计算脉冲在非线性耦合器中演化的Matlab 程序 E0 `Lg
c ,`ZYvF^% % This Matlab script file solves the coupled nonlinear Schrodinger equations of
E kGQ(fZ1| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
F u&EhGm6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
nqwAQhzy( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
o9cM{ya/> 3 %.#}O,( %fid=fopen('e21.dat','w');
G mf B N = 128; % Number of Fourier modes (Time domain sampling points)
e l:9 wq M1 =3000; % Total number of space steps
8]&i-VFof J =100; % Steps between output of space
+ }f9 T =10; % length of time windows:T*T0
K&8dA0i2u2 T0=0.1; % input pulse width
3O7!`Nm@ MN1=0; % initial value for the space output location
_`64gS}^ dt = T/N; % time step
}Tf9S<xpq3 n = [-N/2:1:N/2-1]'; % Index
BD`2l!d t = n.*dt;
L%>n>w u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!S& L*OH, u20=u10.*0.0; % input to waveguide 2
5]M>8ll u1=u10; u2=u20;
o]
mD"3_ U1 = u1;
Qt vY v! U2 = u2; % Compute initial condition; save it in U
a{ {g<< H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P-ri=E}> w=2*pi*n./T;
B<C* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
_/wV;h~R L=4; % length of evoluation to compare with S. Trillo's paper
2Ry1b+\ dz=L/M1; % space step, make sure nonlinear<0.05
D@!=d@V. for m1 = 1:1:M1 % Start space evolution
i;!H!-sM u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
IpP~Uz u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
^h{)Gf,+\ ca1 = fftshift(fft(u1)); % Take Fourier transform
1KjU ]
r2 ca2 = fftshift(fft(u2));
r k)##) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
sg+uBCGB c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
I4&:: y^ C u2 = ifft(fftshift(c2)); % Return to physical space
>Wz;ySEz u1 = ifft(fftshift(c1));
@: KJYm[ if rem(m1,J) == 0 % Save output every J steps.
z )HD`Ho U1 = [U1 u1]; % put solutions in U array
;A#`]-i C U2=[U2 u2];
^5=B`aich MN1=[MN1 m1];
5 Kkdo !z z1=dz*MN1'; % output location
ve\X3"p# end
WJ_IuX51' end
_6wFba@>/n hg=abs(U1').*abs(U1'); % for data write to excel
w:
>5=mfk ha=[z1 hg]; % for data write to excel
q7"7U=W0 t1=[0 t'];
_Gu -
uuy hh=[t1' ha']; % for data write to excel file
{#)0EzV6 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Me=CSQqf< figure(1)
=C~/7N,lW] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
. |/~op4; figure(2)
W^s
;Bi+Nw waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
gB<3-J1R W^G>cC8.L 非线性超快脉冲耦合的数值方法的Matlab程序 |jM4E$
XP @1~$ 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。
4Z/f@Z D 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
@r?Uua s>^dxF!+ # vry0i zL\OB?)5J % This Matlab script file solves the nonlinear Schrodinger equations
|O"lNUW % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
IKi5 v~bE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
-=(!g&0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Kw#i),M {RF-sqce C=1;
z@w Mc
EH M1=120, % integer for amplitude
VZ\B<i M3=5000; % integer for length of coupler
*cEob b N = 512; % Number of Fourier modes (Time domain sampling points)
NOp609\^ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
=KR
NvW T =40; % length of time:T*T0.
L: z?Zt)| dt = T/N; % time step
Y*! qG n = [-N/2:1:N/2-1]'; % Index
ahPoEh t = n.*dt;
4T=u`3pD7l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9k 6r_G" w=2*pi*n./T;
Ud!4"<C_ g1=-i*ww./2;
=MvjLh" s g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Pcw6!xH g3=-i*ww./2;
+-G<c6 | P1=0;
f-% NaTI P2=0;
!&"<oPjr+ P3=1;
4fKC 6UR P=0;
"70WUx(\t for m1=1:M1
Jm42b4 p=0.032*m1; %input amplitude
>ss/D^YS s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:duo#w"K s1=s10;
R%'^ gFk 8 s20=0.*s10; %input in waveguide 2
MX@ _=Sp- s30=0.*s10; %input in waveguide 3
$ mI0Bk s2=s20;
}oNhl^JC s3=s30;
2/0v B> p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
L>YU,I\o %energy in waveguide 1
3Oi
nK[' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
qv@$ZL R %energy in waveguide 2
rp0ZvEX p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
d ,=r 9. %energy in waveguide 3
BN 4_: for m3 = 1:1:M3 % Start space evolution
kP?KXT3y s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
xQ@^$_ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
*q1% IJ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V# `fs|e;y sca1 = fftshift(fft(s1)); % Take Fourier transform
_-#'j2 sca2 = fftshift(fft(s2));
#cCL.p"] sca3 = fftshift(fft(s3));
Q_Gi]M9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
dX)GPC-D7 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
/;utcc sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
AqV7 \gdOC s3 = ifft(fftshift(sc3));
uxzze~_+C s2 = ifft(fftshift(sc2)); % Return to physical space
E~_]Lfs) s1 = ifft(fftshift(sc1));
OdB?_.+ $ end
dx+hhg \L p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
UNkC L4N p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
7=DjI ~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]~E0gsq P1=[P1 p1/p10];
4A2?Uhp y P2=[P2 p2/p10];
l@ap]R P3=[P3 p3/p10];
nTz6LVF P=[P p*p];
<Ce2r"U1e end
7IjQi=#: figure(1)
9s_,crq5 plot(P,P1, P,P2, P,P3);
yfC^x%d7G k+DR]icv 转自：
http://blog.163.com/opto_wang/
