计算脉冲在非线性耦合器中演化的Matlab 程序 19-yM`O ,N|R/Vk$+E % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|9"^s x % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
yb.|7U?/x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
f}ij=Y9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
RJs G ]` |`;1p@w" %fid=fopen('e21.dat','w');
w@$o N = 128; % Number of Fourier modes (Time domain sampling points)
;3?J#e6; M1 =3000; % Total number of space steps
f`]E]5? J =100; % Steps between output of space
kR~4O$riG T =10; % length of time windows:T*T0
E4aCGg T0=0.1; % input pulse width
k+GK1Yl MN1=0; % initial value for the space output location
d!z).G dt = T/N; % time step
j nA_!;b n = [-N/2:1:N/2-1]'; % Index
(Rg!km%2T t = n.*dt;
Qnb?hvb"d u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
pW^ ?g|_} u20=u10.*0.0; % input to waveguide 2
M j% |'dZz u1=u10; u2=u20;
QDT{Xg* I U1 = u1;
n6UU6t{ U2 = u2; % Compute initial condition; save it in U
QRh4f\fY ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
V?z{UZkR
w=2*pi*n./T;
nV xMo_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
D6!+ L=4; % length of evoluation to compare with S. Trillo's paper
)Gp\_(9fc dz=L/M1; % space step, make sure nonlinear<0.05
M "P for m1 = 1:1:M1 % Start space evolution
oUKbzr/C u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*P\_:>bV( u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
rxI&;F# ca1 = fftshift(fft(u1)); % Take Fourier transform
Fl3r!a!P, ca2 = fftshift(fft(u2));
3b[ +m}UWQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
{1U*: @j c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|laKntv 2 u2 = ifft(fftshift(c2)); % Return to physical space
=y]b|"s~2 u1 = ifft(fftshift(c1));
&vvx " if rem(m1,J) == 0 % Save output every J steps.
8 ]MzOGB8 U1 = [U1 u1]; % put solutions in U array
k3.p@8@: U2=[U2 u2];
$yqq.#1 MN1=[MN1 m1];
QuRg(K%: z1=dz*MN1'; % output location
` +UMZc end
p#BvlS=D end
lR2;g:& H hg=abs(U1').*abs(U1'); % for data write to excel
TdIFZ[<7 ha=[z1 hg]; % for data write to excel
5Zm_^IS t1=[0 t'];
4_0/]:~5 hh=[t1' ha']; % for data write to excel file
n)! _HNc9 %dlmwrite('aa',hh,'\t'); % save data in the excel format
6$<o^Ha*R figure(1)
s1$#G !' waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ugPI1'f figure(2)
ko> O ~@r waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
e+ w :k/U7 2 非线性超快脉冲耦合的数值方法的Matlab程序 "g1;TT:1~ !!O{ ppM 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
'nt,+`.y6 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
b!~%a `(suRp8! 0F'UFn>{ d;:&3r|X % This Matlab script file solves the nonlinear Schrodinger equations
xKzFrP;/{ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
)t|Q7$ v1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o YErG] , % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'#::ba[9w D\*_ulc] C=1;
6="&K _Q7 M1=120, % integer for amplitude
at]Q4 M3=5000; % integer for length of coupler
o (NyOC N = 512; % Number of Fourier modes (Time domain sampling points)
<7]
Y\{+ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
$uB(@Ft. T =40; % length of time:T*T0.
@W- f{V dt = T/N; % time step
#R4KBXN n = [-N/2:1:N/2-1]'; % Index
Jxw:Jk
~ t = n.*dt;
Y[?Wt /O; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Cbvl( ( w=2*pi*n./T;
9<CUsq@i: g1=-i*ww./2;
U(LR('-h g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Qnx92 g3=-i*ww./2;
7lPk~0 P1=0;
J lGD.!` P2=0;
;-^9j)31+F P3=1;
gdY/RD xn: P=0;
Qug 'B for m1=1:M1
\9zC?Cw p=0.032*m1; %input amplitude
F <Z=%M3e s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
e-)1K s1=s10;
;FflEL<7Y s20=0.*s10; %input in waveguide 2
f_XCO=8'v s30=0.*s10; %input in waveguide 3
^V]DY!@k3_ s2=s20;
oHnpw U s3=s30;
_'p;V[ (+M p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
%k)I =| %energy in waveguide 1
7 /!C p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
G_4P)G3H %energy in waveguide 2
3 h4"Rv=, p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
& bu`\|V %energy in waveguide 3
)pa|uH +N for m3 = 1:1:M3 % Start space evolution
Utp\}0GZY s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
S` @*zQ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
tTp`e0L*m s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
C,u.!g;lm sca1 = fftshift(fft(s1)); % Take Fourier transform
" T=LHj E sca2 = fftshift(fft(s2));
V@-GQP1 sca3 = fftshift(fft(s3));
L-gF$it\*b sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
)!72^rl sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
kcUt!PL sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
S @($c' s3 = ifft(fftshift(sc3));
JdEb_ c3S s2 = ifft(fftshift(sc2)); % Return to physical space
2F7R,rr
s1 = ifft(fftshift(sc1));
7z&u92dJI end
(@ sKE p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
uB5o
Ghu- p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
1bs95Fh9Q p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
<sOB j' P1=[P1 p1/p10];
CFxs`C^ P2=[P2 p2/p10];
dUSuhT P3=[P3 p3/p10];
}cmL{S P=[P p*p];
>z$|O> j end
S3cQC`^ figure(1)
YO+d+5 plot(P,P1, P,P2, P,P3);
u\?u}t v Fj4:_(% nG 转自：
http://blog.163.com/opto_wang/
