计算脉冲在非线性耦合器中演化的Matlab 程序 e*H$c?7NL GK&Dd"v % This Matlab script file solves the coupled nonlinear Schrodinger equations of
CV "Y40 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Z- (HDn % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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3Jx % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(Ln h> '2 n]Y _C^ %fid=fopen('e21.dat','w');
Q@n k T1o N = 128; % Number of Fourier modes (Time domain sampling points)
dZmq M1 =3000; % Total number of space steps
O]lfs > >x J =100; % Steps between output of space
{eUfwPAa3 T =10; % length of time windows:T*T0
+)S X T0=0.1; % input pulse width
}}_l@5 MN1=0; % initial value for the space output location
[dMxr9 M dt = T/N; % time step
rI/KrBM n = [-N/2:1:N/2-1]'; % Index
]U%Tm>s. t = n.*dt;
zhE7+`` g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
MzD0F#Y u20=u10.*0.0; % input to waveguide 2
K>y+3HN[6 u1=u10; u2=u20;
pdSyx>rJ U1 = u1;
^h=kJR9 U2 = u2; % Compute initial condition; save it in U
e$=|-J z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kZQ;\QL1} w=2*pi*n./T;
M.xEiHz g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
:xCobMs_/ L=4; % length of evoluation to compare with S. Trillo's paper
r$5!KO dz=L/M1; % space step, make sure nonlinear<0.05
d%bL_I) for m1 = 1:1:M1 % Start space evolution
x}d\%* B u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
RMK
U5A7 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9"S3A EI ca1 = fftshift(fft(u1)); % Take Fourier transform
fp0Va!T(V ca2 = fftshift(fft(u2));
.Ko`DH~!,C c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
:%{7Q $Xv< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
uk,f}Xc u2 = ifft(fftshift(c2)); % Return to physical space
M_K&x-H0 u1 = ifft(fftshift(c1));
zdCt#=QV?R if rem(m1,J) == 0 % Save output every J steps.
t2iFd? U1 = [U1 u1]; % put solutions in U array
n :P}K?lg U2=[U2 u2];
2dfA}i> k MN1=[MN1 m1];
r DuG[" z1=dz*MN1'; % output location
STe;Sr&p end
<FE O6YP end
^-ZqS hg=abs(U1').*abs(U1'); % for data write to excel
/hQ!dU.+ ha=[z1 hg]; % for data write to excel
<vs.Ucxx t1=[0 t'];
I /g]9
y hh=[t1' ha']; % for data write to excel file
Lst 5 %dlmwrite('aa',hh,'\t'); % save data in the excel format
_wBPn6gg` figure(1)
^d,d<Uc waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
J3=jC5=J4 figure(2)
w]_a0{Uh waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?= /l@ d %:lQ ~yn 非线性超快脉冲耦合的数值方法的Matlab程序 Sc&_6} K \T0`GpE 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
'PZJ{8= Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
tBrVg<]t Eq
t61O$x SPBXI[[- Z_%>yqD C % This Matlab script file solves the nonlinear Schrodinger equations
/-T%y uU % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
P+[R 0QS % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
U/>5C : % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~0L>l J #]r w@c C=1;
VuGSP]$ q M1=120, % integer for amplitude
@ o] F~x M3=5000; % integer for length of coupler
l<5!R;?$ N = 512; % Number of Fourier modes (Time domain sampling points)
Y3?kj@T`i dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
; ?!sU T =40; % length of time:T*T0.
||qW'kNWM dt = T/N; % time step
gb-n~m[y n = [-N/2:1:N/2-1]'; % Index
nN[,$`JD, t = n.*dt;
,Fb#%r % ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rie1F, w=2*pi*n./T;
rVLA"x 9u g1=-i*ww./2;
$/Mk.(3'P g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
@Z) &3ss g3=-i*ww./2;
>Q YxX<W P1=0;
!)GPI?{^5 P2=0;
di"*K*~y P3=1;
{+!_; zzZ P=0;
B$)KZR(u for m1=1:M1
k,2% %m p=0.032*m1; %input amplitude
t^q/'9Ai&J s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
YPN|qn( s1=s10;
S5j#&i s20=0.*s10; %input in waveguide 2
&kP>qTI^p~ s30=0.*s10; %input in waveguide 3
@^%# ]x,: s2=s20;
M:ttzsd s3=s30;
uy$o%NL-7 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~! @a %energy in waveguide 1
Rc u/ @j{O p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
o;t{Yf K %energy in waveguide 2
cng 1k
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
NS\'o
)J %energy in waveguide 3
1_A< nt?'R for m3 = 1:1:M3 % Start space evolution
}RXm=ArN s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
o^Ms(?K%t s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
|KuH2, n0 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
m$ ]?Jq sca1 = fftshift(fft(s1)); % Take Fourier transform
8E D6C"6 sca2 = fftshift(fft(s2));
! aL L|}S sca3 = fftshift(fft(s3));
YS/4<QA[ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%#=
1?1s sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
(|W@p \Q sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
s+a eP s3 = ifft(fftshift(sc3));
ALhu\x>AY s2 = ifft(fftshift(sc2)); % Return to physical space
)AnX[:y s1 = ifft(fftshift(sc1));
3iDRt&y=. end
}nkX-PG9 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
< d?O#( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
vuHqOAFNs p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
h W(Mf P1=[P1 p1/p10];
0N md*r P2=[P2 p2/p10];
7Kfh:0Ihhy P3=[P3 p3/p10];
u\50,N9Wp{ P=[P p*p];
%|UCs8EFm end
*f1MgP*GKF figure(1)
b*7OIN5h plot(P,P1, P,P2, P,P3);
ZZ#S\* ;as B@Q 转自：
http://blog.163.com/opto_wang/
