计算脉冲在非线性耦合器中演化的Matlab 程序 (Q @m;i> N8KHNTb-M % This Matlab script file solves the coupled nonlinear Schrodinger equations of
{!-w|&bF % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
[0 W^|=#K % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]$z~;\ T % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
P[Qr[74 ) sx/g5 ?zh %fid=fopen('e21.dat','w');
? 56Zw"89 N = 128; % Number of Fourier modes (Time domain sampling points)
.M_;mhRI M1 =3000; % Total number of space steps
'8}\! i& J =100; % Steps between output of space
<
*XC`Ii T =10; % length of time windows:T*T0
QZDGk4GG T0=0.1; % input pulse width
g'mk hF( MN1=0; % initial value for the space output location
>8 RIMW2 dt = T/N; % time step
\TKv3N n = [-N/2:1:N/2-1]'; % Index
*EotYT t = n.*dt;
9 /9 ,[ A u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
wngxVhu8Ld u20=u10.*0.0; % input to waveguide 2
@
#V31im"N u1=u10; u2=u20;
)Dv"seH. U1 = u1;
QJ$]~)w?H U2 = u2; % Compute initial condition; save it in U
| o+ vpy ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A ?_2@6Y^ w=2*pi*n./T;
/ A_
IS ` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
G M@TWwG-B L=4; % length of evoluation to compare with S. Trillo's paper
7C&`i}/t dz=L/M1; % space step, make sure nonlinear<0.05
b?r0n] for m1 = 1:1:M1 % Start space evolution
bi,%QZZ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
& ??)gMM[ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I{ M2nQi ca1 = fftshift(fft(u1)); % Take Fourier transform
F9d][ P@@ ca2 = fftshift(fft(u2));
~)()PO c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
YrB-;R 1+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
EK#w: " u2 = ifft(fftshift(c2)); % Return to physical space
xE + Go u1 = ifft(fftshift(c1));
ysL8w"t if rem(m1,J) == 0 % Save output every J steps.
'dBzv>ngD U1 = [U1 u1]; % put solutions in U array
|=7%Edkd U2=[U2 u2];
( /uL6W d0 MN1=[MN1 m1];
Cu!4ha.e` z1=dz*MN1'; % output location
?l bX.+ end
#ReW#?P%b/ end
#?aR,@n hg=abs(U1').*abs(U1'); % for data write to excel
Q>X ;7nt0 ha=[z1 hg]; % for data write to excel
G"J 6X e t1=[0 t'];
(spX3n%p hh=[t1' ha']; % for data write to excel file
5|AZ/!rb %dlmwrite('aa',hh,'\t'); % save data in the excel format
'o5[ :=K figure(1)
gg6&Fzp waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U~7.aZHPx3 figure(2)
!vG._7lPp waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<nIU]}q F@?QVdY1q7 非线性超快脉冲耦合的数值方法的Matlab程序 qHv W{0E J _`.w 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。
J\2F%kBej? 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
HI:E&20y dedi6Brl M`"2; % 3FI>\3 % This Matlab script file solves the nonlinear Schrodinger equations
B [y1RI|9 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+K+
== mO& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ib&
|271gG % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
SqEO
] ~ :?lSa6de C=1;
6Q\n<&,{ M1=120, % integer for amplitude
hI/p9
`w M3=5000; % integer for length of coupler
e _,_:|t N = 512; % Number of Fourier modes (Time domain sampling points)
j^LnHVHk1 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
;M}bQ88 T =40; % length of time:T*T0.
\QHM7C T dt = T/N; % time step
6g$+ ))g n = [-N/2:1:N/2-1]'; % Index
Ot v{#bB$ t = n.*dt;
=#1/<q)L ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
64zO%F* w=2*pi*n./T;
:@Q_oyWE8 g1=-i*ww./2;
.]8 Jeb g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
I |BLAm6j g3=-i*ww./2;
=. OW sFv P1=0;
c L84}1QD P2=0;
SR8[
7MU P3=1;
qf
]ax!bK P=0;
GT' %HmQI for m1=1:M1
<$ '#@jW p=0.032*m1; %input amplitude
bp5hS/A^1w s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
M~3(4, s1=s10;
t$s)S> s20=0.*s10; %input in waveguide 2
x37r{$ 2 s30=0.*s10; %input in waveguide 3
J&h 3, s2=s20;
8B\,*JGY2 s3=s30;
x~KS;hA p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
{>5 c,L$ %energy in waveguide 1
G.c s -f p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
r?H {Y3 , %energy in waveguide 2
b/E1v,/< p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
UlQ }
%energy in waveguide 3
m@"!=CTKd for m3 = 1:1:M3 % Start space evolution
JB* *z00; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
o'R_kadN[T s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5MiWM2"X\ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
-@AGQ+e sca1 = fftshift(fft(s1)); % Take Fourier transform
@-Gf+*GZys sca2 = fftshift(fft(s2));
yp!Xwq#n sca3 = fftshift(fft(s3));
"BE U%,w sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
arDY@o~ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!L > 'g sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
|RHX2sso s3 = ifft(fftshift(sc3));
7dxY07 yu s2 = ifft(fftshift(sc2)); % Return to physical space
3",6 E( s1 = ifft(fftshift(sc1));
92eS*x2@ end
]_5C5m p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\5X34'7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
I]TL#ywF p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
E&]S No< P1=[P1 p1/p10];
%_} #IS1 P2=[P2 p2/p10];
?c(f6p?% P3=[P3 p3/p10];
sE]eIN P=[P p*p];
-3ha LdRk6 end
b>;5#OQfn figure(1)
awMm&8cIM plot(P,P1, P,P2, P,P3);
5 wr0+Xo TlAY=JwW 转自：
http://blog.163.com/opto_wang/
