计算脉冲在非线性耦合器中演化的Matlab 程序 L+c7.l.yT ZwV`} 2{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
*6-f vqCv % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
9'qU4I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}| k_sx: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
oPX `/ X# r@2{>j8 %fid=fopen('e21.dat','w');
5i+0GN3nd N = 128; % Number of Fourier modes (Time domain sampling points)
j &#A 9! M1 =3000; % Total number of space steps
#q06K2 J =100; % Steps between output of space
c\n&Z'vK T =10; % length of time windows:T*T0
1;\A./FVv T0=0.1; % input pulse width
b)SU8z!NV& MN1=0; % initial value for the space output location
QJcaOXyMS dt = T/N; % time step
A?DgeSm n = [-N/2:1:N/2-1]'; % Index
f1a >C t = n.*dt;
3
e19l!B u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
LEq"g7YH u20=u10.*0.0; % input to waveguide 2
bN ,>,hj u1=u10; u2=u20;
t Z_ni} U1 = u1;
=aWj+ggd@ U2 = u2; % Compute initial condition; save it in U
8 $|< `:~J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Z$0+jpG_s w=2*pi*n./T;
pT90TcI2 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
]vyu! L=4; % length of evoluation to compare with S. Trillo's paper
},"T,t# dz=L/M1; % space step, make sure nonlinear<0.05
2 \$P&L
a for m1 = 1:1:M1 % Start space evolution
6z/ ct|n u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
x2#5"/~4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
yzvNv]Z'* ca1 = fftshift(fft(u1)); % Take Fourier transform
2 kOFyD
ca2 = fftshift(fft(u2));
r ((2.,\Z c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
_h%
:Tu c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
wkn r^A u2 = ifft(fftshift(c2)); % Return to physical space
14[ +PoF^A u1 = ifft(fftshift(c1));
re\@ v8w~ if rem(m1,J) == 0 % Save output every J steps.
P9Gjsu # U1 = [U1 u1]; % put solutions in U array
?P+n0S! U2=[U2 u2];
`5[$ 8; MN1=[MN1 m1];
Y F+hN\ z1=dz*MN1'; % output location
m3apeIEi[ end
KjrUTG 0oA end
V~Zi #o hg=abs(U1').*abs(U1'); % for data write to excel
qk;vn}auD] ha=[z1 hg]; % for data write to excel
Zu4|1 W t1=[0 t'];
fn%Gu s~ hh=[t1' ha']; % for data write to excel file
Z~g I ) %dlmwrite('aa',hh,'\t'); % save data in the excel format
b7
pD#v figure(1)
/Hox]r]'e waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y:U'3G- figure(2)
(,5oqU9s@ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
r/X4Hy0!lT +E8It b, 非线性超快脉冲耦合的数值方法的Matlab程序 kOe %w-_ vv2N;/;I 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*Fs]1+H 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
QT1(= wK3 U
Hej5-B
T 4}SF a@|/D\C % This Matlab script file solves the nonlinear Schrodinger equations
[ }7j0& % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
GM.2bA(y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
)Ir_:lk % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+Za ew679 b#**`Y C=1;
63s<U/N M1=120, % integer for amplitude
!Gv*iWg M3=5000; % integer for length of coupler
FmfPi
.;1 N = 512; % Number of Fourier modes (Time domain sampling points)
uCA! L)$ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
1E(~x;*) T =40; % length of time:T*T0.
?;{fqeJz dt = T/N; % time step
"[` .I*WNo n = [-N/2:1:N/2-1]'; % Index
-hM
nA)+ t = n.*dt;
8 1 \$X ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e
~X<+3< w=2*pi*n./T;
64Ot`=A" g1=-i*ww./2;
8q)wT0A~ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
zeq P:goy g3=-i*ww./2;
q<Zdf P1=0;
'64&'.{#>r P2=0;
CYr2~0<g P3=1;
FiTP-~
P=0;
DzZ)a E for m1=1:M1
@ljvTgZ(X p=0.032*m1; %input amplitude
}yCw| B|a s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-IB f;"8f s1=s10;
/PP \L ]( s20=0.*s10; %input in waveguide 2
sZ,MN F8i s30=0.*s10; %input in waveguide 3
(S :+# v s2=s20;
5: jbd:o s3=s30;
V}1D1. @ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
~R`Rj*Q2Y %energy in waveguide 1
dg%Orvu z p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
&&iZ?JteZ %energy in waveguide 2
fIrl?X'] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
NL e+ %energy in waveguide 3
Vb|;@*=R&Q for m3 = 1:1:M3 % Start space evolution
T [w]w
s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
+k!Y]_&(:f s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
m){.{Vn] s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
uV]4C^k;`[ sca1 = fftshift(fft(s1)); % Take Fourier transform
{VWUK`3 sca2 = fftshift(fft(s2));
PZ/ g D sca3 = fftshift(fft(s3));
,&S ^R yc sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
5xZ *U sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
MC.,n$O}6 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%21i#R`E s3 = ifft(fftshift(sc3));
` [ E zU+ s2 = ifft(fftshift(sc2)); % Return to physical space
U
D9 &k^ s1 = ifft(fftshift(sc1));
0phO1h]2S) end
P# o/S4 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
)7m X]@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
-.A8kJ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=*q|568 P1=[P1 p1/p10];
;H#'9p ,2 P2=[P2 p2/p10];
=e7,d$i P3=[P3 p3/p10];
ICNS+KsI P=[P p*p];
|Rr^K5hmD end
zcrLd={ figure(1)
0B(<I?a/ plot(P,P1, P,P2, P,P3);
2 Wlk] 6qA48:/F= 转自：
http://blog.163.com/opto_wang/
