计算脉冲在非线性耦合器中演化的Matlab 程序 rNdeD~\ @AXRKYQ{t % This Matlab script file solves the coupled nonlinear Schrodinger equations of
986y\9 Zu % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{Z529Ns % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
@ _gCGI>Q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ou r$Ka31 SMMV$;O{9 %fid=fopen('e21.dat','w');
PRs[! EB6 N = 128; % Number of Fourier modes (Time domain sampling points)
v4?qI >/ M1 =3000; % Total number of space steps
q'07 J =100; % Steps between output of space
.,)C^hs@ T =10; % length of time windows:T*T0
Ur`jmB T0=0.1; % input pulse width
F __(iX xC MN1=0; % initial value for the space output location
Fq]ht* dt = T/N; % time step
v<*ga7'S n = [-N/2:1:N/2-1]'; % Index
?0v(_ v t = n.*dt;
g UfLw u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xq?9w $ u20=u10.*0.0; % input to waveguide 2
IfGmA.O u1=u10; u2=u20;
%0>DjzYt U1 = u1;
` ^ rN"\ U2 = u2; % Compute initial condition; save it in U
m&GxL T 6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&\3k(j w=2*pi*n./T;
Km5#$IiP; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
/rKdxsI* L=4; % length of evoluation to compare with S. Trillo's paper
c.-/e u^| dz=L/M1; % space step, make sure nonlinear<0.05
[d( @lbV0 for m1 = 1:1:M1 % Start space evolution
SR,id B&i u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
r%M.rYLG{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
UStNUNCq ca1 = fftshift(fft(u1)); % Take Fourier transform
*r Y@(| ca2 = fftshift(fft(u2));
aoLYw 9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
J j< UtD+ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
k`LoRqF u2 = ifft(fftshift(c2)); % Return to physical space
EcBJ-j 6d u1 = ifft(fftshift(c1));
9?Vy F'r= if rem(m1,J) == 0 % Save output every J steps.
t0 [H_ U1 = [U1 u1]; % put solutions in U array
&P+7Um( U2=[U2 u2];
; TaR1e0 MN1=[MN1 m1];
^8,Y1r9`$ z1=dz*MN1'; % output location
nqG9$!k^t end
)c'5M]V end
Pj4WWK X hg=abs(U1').*abs(U1'); % for data write to excel
QJBzv| ha=[z1 hg]; % for data write to excel
V3<baxdE t1=[0 t'];
o"O=Epg hh=[t1' ha']; % for data write to excel file
~! *xi %dlmwrite('aa',hh,'\t'); % save data in the excel format
54TW8y `h figure(1)
ZRDY `eK waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+- ~:E_G figure(2)
E *[dc waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
QZcdfJck=+ taS2b#6\+ 非线性超快脉冲耦合的数值方法的Matlab程序 )!h(o R /Iwn l 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
[dm&I#m= Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
a[<'%S#3x k7rFbrL Z ^CIO,I zEG6T * % This Matlab script file solves the nonlinear Schrodinger equations
s>=DfE-;" % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
(1~d/u?2\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w2- :!,X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8p4J7 - =0te.io)3O C=1;
QXXB>gOY5 M1=120, % integer for amplitude
{1RI!#[\ M3=5000; % integer for length of coupler
vwVK ^B N = 512; % Number of Fourier modes (Time domain sampling points)
+T*=JHOD dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Fai_v{&? T =40; % length of time:T*T0.
_[zZm* dt = T/N; % time step
uFseO9F.2 n = [-N/2:1:N/2-1]'; % Index
V3%"z t = n.*dt;
~ H [ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mWOW39Ku w=2*pi*n./T;
i$~2pr g1=-i*ww./2;
"N"$B~W* g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
#fq%903=
g3=-i*ww./2;
>s
4 "2X P1=0;
l^.d 3b P2=0;
?LJDBN P3=1;
%4F
Q ~ P=0;
ET]PF ,` for m1=1:M1
j]-0m4QF p=0.032*m1; %input amplitude
8>T#sO?+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3 [R<Jr O s1=s10;
}2W scxL s20=0.*s10; %input in waveguide 2
X9W'.s.[Q s30=0.*s10; %input in waveguide 3
UK YQ @ m s2=s20;
gN2$;hb? s3=s30;
~%SmH [i p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
{M`yYeo %energy in waveguide 1
'q158x p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
cT2 &nZ %energy in waveguide 2
HGuU6@~hu p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
j _`
[Z %energy in waveguide 3
[]i/\0C^ for m3 = 1:1:M3 % Start space evolution
@ |bN[X L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
"r!>p\.0O s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
]} D^?g^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
)-98pp7~BB sca1 = fftshift(fft(s1)); % Take Fourier transform
J1i{n7f=@ sca2 = fftshift(fft(s2));
rF9|xgFK sca3 = fftshift(fft(s3));
MQs!+Z"m> sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w %4SNR sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Ban@$uf sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
cB$OkaG# s3 = ifft(fftshift(sc3));
$w,?%i97 s2 = ifft(fftshift(sc2)); % Return to physical space
-^1}J s1 = ifft(fftshift(sc1));
F52% og~N end
9((BOq p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
tcDWx:Q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
}BF!!* p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
wM$N#K@ P1=[P1 p1/p10];
U2v;[ >=] P2=[P2 p2/p10];
&zuPt5G| P3=[P3 p3/p10];
VI xGD#m P=[P p*p];
<x QvS^|[ end
H7`JqS figure(1)
968<yO] plot(P,P1, P,P2, P,P3);
jeKqS !,Ou:E?Bb 转自：
http://blog.163.com/opto_wang/
