计算脉冲在非线性耦合器中演化的Matlab 程序 g&X
X@I8+v yH]w(z5Z % This Matlab script file solves the coupled nonlinear Schrodinger equations of
L6J.^tpO % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
!qTP % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
D'Uv7Mis % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;up Yam" q m"AatA %fid=fopen('e21.dat','w');
I|_U|H!` N = 128; % Number of Fourier modes (Time domain sampling points)
spTIhZ M1 =3000; % Total number of space steps
GSVLZF'+ J =100; % Steps between output of space
q1Ehl
S T =10; % length of time windows:T*T0
Y/qs\c+ T0=0.1; % input pulse width
rvPmd%nk- MN1=0; % initial value for the space output location
QPKY9.Rvv dt = T/N; % time step
_7,4C? n = [-N/2:1:N/2-1]'; % Index
6nW]Q^N} t = n.*dt;
wSG!.Ejc7 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
bP7 _QYQ6 u20=u10.*0.0; % input to waveguide 2
2bxW`.fa u1=u10; u2=u20;
9''x'E=| U1 = u1;
nS]Ih 0( K U2 = u2; % Compute initial condition; save it in U
a 9Kws[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T) MZ`dM w=2*pi*n./T;
`}~ NZ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
q=;U(,Y L=4; % length of evoluation to compare with S. Trillo's paper
Em/? 4 & dz=L/M1; % space step, make sure nonlinear<0.05
7&1 dr for m1 = 1:1:M1 % Start space evolution
E<77Tj u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
B X Et]+Q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/, JL \b ca1 = fftshift(fft(u1)); % Take Fourier transform
UGQH wz ca2 = fftshift(fft(u2));
pW-aX)\DR c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
W&e}* c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
&o7"L; u2 = ifft(fftshift(c2)); % Return to physical space
VIuzBmR|\ u1 = ifft(fftshift(c1));
wPr!. :MF if rem(m1,J) == 0 % Save output every J steps.
Og2G0s WRf U1 = [U1 u1]; % put solutions in U array
2@:Ztt6~ U2=[U2 u2];
r~PVh? MN1=[MN1 m1];
@Mf ZP~T+ z1=dz*MN1'; % output location
0t -=*7w% end
R'h.lX end
BZk0B ? hg=abs(U1').*abs(U1'); % for data write to excel
&cT@MV5 ha=[z1 hg]; % for data write to excel
n o7Q%O9 t1=[0 t'];
C@rIyBj1g hh=[t1' ha']; % for data write to excel file
\)2~o N %dlmwrite('aa',hh,'\t'); % save data in the excel format
sYd)r%%AU figure(1)
B=|m._OL]n waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%D E_kwL figure(2)
A8 j$c ~ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
7t|011< U2*kuP+n 非线性超快脉冲耦合的数值方法的Matlab程序 zS! +2/( lnt }l 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。
7-4S'rq+ 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
P@8S|#LpZ ; f9a0V s AO]1`b : U_@Dn[/: % This Matlab script file solves the nonlinear Schrodinger equations
5.F/>?< % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
b}Wm-]|+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z{A~d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
""x>-j4 ^%}PRl9 C=1;
-02.n}u> M1=120, % integer for amplitude
9bu1Ax1M M3=5000; % integer for length of coupler
diD[/&k#kh N = 512; % Number of Fourier modes (Time domain sampling points)
.t$1B 5 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Z^% aXaf8 T =40; % length of time:T*T0.
Fqg *H1 I[ dt = T/N; % time step
!_+ok$"d n = [-N/2:1:N/2-1]'; % Index
]s}9-!{O
t = n.*dt;
{1[f9uPS ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{{ +8oRzY w=2*pi*n./T;
Z>J3 DH g1=-i*ww./2;
.pPtBqp g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7 MG<!U g3=-i*ww./2;
iB3C.wd - P1=0;
k5eTfaxl P2=0;
{lN G:o P3=1;
~otV'= /my P=0;
_t@9WA;+\ for m1=1:M1
:\"g}AX p=0.032*m1; %input amplitude
:?H1h8wbCt s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
a_k~z3wG s1=s10;
?xb2jZ/0X s20=0.*s10; %input in waveguide 2
V( 3rTDg s30=0.*s10; %input in waveguide 3
z9ZS& => s2=s20;
xH{ V.n&v s3=s30;
Hw%lT}[O p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Fz^5cx mw %energy in waveguide 1
T,5(JP(h3 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
e/F+Tf %energy in waveguide 2
=[IKwmCX p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
`{'h+v` %energy in waveguide 3
|#x]/AXa0/ for m3 = 1:1:M3 % Start space evolution
9[Xe|5?c s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#gRtCoew s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
RgLk AHA s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
gutf[Ksu sca1 = fftshift(fft(s1)); % Take Fourier transform
0l~z0pvT sca2 = fftshift(fft(s2));
PAs.T4Av^ sca3 = fftshift(fft(s3));
~Ut?'}L(
d sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;-!O +c sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
y.?Q sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
1-?TjR s3 = ifft(fftshift(sc3));
!-s 6B s2 = ifft(fftshift(sc2)); % Return to physical space
!=(M P: s1 = ifft(fftshift(sc1));
z-;yDB:~t end
RbJbVFz8C p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
4B'-tV p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
j$=MJN0 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
;N!W|G P1=[P1 p1/p10];
4/E>k <MA P2=[P2 p2/p10];
bVY sPS P3=[P3 p3/p10];
h SU|rVi P=[P p*p];
!k=~a] end
<x\I*% ( figure(1)
b~O c: plot(P,P1, P,P2, P,P3);
y\}<N6 #5mnSky+s 转自：
http://blog.163.com/opto_wang/
