计算脉冲在非线性耦合器中演化的Matlab 程序 ?' .AeoE- .a]#AFX % This Matlab script file solves the coupled nonlinear Schrodinger equations of
.Zczya % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
I7 oA7@zv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
qEr?4h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
N=BG0 t$ LXK!4(xa W %fid=fopen('e21.dat','w');
/j$=?Rp N = 128; % Number of Fourier modes (Time domain sampling points)
GeTk/tU M1 =3000; % Total number of space steps
/7 Tm2Vj8 J =100; % Steps between output of space
IgG[Pr'D T =10; % length of time windows:T*T0
v^b4WS+.: T0=0.1; % input pulse width
Os@b8V 8,A MN1=0; % initial value for the space output location
6s SwSS dt = T/N; % time step
x_nwD" n = [-N/2:1:N/2-1]'; % Index
Mg.%&vH\ t = n.*dt;
^iMr't\b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
h<U?WtWT-p u20=u10.*0.0; % input to waveguide 2
&7f8\TG| u1=u10; u2=u20;
o=3hWb e U1 = u1;
O `9c!_lis U2 = u2; % Compute initial condition; save it in U
&bW,N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a X^T[ w=2*pi*n./T;
3&+dyhL'w g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
/ooGyF L=4; % length of evoluation to compare with S. Trillo's paper
yx5e dz=L/M1; % space step, make sure nonlinear<0.05
::oFL#+ for m1 = 1:1:M1 % Start space evolution
%hsCB
.r>| u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
e4tIO u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
;Z d_2CZ ca1 = fftshift(fft(u1)); % Take Fourier transform
b$,Hlh,^ ca2 = fftshift(fft(u2));
G kjfDY: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
RW L0@\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+7 H) s u2 = ifft(fftshift(c2)); % Return to physical space
$+'H000x u1 = ifft(fftshift(c1));
Reikf}9Q if rem(m1,J) == 0 % Save output every J steps.
vd4@ jZ5 U1 = [U1 u1]; % put solutions in U array
Io]FDPN U2=[U2 u2];
V:kRr cX MN1=[MN1 m1];
f1MRmp-f' z1=dz*MN1'; % output location
\b"rf697 , end
?8-!hU@QC end
'dwT&v]@ hg=abs(U1').*abs(U1'); % for data write to excel
&J6`Q<U! ha=[z1 hg]; % for data write to excel
(`.OS)& t1=[0 t'];
:Z// hh=[t1' ha']; % for data write to excel file
fY!?rZ)$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
4k ;FZo]S figure(1)
OoSk ^U) waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
! I@w3` figure(2)
<?nI O waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}csA|cC a;HAuy`M x 非线性超快脉冲耦合的数值方法的Matlab程序 r)iEtT !p* I\. |\^ 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。
N)X Tmh2v| 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
!g|O.mt H b=#` |Kd#pYt% O P}@AH02
% This Matlab script file solves the nonlinear Schrodinger equations
4XN
\p % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
"6f`h y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=0)|psCsM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+F; 2FD$ QtW9!p7( C=1;
2Vx4"fHP#N M1=120, % integer for amplitude
#fuUAbU0 X M3=5000; % integer for length of coupler
o<Zlm)"%1 N = 512; % Number of Fourier modes (Time domain sampling points)
I=0c\ U} dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
9-42A7g^C T =40; % length of time:T*T0.
/ Q1*Vh4 dt = T/N; % time step
mU/o%|h n = [-N/2:1:N/2-1]'; % Index
/Y0~BQC7! t = n.*dt;
"V|Rq]_+% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`Ofh zOp w=2*pi*n./T;
J>Ar(p g1=-i*ww./2;
l]]NVBA]) g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
V[tebv! g3=-i*ww./2;
$BwWQ ?lp P1=0;
% N8I'*u P2=0;
P#O" {+` P3=1;
<o(;~ P=0;
hG1$ YE for m1=1:M1
WyO*8b_
D p=0.032*m1; %input amplitude
v
vErzUxN s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
CD`a-]6qA s1=s10;
xs"i_se s20=0.*s10; %input in waveguide 2
]es|%j 2 s30=0.*s10; %input in waveguide 3
<XeDJ8
' s2=s20;
k1B
](@xt s3=s30;
'.| } p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Wmbc
`XC %energy in waveguide 1
{< -s&%/r p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
v$}^$8` %energy in waveguide 2
L ]')=J+ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
FQ WjL>NB %energy in waveguide 3
yq~ for m3 = 1:1:M3 % Start space evolution
'}hSh s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
v `S5[{6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
.}dLqw s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
7Jb&~{DVk sca1 = fftshift(fft(s1)); % Take Fourier transform
[+[ W\6 sca2 = fftshift(fft(s2));
yX&#
rI sca3 = fftshift(fft(s3));
: w^:Z$-hf sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
\] x`f3F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
LK h=jB^bT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$xu2ZBK s3 = ifft(fftshift(sc3));
: /5+p>Ep} s2 = ifft(fftshift(sc2)); % Return to physical space
t #(NfzN s1 = ifft(fftshift(sc1));
2"6L\8hd2 end
@fd< p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Z!v,;MW p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
B V al U p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
^A ]4 P1=[P1 p1/p10];
~A0AB
`7 P2=[P2 p2/p10];
2f(`H SC' P3=[P3 p3/p10];
+ wQ5m8E P=[P p*p];
N<JI^%HBgP end
Sq Az(( figure(1)
dX?j /M- plot(P,P1, P,P2, P,P3);
m-{DhJV /M5.Z~|/ 转自：
http://blog.163.com/opto_wang/
