计算脉冲在非线性耦合器中演化的Matlab 程序 J ]|S0JC` o3HS | % This Matlab script file solves the coupled nonlinear Schrodinger equations of
!L)yI#i4C % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
jV' tcFr4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0oo_ m6ie& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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cH) W=4|ahk$ %fid=fopen('e21.dat','w');
[Vj|f y4 N = 128; % Number of Fourier modes (Time domain sampling points)
tDtqTB} M1 =3000; % Total number of space steps
zKGr(9I J =100; % Steps between output of space
/U tSZ( T =10; % length of time windows:T*T0
n +dRAIqB T0=0.1; % input pulse width
*}Rd%' MN1=0; % initial value for the space output location
:AyZe7:(D dt = T/N; % time step
c+jnQM' n = [-N/2:1:N/2-1]'; % Index
\3whM6tK t = n.*dt;
Fl++rUT u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
%3T:W\h u20=u10.*0.0; % input to waveguide 2
,&jjp eZP u1=u10; u2=u20;
Y^gIvX U1 = u1;
;V^ I>-fnm U2 = u2; % Compute initial condition; save it in U
^ ?T,>ZI ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\>+BvF w=2*pi*n./T;
`!.c_%m2 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
\ $
:) Ka L=4; % length of evoluation to compare with S. Trillo's paper
Tx/ KL%X dz=L/M1; % space step, make sure nonlinear<0.05
kS_3 7-; for m1 = 1:1:M1 % Start space evolution
kp*BAQ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~HXZ-* u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
M+lI,j+ ca1 = fftshift(fft(u1)); % Take Fourier transform
dq3"L!0u ca2 = fftshift(fft(u2));
z_a7HCG2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
>2tosxH M c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
y|Y hDO u2 = ifft(fftshift(c2)); % Return to physical space
rm,h\ u1 = ifft(fftshift(c1));
= %wBC; if rem(m1,J) == 0 % Save output every J steps.
l6!a?C[2T U1 = [U1 u1]; % put solutions in U array
||.Ve,<: U2=[U2 u2];
#}xPOz7: MN1=[MN1 m1];
>IHf5})R z1=dz*MN1'; % output location
#DcK{|ty end
~PC S_ end
i(kr#XsU hg=abs(U1').*abs(U1'); % for data write to excel
DkBVk+ ha=[z1 hg]; % for data write to excel
<@=w4\5j9 t1=[0 t'];
c1StA hh=[t1' ha']; % for data write to excel file
< !] 7Gt %dlmwrite('aa',hh,'\t'); % save data in the excel format
kYkck]| figure(1)
KQ. cd]6 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
rE\.[mFI figure(2)
IeBb#Qedz waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Xj21:IM R n/IDq$/P 非线性超快脉冲耦合的数值方法的Matlab程序 I)4NCjcCw Fi"TY^-E; 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ooT~R2u Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
n:YA4t7S el,n5O Z7 SMh[7lU` YQ5d!a. % This Matlab script file solves the nonlinear Schrodinger equations
fh e%5#3 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
k!m9
l1x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
H/O v8| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^os|yRzV*M ,T7(!)dR C=1;
SL>0 _ M1=120, % integer for amplitude
jVdB- y/r M3=5000; % integer for length of coupler
U`ELd: N = 512; % Number of Fourier modes (Time domain sampling points)
!,PoH dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
7 *HBb- T =40; % length of time:T*T0.
z>W'Ra6 dt = T/N; % time step
R~(_m#6`: n = [-N/2:1:N/2-1]'; % Index
)9> E} SU/ t = n.*dt;
'>r"+X^W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
o^~KAB7 w=2*pi*n./T;
Sc&p*G g1=-i*ww./2;
NeY,Of| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
04R- } g3=-i*ww./2;
u\|Ys P1=0;
>zB0+ l P2=0;
j0[9Cj^%c P3=1;
)NS& 1$ P=0;
!Ql& Ls for m1=1:M1
I;Bci m; p=0.032*m1; %input amplitude
\}mn"y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
JD$;6Jv3P s1=s10;
f}F
s20=0.*s10; %input in waveguide 2
&sJ%ur+G s30=0.*s10; %input in waveguide 3
a,* ~wmg s2=s20;
2u'h,on? s3=s30;
$qj||zA p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
?BnjtefIe %energy in waveguide 1
4
g^oy^~ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
?]u=5gqUU %energy in waveguide 2
%1Vf T r5 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-dsE9)&8DX %energy in waveguide 3
ZtqN8$[6n for m3 = 1:1:M3 % Start space evolution
0^rDf
L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
B>W! RyH8o s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Fr ryZe= s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
_m|Tr*i8 sca1 = fftshift(fft(s1)); % Take Fourier transform
U49
`!~b7 sca2 = fftshift(fft(s2));
\Lu] %} sca3 = fftshift(fft(s3));
-|~tZuf sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
4Fpu68y sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
'w5g s}1D sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Y:} !W s3 = ifft(fftshift(sc3));
(}LLk + s2 = ifft(fftshift(sc2)); % Return to physical space
AjA.="3 s1 = ifft(fftshift(sc1));
73OYHp_j end
<v =T31aS p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
B7!dp`rP p p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
;nB.f.e` p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
j:6VWd gq P1=[P1 p1/p10];
r*t\\2 P2=[P2 p2/p10];
1ti 4 ZM P3=[P3 p3/p10];
y6S:[Z{~A P=[P p*p];
t!,GI& end
c$HZvv figure(1)
Y^@Nvt$<K plot(P,P1, P,P2, P,P3);
Iz[ T.$9 X m! ; 转自：
http://blog.163.com/opto_wang/
