计算脉冲在非线性耦合器中演化的Matlab 程序 Mn$]I) $ .s<*'B7& % This Matlab script file solves the coupled nonlinear Schrodinger equations of
%/c+`Wd/l$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
6*qL[m.F[o % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
JOb*-q|y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Rx*BwZ I=7Y]w= %fid=fopen('e21.dat','w');
4B4Z])$3 N = 128; % Number of Fourier modes (Time domain sampling points)
i]=&
M1 =3000; % Total number of space steps
dWX stb:[ J =100; % Steps between output of space
:U
d T =10; % length of time windows:T*T0
JXixYwm T0=0.1; % input pulse width
5GA\xM - MN1=0; % initial value for the space output location
{^ m(,K_ dt = T/N; % time step
/erN;Oo%< n = [-N/2:1:N/2-1]'; % Index
CW )Z[<d8 t = n.*dt;
e/*$^i+S u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
4\pWB90V u20=u10.*0.0; % input to waveguide 2
RbGJ)K! u1=u10; u2=u20;
R g?1-|Tj U1 = u1;
Y XU|h U2 = u2; % Compute initial condition; save it in U
KJ?y@Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l"{Sm6:;- w=2*pi*n./T;
6
4D]Ypx g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
W(25TbQ L=4; % length of evoluation to compare with S. Trillo's paper
u>Rb
?` dz=L/M1; % space step, make sure nonlinear<0.05
yJsH=5A for m1 = 1:1:M1 % Start space evolution
Og2vGzD u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
|+:h|UIUQ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9D 0dg( ca1 = fftshift(fft(u1)); % Take Fourier transform
/w8"=6Vv~ ca2 = fftshift(fft(u2));
d'*]ns c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g|Y] wd c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
O1D6^3w u2 = ifft(fftshift(c2)); % Return to physical space
>S1)YKgz u1 = ifft(fftshift(c1));
!@I}mQ ~ if rem(m1,J) == 0 % Save output every J steps.
t p:\j@dB U1 = [U1 u1]; % put solutions in U array
=H %-.m'f2 U2=[U2 u2];
6 CC &Z> MN1=[MN1 m1];
MlJVeo d z1=dz*MN1'; % output location
;' nL:\ end
T"T;`y@ ( end
iB1i/l hg=abs(U1').*abs(U1'); % for data write to excel
p0{EQT`tMG ha=[z1 hg]; % for data write to excel
?\/qeGW6G t1=[0 t'];
1z*kc)=JF8 hh=[t1' ha']; % for data write to excel file
Bi~:>X\[^6 %dlmwrite('aa',hh,'\t'); % save data in the excel format
P F`rWw figure(1)
:Pq., s waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Fl{ WAg figure(2)
D -IR!js ] waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?X9]HlH IN7<@OS7 非线性超快脉冲耦合的数值方法的Matlab程序 T;\^#1 y/? &pKH^ 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。
m7=1%6FN3 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
TFR(
4W 3Z>YV]YbeU 2X88: |<`.fOxJP % This Matlab script file solves the nonlinear Schrodinger equations
maS gRf[g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
-$ <O\5cAQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
9
L?;FY)_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7OVbP%n)d2 G{x[uE2X&f C=1;
~%#mK:+ M1=120, % integer for amplitude
Nf9fb? M3=5000; % integer for length of coupler
K{cbn1\,H N = 512; % Number of Fourier modes (Time domain sampling points)
/^#G0f*N dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p|XAl ia T =40; % length of time:T*T0.
Rt( J/%; dt = T/N; % time step
+VU4s$w6 n = [-N/2:1:N/2-1]'; % Index
K(T\9J. t = n.*dt;
f+Dn9t ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7Bz*r0 9S w=2*pi*n./T;
x.$1<w64t g1=-i*ww./2;
JmOW~W g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
GZ }/leR g3=-i*ww./2;
5V- jMB P1=0;
% do1i W P2=0;
#T~&]|{, P3=1;
W W " i P=0;
DFe;4BdC for m1=1:M1
~! + _[ uJ p=0.032*m1; %input amplitude
Nm]%
} s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Di=9m HC s1=s10;
qJ8-9^E,L s20=0.*s10; %input in waveguide 2
|G=[5e^s[ s30=0.*s10; %input in waveguide 3
BH@b1} s2=s20;
PI|`vC|yy& s3=s30;
h ? #@~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Xt,X_o2m|] %energy in waveguide 1
)QY![&k}1z p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
kJ=L2g>W<. %energy in waveguide 2
,#'7)M D8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Sl~x$9` %energy in waveguide 3
.Gb +\E{M for m3 = 1:1:M3 % Start space evolution
;?IT)sNY s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(TSqc5^H s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
ilEi")b = s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Ff"gadRXd sca1 = fftshift(fft(s1)); % Take Fourier transform
Eych R/ s sca2 = fftshift(fft(s2));
2HOe__Ns sca3 = fftshift(fft(s3));
s` >H sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
3;$b S<> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!Qu PG/=X sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
R Td^ImV s3 = ifft(fftshift(sc3));
"D> ]ES%5 s2 = ifft(fftshift(sc2)); % Return to physical space
R]b! $6Lt s1 = ifft(fftshift(sc1));
]TK=>;& end
)&Z>@S^ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
T!(
4QRh[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
T$b\Q p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
9NIy# P1=[P1 p1/p10];
4nX(:K}> P2=[P2 p2/p10];
Uh6mGL z*& P3=[P3 p3/p10];
mf 4z?G@6 P=[P p*p];
(Nz]h: }r end
L :U4N* figure(1)
kl{6 ]39 plot(P,P1, P,P2, P,P3);
I}:L ]H{E z
Bf;fi 转自：
http://blog.163.com/opto_wang/
