计算脉冲在非线性耦合器中演化的Matlab 程序 .Exvuo`F |#_p0yPy % This Matlab script file solves the coupled nonlinear Schrodinger equations of
v":q_w <k % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
:GIBB=D9 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_z#" BN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<G }Lc N~,Ipf %fid=fopen('e21.dat','w');
_3aE]\O[ N = 128; % Number of Fourier modes (Time domain sampling points)
9K@ I M1 =3000; % Total number of space steps
P gA<pfEHE J =100; % Steps between output of space
;}SGJ7 T =10; % length of time windows:T*T0
AJ}FHym_ZQ T0=0.1; % input pulse width
)7 & -DI1 MN1=0; % initial value for the space output location
9I/l+IS"X dt = T/N; % time step
+g
g_C' " n = [-N/2:1:N/2-1]'; % Index
4z(~)#'^ t = n.*dt;
b WNa6x u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
K[icVT2v~ u20=u10.*0.0; % input to waveguide 2
G*4I ;'6 u1=u10; u2=u20;
W\~ie}D{ U1 = u1;
L ?/AKg U2 = u2; % Compute initial condition; save it in U
fM ID}S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ms0V 1 ` w=2*pi*n./T;
3*<@PXpK& g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
8lM=v> Xc L=4; % length of evoluation to compare with S. Trillo's paper
h}a}Ha bA dz=L/M1; % space step, make sure nonlinear<0.05
$U ?]^ for m1 = 1:1:M1 % Start space evolution
C$[iduS u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
7"'RE95 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
h,$CJdDY] ca1 = fftshift(fft(u1)); % Take Fourier transform
n riSVGi ca2 = fftshift(fft(u2));
th73eC' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~2k.x*$ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
i?!9 %U!z4 u2 = ifft(fftshift(c2)); % Return to physical space
r<ww%2HTS u1 = ifft(fftshift(c1));
v)Y)tu> if rem(m1,J) == 0 % Save output every J steps.
q\<l"b z U1 = [U1 u1]; % put solutions in U array
p? L %' U2=[U2 u2];
MAYb.>X#> MN1=[MN1 m1];
QQW}.> N z1=dz*MN1'; % output location
=H)]HxEEM end
:"Xnu% 1 end
uaO.7QSwN hg=abs(U1').*abs(U1'); % for data write to excel
q%x i>H.:{ ha=[z1 hg]; % for data write to excel
2L&c91=wE t1=[0 t'];
aM
$2lR])J hh=[t1' ha']; % for data write to excel file
/[_aK0 U3 %dlmwrite('aa',hh,'\t'); % save data in the excel format
e#/&A5#Ya figure(1)
sY!JB7!j waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
9HJYrzf{% figure(2)
_$R =F/88 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
o6A$)m5V Nqj@p<y/q 非线性超快脉冲耦合的数值方法的Matlab程序 b3%x&H<j Kn->R9Tl 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
?TpjU*Cxy Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=W7-;& |aLK_]! ei4LE
XQ16 [@9S-$Xa % This Matlab script file solves the nonlinear Schrodinger equations
`:=1*7)? % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
5)< Y3nU~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z"
tz-~ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4tm%F\Izy eOb--@~8 C=1;
4v bGX b}! M1=120, % integer for amplitude
Q &W >h/ M3=5000; % integer for length of coupler
B(M-;F N = 512; % Number of Fourier modes (Time domain sampling points)
b|-)p+ba dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`T*Y1@FV T =40; % length of time:T*T0.
[RKk-8I dt = T/N; % time step
pG "wQ n = [-N/2:1:N/2-1]'; % Index
.hH_1Mo8 t = n.*dt;
MDytA0M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:jv(-RTI w=2*pi*n./T;
_OG9wi(Fpx g1=-i*ww./2;
aUNA`
L g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
#~'d
Y\& g3=-i*ww./2;
=l:V9u-I^ P1=0;
u)Kiwa P2=0;
[KR%8[e P3=1;
BR|0uJ.M P=0;
*j hgCm for m1=1:M1
I ;rW!Hb p=0.032*m1; %input amplitude
ifS#9N|8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?<jWEz= s1=s10;
((`\i=-o5 s20=0.*s10; %input in waveguide 2
nam]eW s30=0.*s10; %input in waveguide 3
FNUs
.d" s2=s20;
|9XoRGgXU s3=s30;
m4~
|z p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Ee MKo %energy in waveguide 1
=iB[sLEJ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
zlP{1z;nV %energy in waveguide 2
G~y:ZEnN[ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
+JYb )rn$^ %energy in waveguide 3
Wi=zu[[qc for m3 = 1:1:M3 % Start space evolution
lha;| s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
_'w:Sx?d7 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
! 7V>gWhR s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
IT:WiMDQ} sca1 = fftshift(fft(s1)); % Take Fourier transform
Ba?1q%eG sca2 = fftshift(fft(s2));
*bo| F%NAz sca3 = fftshift(fft(s3));
7yu-x nt3s sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
(<_kq;XtN0 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
uxn+.fA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
w/
~\NI s3 = ifft(fftshift(sc3));
hpXW t Q s2 = ifft(fftshift(sc2)); % Return to physical space
=c \(]xX s1 = ifft(fftshift(sc1));
\},H\kK+^ end
s:l H4B p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
^ U,iDK_ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
jY\z+lW6A p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'y!qrmMRr P1=[P1 p1/p10];
].d%R a :{ P2=[P2 p2/p10];
q}p$S2 ` P3=[P3 p3/p10];
&I=o1F2B) P=[P p*p];
o]tfvGvU* end
G^ k8Or2 figure(1)
<gi~:%T plot(P,P1, P,P2, P,P3);
ZRYlm$C a$?d_BX 转自：
http://blog.163.com/opto_wang/
