计算脉冲在非线性耦合器中演化的Matlab 程序 M&faa7 p-EU"O % This Matlab script file solves the coupled nonlinear Schrodinger equations of
6~W@$SP,F % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
!plu;w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
I''n1v?N % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<pHm=q/U eu_ZsseZ %fid=fopen('e21.dat','w');
VE I ct{ N = 128; % Number of Fourier modes (Time domain sampling points)
f#GMJ mCQs M1 =3000; % Total number of space steps
?r8hl.Z> J =100; % Steps between output of space
$2i@@#g8 T =10; % length of time windows:T*T0
(&v|,.c^)1 T0=0.1; % input pulse width
l ic-68T MN1=0; % initial value for the space output location
e`7>QS ;. dt = T/N; % time step
,5} w]6bCr n = [-N/2:1:N/2-1]'; % Index
#<e D t = n.*dt;
A4#F AFy u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
#Y'b?&b u20=u10.*0.0; % input to waveguide 2
=VZ_';b h u1=u10; u2=u20;
} }~a4p>% U1 = u1;
CqZHs
9+e& U2 = u2; % Compute initial condition; save it in U
+5Dc5Bl ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+s8R]3NJ_H w=2*pi*n./T;
qs bo"29 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
m }RZ )c L=4; % length of evoluation to compare with S. Trillo's paper
,>kVVpu dz=L/M1; % space step, make sure nonlinear<0.05
NqOX);'L0 for m1 = 1:1:M1 % Start space evolution
!yrh50tD u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
a`f@&A`z u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
dlCYdwP ca1 = fftshift(fft(u1)); % Take Fourier transform
v;;3 K*c> ca2 = fftshift(fft(u2));
2;
,8 u c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
J!5b~8`v c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
_< sN54 u2 = ifft(fftshift(c2)); % Return to physical space
o}/|"( K u1 = ifft(fftshift(c1));
DQXc f*R if rem(m1,J) == 0 % Save output every J steps.
.f-=gZ* * U1 = [U1 u1]; % put solutions in U array
#Mk: 4 U2=[U2 u2];
v3M$UiN,: MN1=[MN1 m1];
{GnZ@Q:F z1=dz*MN1'; % output location
dz +Dk6" R end
_FE uQ9E end
T7.SjR6X> hg=abs(U1').*abs(U1'); % for data write to excel
qA`@~\ qh" ha=[z1 hg]; % for data write to excel
2Zuo).2a. t1=[0 t'];
$rr@3H+
hh=[t1' ha']; % for data write to excel file
h{ix$Xn~ %dlmwrite('aa',hh,'\t'); % save data in the excel format
~v pIy - figure(1)
u?dPC gs;h waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wW)(mY? figure(2)
OM\1TD/- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
AL3iNkEa FibZT1-k 非线性超快脉冲耦合的数值方法的Matlab程序 _[Imwu} HSRO gBNI: 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。
pl1CPxSdO 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
Bh cp=# ^4 "AWps y||RK` H u4SL:IH{D % This Matlab script file solves the nonlinear Schrodinger equations
fDqT7}L % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
j"h/v7~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
$>O~7Nfst7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}a~h d*-# e]88 4FP C=1;
;2 &" M1=120, % integer for amplitude
O |P <s+ M3=5000; % integer for length of coupler
OQ? N_zs, N = 512; % Number of Fourier modes (Time domain sampling points)
\-;f <%+ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
At=d//5FFP T =40; % length of time:T*T0.
0] c&K dt = T/N; % time step
x@ rQ7K > n = [-N/2:1:N/2-1]'; % Index
hd9HM5{p t = n.*dt;
mi Q*enZi ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lm;hW&O9 w=2*pi*n./T;
P o @;PR= g1=-i*ww./2;
([< HFc` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
; ]=w6'dP! g3=-i*ww./2;
Wmcd{MOS P1=0;
]& Y^ P2=0;
Z8xB
a0 P3=1;
1r $-U h P=0;
G)}[!'<rR for m1=1:M1
Ri" hU/H{ p=0.032*m1; %input amplitude
X=]utn s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
OR~ui[w s1=s10;
=#W:z.w s20=0.*s10; %input in waveguide 2
T*C25l;w s30=0.*s10; %input in waveguide 3
eZT8gKbjJ) s2=s20;
;n(f?RO3X s3=s30;
a,RCK~GR p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
z6E =%-` %energy in waveguide 1
U0j>u*yE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
PZ8,E{V %energy in waveguide 2
>;c);|'}q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
oxc; DfJ_ %energy in waveguide 3
?c RF;!o" for m3 = 1:1:M3 % Start space evolution
BK%B[f*[OA s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
P1LOj s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5>f " s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ANu>* sca1 = fftshift(fft(s1)); % Take Fourier transform
[//i "Nm sca2 = fftshift(fft(s2));
aHW34e@ebL sca3 = fftshift(fft(s3));
gU x}vE- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8N'hG, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
xo'!$a}I2 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
:\"0jQ.y| s3 = ifft(fftshift(sc3));
raPOF6-_rH s2 = ifft(fftshift(sc2)); % Return to physical space
@s-P!uCaT s1 = ifft(fftshift(sc1));
nahq O|~ end
3qe`#j p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
OmWEa p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"PI;/(kR p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
/)_4QSz7 P1=[P1 p1/p10];
(cLK hn@ P2=[P2 p2/p10];
e*}zl>f P3=[P3 p3/p10];
X13+n2^8] P=[P p*p];
(X"5x]7] end
a4^hC[a figure(1)
KUZi3\p9W> plot(P,P1, P,P2, P,P3);
q\o#<'F1J z U[pn)pe 转自：
http://blog.163.com/opto_wang/
