计算脉冲在非线性耦合器中演化的Matlab 程序 ^K
n{L 6$*ZH * % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l<=Y.P_2 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
u P veAK}h % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\*k}RKDwT % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7>>6c7e 0*}%v:uN9 %fid=fopen('e21.dat','w');
nA>kJSL'$ N = 128; % Number of Fourier modes (Time domain sampling points)
gl~>MasV& M1 =3000; % Total number of space steps
?:XbZ"25pJ J =100; % Steps between output of space
/4PV<[
:_ T =10; % length of time windows:T*T0
Ju.B!)uS# T0=0.1; % input pulse width
3,RaM^5dV MN1=0; % initial value for the space output location
6Cd% @Q2cr dt = T/N; % time step
6`Af2Y_ n = [-N/2:1:N/2-1]'; % Index
9py *gN# t = n.*dt;
~]&,v|g& u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
*%wfR7G[B u20=u10.*0.0; % input to waveguide 2
}hd:avze u1=u10; u2=u20;
p ?,: U1 = u1;
?A7_&=J% U2 = u2; % Compute initial condition; save it in U
(R)( %I1Oz ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
U$5 lh w=2*pi*n./T;
`cBV+00YS g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
&?mJ L0fy L=4; % length of evoluation to compare with S. Trillo's paper
vkQkU,q dz=L/M1; % space step, make sure nonlinear<0.05
;.4A,7w# for m1 = 1:1:M1 % Start space evolution
b 5X~^L u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
'8b/TL u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
pk0C x ca1 = fftshift(fft(u1)); % Take Fourier transform
1hn4YcHb ca2 = fftshift(fft(u2));
s9'l w' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
KixS)sG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
o|?bvFC u2 = ifft(fftshift(c2)); % Return to physical space
E
Z}c8b u1 = ifft(fftshift(c1));
N1O.U"L; if rem(m1,J) == 0 % Save output every J steps.
6(uK5eD(!n U1 = [U1 u1]; % put solutions in U array
$<(FZb= U2=[U2 u2];
1JI\e6]I MN1=[MN1 m1];
~@wM[}ThP$ z1=dz*MN1'; % output location
<p 7 4U( V end
"\9!9U#! end
`pzXh0}| hg=abs(U1').*abs(U1'); % for data write to excel
uYv"5U]MFv ha=[z1 hg]; % for data write to excel
- s,M+Q(< t1=[0 t'];
a*Oc:$ hh=[t1' ha']; % for data write to excel file
0[qU k(=}[ %dlmwrite('aa',hh,'\t'); % save data in the excel format
ub0uxvz figure(1)
{:;59 9l waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
2HemPth figure(2)
9j;L- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
XH?} 0D( "V;5Lp b 非线性超快脉冲耦合的数值方法的Matlab程序 mu?6Phj 3 0fsVwE2 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。
!F_BLHig 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
9$u'2TV |%@.@c }
: @s [8o!X) % This Matlab script file solves the nonlinear Schrodinger equations
?/ @~ d % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
^/ <0r] = % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
c3>#.NP_ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$YX\&%N k9ThWo/#u C=1;
u&!QP4$"z M1=120, % integer for amplitude
q@}eYQ=P|e M3=5000; % integer for length of coupler
P sLMV:O9S N = 512; % Number of Fourier modes (Time domain sampling points)
H~IN<3ko dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
#=G[ ~m\ T =40; % length of time:T*T0.
AI|8E8h+D dt = T/N; % time step
LXIQpD ,M n = [-N/2:1:N/2-1]'; % Index
%ifq4'?Z t = n.*dt;
?5A!/`E& % ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
-Tw96 dv w=2*pi*n./T;
s:6pPJL g1=-i*ww./2;
Nl3@i `; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
;!JI$_ -\ g3=-i*ww./2;
/=5YHq> P1=0;
q ^e4 P2=0;
&3SQVOW ~T P3=1;
u7oHqo` P=0;
gRk%ObJGqm for m1=1:M1
l 4 zl|6% p=0.032*m1; %input amplitude
1q])"l"< s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
=lzRx%tm s1=s10;
ZZ<uiN$ s20=0.*s10; %input in waveguide 2
b#:Pl`n6u s30=0.*s10; %input in waveguide 3
rHir>
p s2=s20;
]ZQ3|ZJ?< s3=s30;
b>B.3E\Pc p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\M
H\! %energy in waveguide 1
S+mZ.aFS0z p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
jb!R %energy in waveguide 2
FZW )C'j p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
F
;o ^. %energy in waveguide 3
P,2FH2Eyj for m3 = 1:1:M3 % Start space evolution
5ayM}u%\~ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
{R2gz]v4 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
1<y|, s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
yA8e"$ sca1 = fftshift(fft(s1)); % Take Fourier transform
x-Kq=LFy. sca2 = fftshift(fft(s2));
V t {uG sca3 = fftshift(fft(s3));
z$VA]tI( sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
VOk EDH sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
jm_b3!J sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
1k e H 1[ s3 = ifft(fftshift(sc3));
I. [2 -~yf s2 = ifft(fftshift(sc2)); % Return to physical space
T ~9)0A"] s1 = ifft(fftshift(sc1));
|mSF a8G@ end
!$/1Q+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
03WLVP@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
y#4f^J!V p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
`aj;FrF P1=[P1 p1/p10];
u~| D;e P2=[P2 p2/p10];
@WV}VKm P3=[P3 p3/p10];
HA?<j|M P=[P p*p];
kEH(\3,l end
3yWu-U \k figure(1)
i?.7o*w8 plot(P,P1, P,P2, P,P3);
bbDl?m&bq *o}LI6_u 转自：
http://blog.163.com/opto_wang/
