计算脉冲在非线性耦合器中演化的Matlab 程序 e|y~q0Q$ [wYQP6Cyy % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IW*.B6Hw8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&|*| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8G<.5!f7`N % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\zyGJyy. /Vc!N)
%fid=fopen('e21.dat','w');
? GW3E N = 128; % Number of Fourier modes (Time domain sampling points)
mJT
m/C M1 =3000; % Total number of space steps
CB)#;
|aDB J =100; % Steps between output of space
Mq$=zsj T =10; % length of time windows:T*T0
xy>mM"DOH T0=0.1; % input pulse width
inrL'z MN1=0; % initial value for the space output location
nfB9M1Svn dt = T/N; % time step
P*]g*&*Y + n = [-N/2:1:N/2-1]'; % Index
[%:NR t = n.*dt;
:wm^04<i u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
na)ceN2h u20=u10.*0.0; % input to waveguide 2
N%yFL u1=u10; u2=u20;
d0az#Yg! U1 = u1;
:{2$X|f
3 U2 = u2; % Compute initial condition; save it in U
;'}xD5] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P]GGnT(! w=2*pi*n./T;
^\%%9jY g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
v>R.ou( L=4; % length of evoluation to compare with S. Trillo's paper
ln7.>.F dz=L/M1; % space step, make sure nonlinear<0.05
XF6=xD for m1 = 1:1:M1 % Start space evolution
#$E
vybETx u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
kEh# 0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_i#Z'4?2E ca1 = fftshift(fft(u1)); % Take Fourier transform
ok'1 ca2 = fftshift(fft(u2));
uv!/DX# c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
!$HWUxM;p c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
&-A7%" u2 = ifft(fftshift(c2)); % Return to physical space
~5b %~: u1 = ifft(fftshift(c1));
{ar}.U if rem(m1,J) == 0 % Save output every J steps.
:nt%z0_ U1 = [U1 u1]; % put solutions in U array
~MX@-Ff U2=[U2 u2];
N8TO"`wdbs MN1=[MN1 m1];
Mv3Ch'X[ z1=dz*MN1'; % output location
zO,sq%vQn' end
xAflcY>Ozs end
XA68H!I hg=abs(U1').*abs(U1'); % for data write to excel
I
uDk9<[b: ha=[z1 hg]; % for data write to excel
zD'gGxM1 t1=[0 t'];
A
3l1$t#w hh=[t1' ha']; % for data write to excel file
I$&/?ns@O %dlmwrite('aa',hh,'\t'); % save data in the excel format
-~g3?!+Hb figure(1)
Yu=^`I waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>J1o@0tk figure(2)
=zKp(_[D waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
TH-^tw \Ip<bbB0 非线性超快脉冲耦合的数值方法的Matlab程序 \?ZdUY 6dh PqL 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。
5V0=-K 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
'"EOLr\Z, <~3 aaO +-"#GL~cC v3p..A~XZ. % This Matlab script file solves the nonlinear Schrodinger equations
ntT|G0E % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
g6farLBF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@fwU%S[v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>cp9{+#f m`|Z1CT C=1;
#3S/TBy, M1=120, % integer for amplitude
fITml6mbE M3=5000; % integer for length of coupler
C{D2mSS N = 512; % Number of Fourier modes (Time domain sampling points)
'coqm8V[% dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
H_Yy.yi T =40; % length of time:T*T0.
!l~hO dt = T/N; % time step
SCo9[EJ n = [-N/2:1:N/2-1]'; % Index
qrdI" t = n.*dt;
qhtc?A/0} ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
B@4#y9`5 w=2*pi*n./T;
z(xvt> g1=-i*ww./2;
]1K
&U5p g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
;Cwn1N9S g3=-i*ww./2;
C9z{8 ; P1=0;
VYwaU^ P2=0;
E*%{Nn P3=1;
QqDF_ P=0;
[Xrq+O, for m1=1:M1
dx~Wm1 p=0.032*m1; %input amplitude
;?rW`e2 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
TcC=_je460 s1=s10;
GHkSU;}) s20=0.*s10; %input in waveguide 2
rk~/^(! s30=0.*s10; %input in waveguide 3
H\^^p!^) s2=s20;
KQqlM s3=s30;
u32<=Q[ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]8^2(^3ct %energy in waveguide 1
yU\|dL p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
AIeYy-f %energy in waveguide 2
\8pbPo=x p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
sOJ~PRA %energy in waveguide 3
myo/}58Nv for m3 = 1:1:M3 % Start space evolution
B[$e;h*Aw[ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
iPIA&)x}
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
]Cj&C/( s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
B5cTzY.h- sca1 = fftshift(fft(s1)); % Take Fourier transform
qHj4`& sca2 = fftshift(fft(s2));
#\jPBLc sca3 = fftshift(fft(s3));
IJ0RHDod: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
6?~pWZ&k_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
dU\fC{1Z sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
1{wy%|H\ s3 = ifft(fftshift(sc3));
~UnfS};U s2 = ifft(fftshift(sc2)); % Return to physical space
o
2DnkzpJ s1 = ifft(fftshift(sc1));
B4b UcYk end
GP[$&8\M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
ZpdM[\Q- p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
-&&mkK
B! p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
cr!I"kTgD P1=[P1 p1/p10];
9> |rIw P2=[P2 p2/p10];
hk=+t&Y<H P3=[P3 p3/p10];
B)(A#&nrb P=[P p*p];
2@H~nw 0 end
s)C.e# xl figure(1)
3drgB;:g` plot(P,P1, P,P2, P,P3);
[W;14BD7 ED6H 转自:
http://blog.163.com/opto_wang/