计算脉冲在非线性耦合器中演化的Matlab 程序 pNc4o@- Z4tc3e
% This Matlab script file solves the coupled nonlinear Schrodinger equations of
D ?r% Y % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
QykHB
k % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
sW!MV v % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
A|BN >?.t 5!7vD |6 %fid=fopen('e21.dat','w');
(:|1h@K/ R N = 128; % Number of Fourier modes (Time domain sampling points)
fG|+ ! M1 =3000; % Total number of space steps
LH>h]OTQF J =100; % Steps between output of space
* |)O T =10; % length of time windows:T*T0
bs_rw+ T0=0.1; % input pulse width
}r:8w*4 7 MN1=0; % initial value for the space output location
"Kf4v|6; dt = T/N; % time step
D0 rqte n = [-N/2:1:N/2-1]'; % Index
{fu[&@XV t = n.*dt;
09Y:(2Qri u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
anFl:= u20=u10.*0.0; % input to waveguide 2
i|G /x u1=u10; u2=u20;
YPS,[F'B. U1 = u1;
UQCon d+K U2 = u2; % Compute initial condition; save it in U
vjYG>YhV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-|_io,eL; w=2*pi*n./T;
[ jgC` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Ox+}JB
[ L=4; % length of evoluation to compare with S. Trillo's paper
J*]J H{ dz=L/M1; % space step, make sure nonlinear<0.05
]8EkZC for m1 = 1:1:M1 % Start space evolution
|sV@j_TX u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
((tWgSZ3 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
q@iZo,Yk ca1 = fftshift(fft(u1)); % Take Fourier transform
*uMtl' ca2 = fftshift(fft(u2));
[`=:uUf3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~Ec@hz]j s c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Z n]e2 u2 = ifft(fftshift(c2)); % Return to physical space
a|@1RH>7H u1 = ifft(fftshift(c1));
WvHy}1 W if rem(m1,J) == 0 % Save output every J steps.
<^B!. zQ U1 = [U1 u1]; % put solutions in U array
JL&ni]m U2=[U2 u2];
dF0 :'y MN1=[MN1 m1];
jX
6 +~ z1=dz*MN1'; % output location
$
iU~p end
"aeKrMgc6V end
? p^ ':@= hg=abs(U1').*abs(U1'); % for data write to excel
Y'M}lv$sa ha=[z1 hg]; % for data write to excel
|NaEXzo|qY t1=[0 t'];
S3_QO L hh=[t1' ha']; % for data write to excel file
O<6!?1 |KP %dlmwrite('aa',hh,'\t'); % save data in the excel format
;#6j9M0 figure(1)
9NcC.}#-5 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
SLI358]$< figure(2)
-vBk ,;^> waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ru1FJ{n 9/L J tM 非线性超快脉冲耦合的数值方法的Matlab程序 d)jX%Z$LC !FJ_\UST0 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。
/ S)&d N` 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
aFwfF^\(|, %dA7`7j 0Kenyn4 ? p4I6oS`/. % This Matlab script file solves the nonlinear Schrodinger equations
iC\t@BVS % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
^tFgkzXm % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Wy,Tf*[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3 Ho<4_I, S h RkL< C=1;
h5R5FzY0& M1=120, % integer for amplitude
NuKx{y }P M3=5000; % integer for length of coupler
R B M4_L N = 512; % Number of Fourier modes (Time domain sampling points)
vt-5 3fa| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
&y=~:1&f T =40; % length of time:T*T0.
s7TV@Y) dt = T/N; % time step
IEJp!P,E n = [-N/2:1:N/2-1]'; % Index
>QM$
NIf@ t = n.*dt;
4>x v7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
za@`,Yq w=2*pi*n./T;
H&zhYKw
g1=-i*ww./2;
&`4v,l^Zi6 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
7A[`%.!F6 g3=-i*ww./2;
$N1UEvC%Q P1=0;
u6( >?r- P2=0;
L(!mm P3=1;
jNA ^
(|: P=0;
E-q*u(IW for m1=1:M1
="*8ja-K p=0.032*m1; %input amplitude
^zr]#`@G s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
7`f',ZK% s1=s10;
4? {e?5) s20=0.*s10; %input in waveguide 2
E64d6z^7u s30=0.*s10; %input in waveguide 3
~
-hH#5 s2=s20;
W8
m*co s3=s30;
h^KLqPBt{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
enG jom %energy in waveguide 1
i@M^9|Gh p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
pZ4 ]oK\* %energy in waveguide 2
X6dv+&=? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Y SE6PG %energy in waveguide 3
Zu/ }TS9bi for m3 = 1:1:M3 % Start space evolution
e .|_=Gd2/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
} 6Uw4D61 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
H]7 ;O M/g s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
^L 1 # sca1 = fftshift(fft(s1)); % Take Fourier transform
D,r s) sca2 = fftshift(fft(s2));
2 nRL;[L*. sca3 = fftshift(fft(s3));
g qRwN p sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
&m6x*i-5\f sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
WwF4`kx T sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
B^SD 5 s3 = ifft(fftshift(sc3));
@ 0RB.- s2 = ifft(fftshift(sc2)); % Return to physical space
uI I:Y{G s1 = ifft(fftshift(sc1));
nVC:5ie end
=wW3 Tr7~ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
B|Rnh;B- p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
x`vIY-DS p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
u9*}@{, P1=[P1 p1/p10];
-PSI^%TR# P2=[P2 p2/p10];
bt,^- gt@ P3=[P3 p3/p10];
j:9kJq>mv P=[P p*p];
^vjN$JB
end
)k8=< =s figure(1)
|6pNe T[ plot(P,P1, P,P2, P,P3);
0pS|t/h0 c2z%|\q 转自：
http://blog.163.com/opto_wang/
