计算脉冲在非线性耦合器中演化的Matlab 程序 .GvZv> |pE
~ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
7Kt i& T % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
#_zj5B38E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~$YasFEz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
#y1M1O g Rd|^C$6 %fid=fopen('e21.dat','w');
bs)Ro/7} N = 128; % Number of Fourier modes (Time domain sampling points)
^ j<2s"S M1 =3000; % Total number of space steps
m
[BV{25 J =100; % Steps between output of space
h#u k-7 T =10; % length of time windows:T*T0
avUdv V- T0=0.1; % input pulse width
'i 8`LPQ MN1=0; % initial value for the space output location
zvT8r(<n} dt = T/N; % time step
cd4H bSp n = [-N/2:1:N/2-1]'; % Index
%
xBQX t = n.*dt;
5E2T*EXSh u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xC2y/ ? u20=u10.*0.0; % input to waveguide 2
3
op{h6 u1=u10; u2=u20;
%/RT}CBBsW U1 = u1;
%%lJyLq'Vk U2 = u2; % Compute initial condition; save it in U
`r0MQkk ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
8>DX
:` w=2*pi*n./T;
'fY29Xr^ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ePTxu Cf> L=4; % length of evoluation to compare with S. Trillo's paper
s_U--y.2r( dz=L/M1; % space step, make sure nonlinear<0.05
K^%ONultv for m1 = 1:1:M1 % Start space evolution
B8zc#0!1 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
mh#_lbe' u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
HcHwvf6y ca1 = fftshift(fft(u1)); % Take Fourier transform
r^,"OM] ca2 = fftshift(fft(u2));
yRt7&,}zL c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
/ & yc?Ui c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
`=2p6<#z u2 = ifft(fftshift(c2)); % Return to physical space
%5j* e u1 = ifft(fftshift(c1));
z!)@` ? if rem(m1,J) == 0 % Save output every J steps.
[vxHsY3z U1 = [U1 u1]; % put solutions in U array
`Cz_^>]|= U2=[U2 u2];
|^gnT`+ MN1=[MN1 m1];
24
RD z1=dz*MN1'; % output location
1/c+ug!y end
]vH:@%3U end
_BG7 JvI hg=abs(U1').*abs(U1'); % for data write to excel
seZb;0 ha=[z1 hg]; % for data write to excel
^(7 Qz&q t1=[0 t'];
)-\qo#0l hh=[t1' ha']; % for data write to excel file
:13u{5:th %dlmwrite('aa',hh,'\t'); % save data in the excel format
o>HGfr,N figure(1)
E|_}?>{R waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
z]!w@: figure(2)
mnU8i=v0 A waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
2FR 5RG
oD fRp(&%8E 非线性超快脉冲耦合的数值方法的Matlab程序 1? ,C d fPG3$<Zr 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。
Kr+#)S 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
q<4{&omUJ i>(TPj | Raf-I+ DDZnNSo<JQ % This Matlab script file solves the nonlinear Schrodinger equations
&@'+ h*
b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Twk<< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
UtHloq(r % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>C` #4e?} AL|3_+G C=1;
=sk#`,,: M1=120, % integer for amplitude
n'!x"O7 M3=5000; % integer for length of coupler
=:\5* N = 512; % Number of Fourier modes (Time domain sampling points)
I 1Yr{(ho dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
% {0F. T =40; % length of time:T*T0.
Us% _'}(/U dt = T/N; % time step
I^G6aw n = [-N/2:1:N/2-1]'; % Index
%I@ vM s^ t = n.*dt;
ul!q)cPb{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\ !IEZ w=2*pi*n./T;
P[r$KGz g1=-i*ww./2;
a Ts9 lr: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
xsU3c0wbr8 g3=-i*ww./2;
N3w y][bo P1=0;
$ SZIJe"K P2=0;
NosOd*S P3=1;
7yOBxb P=0;
w4l]rH for m1=1:M1
N[N4!k )!$ p=0.032*m1; %input amplitude
}$s QmR R s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:0Fc E,1 s1=s10;
nIqF:6/ s20=0.*s10; %input in waveguide 2
[C@ Ro,mI s30=0.*s10; %input in waveguide 3
a >k9&
w s2=s20;
GK#D R/OM s3=s30;
-jVg {f! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
38%"#T3# %energy in waveguide 1
n2Q ?sV;m p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
F1p|^hYDW %energy in waveguide 2
\!*F:v0g^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
juxAyds %energy in waveguide 3
"tu*(>'~5 for m3 = 1:1:M3 % Start space evolution
5[~ C!t; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Sp]ov:]%f s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
::@ JL s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
#z}0]GJKj sca1 = fftshift(fft(s1)); % Take Fourier transform
#hXuGBZEI sca2 = fftshift(fft(s2));
AG"iS<u sca3 = fftshift(fft(s3));
{ea*dX872: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
(@S 9>z4s sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
zR?1iV.] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
_w
FK+> s3 = ifft(fftshift(sc3));
>E
WK
cocM s2 = ifft(fftshift(sc2)); % Return to physical space
tZ:fOM s1 = ifft(fftshift(sc1));
o%K1 !' end
GE\({V.W p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
]N Kz5[9D p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
1 K] p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
m~F ~9& P1=[P1 p1/p10];
\!k\%j 9 P2=[P2 p2/p10];
#q8/=,3EG P3=[P3 p3/p10];
lE3&8~2 P=[P p*p];
nFwdW@E9 end
^$<:~qq ! figure(1)
<f0yh"?6VH plot(P,P1, P,P2, P,P3);
:^]Fp UY jI$7vmO 转自：
http://blog.163.com/opto_wang/
