sn N} U2=[U2 u2];
'*{Rn7B5 MN1=[MN1 m1];
0~L 8yMM z1=dz*MN1'; % output location
ppo$&W
&z end
A5H8+gATK end
Wes "t}[25 hg=abs(U1').*abs(U1'); % for data write to excel
bFdg '_ ha=[z1 hg]; % for data write to excel
-bb 7Y t1=[0 t'];
S$_Ts1Ge6 hh=[t1' ha']; % for data write to excel file
Sw9mrhzJfe %dlmwrite('aa',hh,'\t'); % save data in the excel format
]( 6vG $\ figure(1)
X1PlW8pd waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
&#\7w85$ figure(2)
MKYE]D; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Kz2^f@5=F [-94=|S @ 非线性超快脉冲耦合的数值方法的Matlab程序 &IPK5o, ;%.k}R%O@ 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。
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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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ex)D T`0gtS S JRs[%w`kD n~cm?" % This Matlab script file solves the nonlinear Schrodinger equations
zgOwSg8 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
r\- k/ 0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J y[8,X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
RpXG gw lSv;wwEg C=1;
gK_[3FiKt M1=120, % integer for amplitude
K]Cs2IpI M3=5000; % integer for length of coupler
> l*9DaZ N = 512; % Number of Fourier modes (Time domain sampling points)
[*E.G~IS` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
+uXnFf d^ T =40; % length of time:T*T0.
.Eyk?"^ dt = T/N; % time step
C^v - &*v n = [-N/2:1:N/2-1]'; % Index
oa|*-nw t = n.*dt;
EF{' J8A Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
h/~BUg' w=2*pi*n./T;
8pt<)Rs} g1=-i*ww./2;
dllf~:b g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
:rc[j@|pH g3=-i*ww./2;
tF1%=&ss P1=0;
*J5euA5= P2=0;
4gt "dfy+ P3=1;
3sIM7WD? P=0;
iz5wUye g for m1=1:M1
TTak[e&j3 p=0.032*m1; %input amplitude
JJ06f~Iw[ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
QRa6*AYm s1=s10;
rZ4<*Zegv s20=0.*s10; %input in waveguide 2
mV]g5>Q\ s30=0.*s10; %input in waveguide 3
]Y!
Vyn s2=s20;
ai9,4 s3=s30;
RxG./GY p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
4?uG> ;V %energy in waveguide 1
1caod0gor p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
HBGA
lZ %energy in waveguide 2
UHHKI)( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
70(?X/5# %energy in waveguide 3
H5t`E^E for m3 = 1:1:M3 % Start space evolution
% E _{L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
| ^!@ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6;V 1PK>9 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
IcA~f@ sca1 = fftshift(fft(s1)); % Take Fourier transform
1< e%)? G sca2 = fftshift(fft(s2));
K0a
50@B] sca3 = fftshift(fft(s3));
SXF_)1QO\W sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
L #b Q`t sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
e:occT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
"b 7C0NE s3 = ifft(fftshift(sc3));
bUL9*{>G s2 = ifft(fftshift(sc2)); % Return to physical space
j o#F& s1 = ifft(fftshift(sc1));
1OS3Gv8jc~ end
^ Z+ D7Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:N:8O^D^< p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
3&:fS|L~c p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
EOC"a}Cq- P1=[P1 p1/p10];
F\72^,0 P2=[P2 p2/p10];
>*CK@"o P3=[P3 p3/p10];
#C}(7{Vt P=[P p*p];
=1Jo-!{{ end
l]&)an figure(1)
Okc*)crw plot(P,P1, P,P2, P,P3);
9x,+G['Zt k JF HUR 转自：
http://blog.163.com/opto_wang/
