计算脉冲在非线性耦合器中演化的Matlab 程序 SW Hi iF@ W=,]#Z+M; % This Matlab script file solves the coupled nonlinear Schrodinger equations of
v,US4C|^3i % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
0iz\<'
p % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
q-e3 ;$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cQ0+kX< 0 Gq<APtr %fid=fopen('e21.dat','w');
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h<S N = 128; % Number of Fourier modes (Time domain sampling points)
%B| Ca& M1 =3000; % Total number of space steps
YCyh+%Q( J =100; % Steps between output of space
VxU{ZD~<Z" T =10; % length of time windows:T*T0
+V#dJ[,8;. T0=0.1; % input pulse width
|s!n7%|,7 MN1=0; % initial value for the space output location
5[^Rf' wy dt = T/N; % time step
ZPH atC n = [-N/2:1:N/2-1]'; % Index
\r &(l1R t = n.*dt;
[Fr <tKtB u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
q c6d,z/ u20=u10.*0.0; % input to waveguide 2
^5-SL?E u1=u10; u2=u20;
sT91>'& U1 = u1;
x0xQFlG k U2 = u2; % Compute initial condition; save it in U
V j[,o
Vt$ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
A .<M*[{q w=2*pi*n./T;
5"Y:^_8 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
0'R}' L=4; % length of evoluation to compare with S. Trillo's paper
YRj"]=
5N dz=L/M1; % space step, make sure nonlinear<0.05
P_M!h~ for m1 = 1:1:M1 % Start space evolution
) =|8%IrB u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
@%6"xnb ` u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
vGp`P ca1 = fftshift(fft(u1)); % Take Fourier transform
nB%[\LtZ? ca2 = fftshift(fft(u2));
$ u,`bX c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Lx3`.F\mG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
7#9 fcfL u2 = ifft(fftshift(c2)); % Return to physical space
'^.3}N{Fo u1 = ifft(fftshift(c1));
"GAKi}y">v if rem(m1,J) == 0 % Save output every J steps.
g<i>252> U1 = [U1 u1]; % put solutions in U array
i6E ~]&~.v U2=[U2 u2];
1xU) nXXb MN1=[MN1 m1];
4o( Q+6m z1=dz*MN1'; % output location
x |3G}[= end
$X rX(l5 end
B)Dsen hg=abs(U1').*abs(U1'); % for data write to excel
A) kdY!} ha=[z1 hg]; % for data write to excel
Kp/l2?J"
t1=[0 t'];
{z8wFL \ hh=[t1' ha']; % for data write to excel file
fyv S1_ %dlmwrite('aa',hh,'\t'); % save data in the excel format
SdJk no figure(1)
IVG77+O# } waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
D*)"?L G figure(2)
,f[Oy:fr waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
@G=_nZxv iM{cr&0 非线性超快脉冲耦合的数值方法的Matlab程序 -M`+hVs? 5K$d4 KT 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。
BU%gXr4Ra 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
. Kk'N 7T=:dv *G M.2``e
C0j`H( % This Matlab script file solves the nonlinear Schrodinger equations
wUmcA~3D % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
n*N`].r#{= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
CSMx]jbb % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\2)~dV:6+ _Ns_$_ C=1;
AJt4I
W@ M1=120, % integer for amplitude
ks<+gL{K|i M3=5000; % integer for length of coupler
l`*R !\ N = 512; % Number of Fourier modes (Time domain sampling points)
7]8apei| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Br"K{ g? T =40; % length of time:T*T0.
B et?]4\_ dt = T/N; % time step
wmFS+F4`2 n = [-N/2:1:N/2-1]'; % Index
/3 d 6 Og t = n.*dt;
S{qsq\X ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9 H~OC8R: w=2*pi*n./T;
`qj24ehc g1=-i*ww./2;
fMRMQR=6B g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
mvGj
!' g3=-i*ww./2;
4G=KyRKh P1=0;
'V:ah3 8 P2=0;
)dI `yf P3=1;
XE : JL_ P=0;
hdxq@%Vs for m1=1:M1
x5W.
3* p=0.032*m1; %input amplitude
o$,e#q)8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
U j> bWa` s1=s10;
KoTQc0b! s20=0.*s10; %input in waveguide 2
}%k 3 s30=0.*s10; %input in waveguide 3
}e&Z"H | s2=s20;
hx sW9 s3=s30;
+ Scw;gO p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
R}\n @ X* %energy in waveguide 1
EB[B0e 7} p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
_9"%;:t %energy in waveguide 2
6?KJ"Ai9 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
TllIs&MCe %energy in waveguide 3
" IC0v9 for m3 = 1:1:M3 % Start space evolution
_.3O(? p, s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
hdx"/.s s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
mdukl!_x s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
w:o,mzuXK sca1 = fftshift(fft(s1)); % Take Fourier transform
2< Q3-|/i sca2 = fftshift(fft(s2));
i 9w k) sca3 = fftshift(fft(s3));
_ tpqo > sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@wO X</_g sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
h$q=NTV sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
+(J{~A~ s3 = ifft(fftshift(sc3));
i?CX DuL s2 = ifft(fftshift(sc2)); % Return to physical space
~> |o3&G{ s1 = ifft(fftshift(sc1));
wdTjJf r end
Cw&U* H p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
ma(E} s p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
R(N5K4J p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
{/SLDyf%Z P1=[P1 p1/p10];
w&^_2<a2 P2=[P2 p2/p10];
P+[\9G g P3=[P3 p3/p10];
hQ}B?'> P=[P p*p];
J O"-"&> end
UqaV9 figure(1)
eU.HS78 plot(P,P1, P,P2, P,P3);
T_b$8GYfCY AH#klY K 转自：
http://blog.163.com/opto_wang/
