计算脉冲在非线性耦合器中演化的Matlab 程序 ;b-XWK= ER,1(1]N % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ou dxm[/U % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
)GHq/:1W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
U&O:
_>~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)1X#*mCxk E>l~-PaZY %fid=fopen('e21.dat','w');
98^V4maR: N = 128; % Number of Fourier modes (Time domain sampling points)
13taF V dU M1 =3000; % Total number of space steps
03C0 L& J =100; % Steps between output of space
a+n0 |CvF T =10; % length of time windows:T*T0
m * JaXa T0=0.1; % input pulse width
yPq'( PV MN1=0; % initial value for the space output location
GSH>7!.# dt = T/N; % time step
5oAK8I n = [-N/2:1:N/2-1]'; % Index
p5G? N(l t = n.*dt;
Jv^h\~*jH u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
;^Dpl'v%\ u20=u10.*0.0; % input to waveguide 2
wm Tb97o u1=u10; u2=u20;
P&f7@MOV.P U1 = u1;
h $2</J" U2 = u2; % Compute initial condition; save it in U
)ut &@] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%7|9sQ: w=2*pi*n./T;
&Xf}8^T<V g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
YPxM<Gfa8 L=4; % length of evoluation to compare with S. Trillo's paper
.mR8q+I6 dz=L/M1; % space step, make sure nonlinear<0.05
{;2PL^i for m1 = 1:1:M1 % Start space evolution
YOcO4
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
a |X a3E u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
lnjXD oVb< ca1 = fftshift(fft(u1)); % Take Fourier transform
v/ _ ca2 = fftshift(fft(u2));
wRVUu ) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$ ` "" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
vX.VfY u2 = ifft(fftshift(c2)); % Return to physical space
+U3DG $ u1 = ifft(fftshift(c1));
}~L.qG if rem(m1,J) == 0 % Save output every J steps.
Abc)i7!.,. U1 = [U1 u1]; % put solutions in U array
,y#Kv|R U2=[U2 u2];
> ;*b|Ik MN1=[MN1 m1];
HAa; hb z1=dz*MN1'; % output location
A6thXs2 end
c24dSNJg, end
\2h!aRWR hg=abs(U1').*abs(U1'); % for data write to excel
x<ZJb ha=[z1 hg]; % for data write to excel
DW[N|-L t1=[0 t'];
#"G]ke1l $ hh=[t1' ha']; % for data write to excel file
NPp ;78O0[ %dlmwrite('aa',hh,'\t'); % save data in the excel format
.:F%_dS D figure(1)
#AJM6* G9 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
t7aefV&_, figure(2)
tVN waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
) AvN\sC s*. hl.k. 非线性超快脉冲耦合的数值方法的Matlab程序 8)_XJ"9)G ?82x dp g 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。
"~|6tQLc 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
|IzPgC rD 3v$B Hquc
o 8.O8No:'& % This Matlab script file solves the nonlinear Schrodinger equations
K &N % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
3`DQo%< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
, s"^kFl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s;ls qQk H& -zZc4\ C=1;
P/W
XaE4 M1=120, % integer for amplitude
T 4Pgbop M3=5000; % integer for length of coupler
Q' {M L4 N = 512; % Number of Fourier modes (Time domain sampling points)
z7fp#>uw dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
AP 2_MV4W T =40; % length of time:T*T0.
8}O lL,fP dt = T/N; % time step
4O^xY
6m n = [-N/2:1:N/2-1]'; % Index
lR6@
xJd:@ t = n.*dt;
KW pVw! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%]} w=2*pi*n./T;
A P?R"% g1=-i*ww./2;
ia!y!_L\' g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Ng2twfSl$ g3=-i*ww./2;
vN;N/mL P1=0;
r@H /kD P2=0;
&]|?o_p3W P3=1;
#lL^?|M P=0;
P@V0 Mi), for m1=1:M1
K0|FY=#2y p=0.032*m1; %input amplitude
KPKt^ C s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2} /aFR s1=s10;
V ]lLw) s20=0.*s10; %input in waveguide 2
NJWA3 zz
s30=0.*s10; %input in waveguide 3
];[}:f s2=s20;
7x|9n s3=s30;
g}k`o!q p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
E Nh l&J %energy in waveguide 1
f@wquG' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
B" 1 c %energy in waveguide 2
Jc sHt; p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
he;dq)-e9 %energy in waveguide 3
U ]H#MiC! for m3 = 1:1:M3 % Start space evolution
hF~n)oQ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
P~ >O S5^ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
*v^Jb/E315 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
|"8b_Cq{ sca1 = fftshift(fft(s1)); % Take Fourier transform
o,\$Zx Slm sca2 = fftshift(fft(s2));
Tztu}t]N sca3 = fftshift(fft(s3));
\kL 3.W_ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
l *(8i ^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
8mvy\l
EEH sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
aFX=C >M s3 = ifft(fftshift(sc3));
) -I { ^( s2 = ifft(fftshift(sc2)); % Return to physical space
&
p s1 = ifft(fftshift(sc1));
/L
g)i\R; end
S6 Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
q$d>(vb q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
JzQ_{J`k p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
H(A Rw'M P1=[P1 p1/p10];
r=
`Jn6@ P2=[P2 p2/p10];
U2#"p
P3=[P3 p3/p10];
{T$9?`h~M P=[P p*p];
q_[o" wq/ end
G:<aB figure(1)
A4x]Qh3OO plot(P,P1, P,P2, P,P3);
iy.p n i+ ?^8 # 转自：
http://blog.163.com/opto_wang/
