计算脉冲在非线性耦合器中演化的Matlab 程序 }ak F=/M nlq"OzcH04 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
5x2m ]u % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
6T qs6* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*_ U=KpZF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J7RO*.O&Iq oMUyP~1 %fid=fopen('e21.dat','w');
'yw7|i2 N = 128; % Number of Fourier modes (Time domain sampling points)
f\|R<3 L M1 =3000; % Total number of space steps
,rU>)X J =100; % Steps between output of space
7 { n>0@_ T =10; % length of time windows:T*T0
RT~6 #Caf T0=0.1; % input pulse width
(6Y.|u]bq MN1=0; % initial value for the space output location
z'!sc"]W6 dt = T/N; % time step
'QP~uK n = [-N/2:1:N/2-1]'; % Index
smJ#.I6/L t = n.*dt;
< %t$0' u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@hG]Gs[,o u20=u10.*0.0; % input to waveguide 2
GGW dM GI/ u1=u10; u2=u20;
$q%l)]+ U1 = u1;
vJ a? 5Jr U2 = u2; % Compute initial condition; save it in U
m%p ;>:"R ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'KU)]v w=2*pi*n./T;
:~ ; 48m g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
!8Mi+ZV L=4; % length of evoluation to compare with S. Trillo's paper
~stG2^ "[ dz=L/M1; % space step, make sure nonlinear<0.05
%8]~+ #]p for m1 = 1:1:M1 % Start space evolution
B7u4e8(E* u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
=iFI@2 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9EU0R
H ca1 = fftshift(fft(u1)); % Take Fourier transform
~\QN.a ca2 = fftshift(fft(u2));
BMJsR0 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
KB\A<(o, c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
o6@`aU u2 = ifft(fftshift(c2)); % Return to physical space
}R\;htmc; u1 = ifft(fftshift(c1));
jg3 X6 /' if rem(m1,J) == 0 % Save output every J steps.
d>YX18'<Q U1 = [U1 u1]; % put solutions in U array
h%[1V U2=[U2 u2];
<W2 YG6^i MN1=[MN1 m1];
.1@8rVp7 z1=dz*MN1'; % output location
nu<kx end
ol #4 AU` end
#FwTV@ hg=abs(U1').*abs(U1'); % for data write to excel
$;Nw_S@ ha=[z1 hg]; % for data write to excel
+DR ,&; t1=[0 t'];
iYR`|PJi hh=[t1' ha']; % for data write to excel file
f.{/PL %dlmwrite('aa',hh,'\t'); % save data in the excel format
[izP1A$r#Q figure(1)
-NL=^O$G waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ys DGF@wZC figure(2)
pLtAusx waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
)"sJaHx< Y2&hf6BE 非线性超快脉冲耦合的数值方法的Matlab程序 p8bAz B HrN Dpv 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
11Y4oS Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1!"iN~ tg#d.( TMAart; < : 3 p&h[M % This Matlab script file solves the nonlinear Schrodinger equations
M WHzrqCA % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
_u QxrB"9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\1[v-hvK % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Nxr %xTD *{1]b_< C=1;
!IAd.<, M1=120, % integer for amplitude
*T:gx:Sg/ M3=5000; % integer for length of coupler
h5p,BRtu N = 512; % Number of Fourier modes (Time domain sampling points)
ELa:yIl0 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^Sj* T =40; % length of time:T*T0.
+|c1G[Jh dt = T/N; % time step
QKt+Orz n = [-N/2:1:N/2-1]'; % Index
f
J$>VN t = n.*dt;
mJFFst, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
I>n2# -8 w=2*pi*n./T;
F b ^f`UI g1=-i*ww./2;
|*te69RX g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3^2P7$W= g3=-i*ww./2;
US2Tdmy@05 P1=0;
=c Krp' P2=0;
em, j>qp P3=1;
D F N P=0;
o)SA^5 for m1=1:M1
?I}0[+)V p=0.032*m1; %input amplitude
Ps=<@,dks s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
#1VejeTi s1=s10;
y>iot e~ s20=0.*s10; %input in waveguide 2
z>9gt s30=0.*s10; %input in waveguide 3
;UoXj+Z s2=s20;
yaW HGre s3=s30;
x^u [L$ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,`. `}' %energy in waveguide 1
V(6GM+ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)uxXG `,h %energy in waveguide 2
03^?+[C p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
_ ;8+L\ %energy in waveguide 3
"Qfw)!# for m3 = 1:1:M3 % Start space evolution
8iKupaaOX s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
l.AG ^b s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
!P uW6 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
kf >L sca1 = fftshift(fft(s1)); % Take Fourier transform
` 8OA:4). sca2 = fftshift(fft(s2));
01AzM)U3"m sca3 = fftshift(fft(s3));
F]k$ O $)0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
q@ 8j[15 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0$e]?]X6 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Zg2F%f$Y s3 = ifft(fftshift(sc3));
MsLQ'9%Au s2 = ifft(fftshift(sc2)); % Return to physical space
l! 9G s1 = ifft(fftshift(sc1));
D`f i\A end
?KF.v1w7 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
oMer+=vH p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
(25v7 Y ] p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
97~*Z|#<+ P1=[P1 p1/p10];
(U#9 P2=[P2 p2/p10];
eq(Xzh P3=[P3 p3/p10];
F2k)hG*|{ P=[P p*p];
\ 5=fC9*G end
"H!2{l{ figure(1)
Fm,} sP"Qx plot(P,P1, P,P2, P,P3);
y*fU_Il|! Kl )PF), 转自：
http://blog.163.com/opto_wang/
