计算脉冲在非线性耦合器中演化的Matlab 程序 _ yu d $CXMeY{tOo % This Matlab script file solves the coupled nonlinear Schrodinger equations of
NQFMExg, % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
]+!{^ h$ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h^)R}jy+f % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8n[6BF); '1jG?D %fid=fopen('e21.dat','w');
;VL v2J* N = 128; % Number of Fourier modes (Time domain sampling points)
FK^JCs^ M1 =3000; % Total number of space steps
aLWNq e&1 J =100; % Steps between output of space
|3a1hCxt T =10; % length of time windows:T*T0
3p%B T0=0.1; % input pulse width
us_o{ MN1=0; % initial value for the space output location
T[z}^" dt = T/N; % time step
S m%\,/3 n = [-N/2:1:N/2-1]'; % Index
{D6E@a t = n.*dt;
vLc7RL u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
v}G pw6 u20=u10.*0.0; % input to waveguide 2
HkP')= sa u1=u10; u2=u20;
6c?;-5. U1 = u1;
w6P Kr^ U2 = u2; % Compute initial condition; save it in U
o)(N*tC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
L$Uy w=2*pi*n./T;
&V$qIvN$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
_4#8o\ L=4; % length of evoluation to compare with S. Trillo's paper
{x-iBg9#l2 dz=L/M1; % space step, make sure nonlinear<0.05
s y ]k for m1 = 1:1:M1 % Start space evolution
[\Ks+ S u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{ hXIP` u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5Oa`1?C1 ca1 = fftshift(fft(u1)); % Take Fourier transform
9(\e L9^ ca2 = fftshift(fft(u2));
<3 b|Sk:T c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
tR! !Q c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|>Q ] q u2 = ifft(fftshift(c2)); % Return to physical space
R>r @I_ u1 = ifft(fftshift(c1));
9i&(VzY[= if rem(m1,J) == 0 % Save output every J steps.
|#&{`3$CG[ U1 = [U1 u1]; % put solutions in U array
qH GwD20 ~ U2=[U2 u2];
a-A>A_. MN1=[MN1 m1];
!vaS fL*] z1=dz*MN1'; % output location
x D:t$~ end
J$]-)`[G& end
\o&\r)F X hg=abs(U1').*abs(U1'); % for data write to excel
X\z `S##kj ha=[z1 hg]; % for data write to excel
/8)-j}gZa t1=[0 t'];
#[Z1W8e hh=[t1' ha']; % for data write to excel file
eaG _)y %dlmwrite('aa',hh,'\t'); % save data in the excel format
ke+3J\;> figure(1)
S\,~ 6]^T waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
U #u =9%' figure(2)
:c*_W
/ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
P0Q]Ds| ,n}h_ct 非线性超快脉冲耦合的数值方法的Matlab程序 (O&R-5m 4TP AD)C 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
p)dD{+"/2 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
JGJy _.C W N5`zD$ ![>j` i fP:n=A{ % This Matlab script file solves the nonlinear Schrodinger equations
Ojh \H % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
\V1geSoE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
kF1Tg KSd % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ZFJ qI ||}k99y + C=1;
cE|Z=}4I7 M1=120, % integer for amplitude
d,hKy 2 M3=5000; % integer for length of coupler
U= Gw( N = 512; % Number of Fourier modes (Time domain sampling points)
']x`d dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]]EOCGZ" T =40; % length of time:T*T0.
hxXl0egI dt = T/N; % time step
2b[R^O} n = [-N/2:1:N/2-1]'; % Index
8Hdm(> t = n.*dt;
vFz#A/1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&e-MOM2& w=2*pi*n./T;
dr54 D g1=-i*ww./2;
^#V7\;v$G g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
&&Uc%vIN g3=-i*ww./2;
l2&s4ERqSm P1=0;
c=^A3[AM P2=0;
%6%Q E'D P3=1;
dYEsSFB m P=0;
/^2& @P7 for m1=1:M1
vmY 88Kx&S p=0.032*m1; %input amplitude
MYmH ?A s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
)Rlh[Y& r s1=s10;
, sOdc!![ s20=0.*s10; %input in waveguide 2
Im<i.a
<` s30=0.*s10; %input in waveguide 3
DJ!<:9FD s2=s20;
0tFR.
sS? s3=s30;
jNC@b>E?~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\i2S'AblYq %energy in waveguide 1
[yEH!7 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
03!!# 5iJ %energy in waveguide 2
> U.f`24 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/'ukeK+' %energy in waveguide 3
5, j&-{ 0W for m3 = 1:1:M3 % Start space evolution
Yu`KHvur s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
BM }{};p6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
-J`VXG:M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
|)4aIa sca1 = fftshift(fft(s1)); % Take Fourier transform
2JMM Npya sca2 = fftshift(fft(s2));
#guq/g$ sca3 = fftshift(fft(s3));
Q!T+Jc9N sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
WlF}R\N! sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
|E(`9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
u> @ Yoyc s3 = ifft(fftshift(sc3));
4(hHp6}b s2 = ifft(fftshift(sc2)); % Return to physical space
<* vWcCS1 s1 = ifft(fftshift(sc1));
g?mfpw Zj end
#c F ?a5 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
iVQ)hs W/ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
G'dN_6ho3 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
s^QXC mb$8 P1=[P1 p1/p10];
s4&JBm(33N P2=[P2 p2/p10];
1p DL()t P3=[P3 p3/p10];
v=Y)
A ? P=[P p*p];
F s{}bQyQ end
O^_$cq figure(1)
d*= ==~ plot(P,P1, P,P2, P,P3);
]i@WZ( Z7G l^4zn 转自：
http://blog.163.com/opto_wang/
