计算脉冲在非线性耦合器中演化的Matlab 程序 s\d3u` G s,_ +5ukv % This Matlab script file solves the coupled nonlinear Schrodinger equations of
^(; x-d3 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
g clj:7U % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iF`_-t/k % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1sXCu|\q KGJSGvo+y %fid=fopen('e21.dat','w');
z_'^=9m N = 128; % Number of Fourier modes (Time domain sampling points)
WoXAOj%iW M1 =3000; % Total number of space steps
rai'x/Ut}+ J =100; % Steps between output of space
j"jssbu} T =10; % length of time windows:T*T0
B>i%:[-e T0=0.1; % input pulse width
1XN%&VR>^D MN1=0; % initial value for the space output location
<);j5) / dt = T/N; % time step
`6rLd>= R n = [-N/2:1:N/2-1]'; % Index
)nHMXZ>Td t = n.*dt;
}P2*MrkcHB u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
yl>^QMmo u20=u10.*0.0; % input to waveguide 2
i<S \x u1=u10; u2=u20;
m !:F /?B U1 = u1;
ta&z lZt U2 = u2; % Compute initial condition; save it in U
UW":&`i ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
k[mp( w=2*pi*n./T;
D?ic~ -& g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
7UBW3{d/u5 L=4; % length of evoluation to compare with S. Trillo's paper
nIH(2j dz=L/M1; % space step, make sure nonlinear<0.05
@IL@|Srs8 for m1 = 1:1:M1 % Start space evolution
k8E2?kbF u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,% yC 4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
J|xXo ca1 = fftshift(fft(u1)); % Take Fourier transform
9@t&jznt< ca2 = fftshift(fft(u2));
T \34<+n1N c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
tLJ 7tnB c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
u9;3Xn8 u2 = ifft(fftshift(c2)); % Return to physical space
e`+ u1 = ifft(fftshift(c1));
GGHMpQ if rem(m1,J) == 0 % Save output every J steps.
~a=]w#-KD U1 = [U1 u1]; % put solutions in U array
';eA aDM U2=[U2 u2];
n}NUe`E_h MN1=[MN1 m1];
fCa
lR7! z1=dz*MN1'; % output location
v2|zIZ end
wB 8548C}- end
+2E~=xX hg=abs(U1').*abs(U1'); % for data write to excel
CEk [&39" ha=[z1 hg]; % for data write to excel
#d8]cm= t1=[0 t'];
34k(:]56| hh=[t1' ha']; % for data write to excel file
Q]/g=Nn
^~ %dlmwrite('aa',hh,'\t'); % save data in the excel format
_u-tRHh|A figure(1)
j.Y!E<e4] waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
>Dv=lgPF figure(2)
7 <jr0) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
!OV+2suu1 7OZ0 ;fK 非线性超快脉冲耦合的数值方法的Matlab程序 7T X$ #\~m}O, 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。
K0*er 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%' K}.C U&kdR+dB *[nS*D\: :@~3wD[y % This Matlab script file solves the nonlinear Schrodinger equations
-}qay@cDt % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
mznE Cy % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
9MRe? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Xa8_kv_ =aT8=ihP C=1;
i+-Y"vRi M1=120, % integer for amplitude
gO~ >*q & M3=5000; % integer for length of coupler
-% B)+yq> N = 512; % Number of Fourier modes (Time domain sampling points)
.:['&; k dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
@ceL9#:uc T =40; % length of time:T*T0.
^YPw'cZZ& dt = T/N; % time step
TGPdi5Eq n = [-N/2:1:N/2-1]'; % Index
P`hg*"<V t = n.*dt;
q[Y* .%~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mpCKF=KL. w=2*pi*n./T;
K0^+2lx g1=-i*ww./2;
Rm.9` <Y g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
b |Ed@C g3=-i*ww./2;
9hwn,=Vh) P1=0;
h1_KZ[X P2=0;
wCr+/" t P3=1;
e3&.R rA P=0;
$/i;UUd for m1=1:M1
'UCF2 L p=0.032*m1; %input amplitude
=dC5q{ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+QrbW s1=s10;
.=b)Ae c s20=0.*s10; %input in waveguide 2
1lUY27MF s30=0.*s10; %input in waveguide 3
g|3FJA/ s2=s20;
bO{wQ1)Z_ s3=s30;
\h/aD1 &g p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Y'LIk Q\ %energy in waveguide 1
Ps MCs|* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
;(Qm<JAa %energy in waveguide 2
h "r)z6Q/ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
T xwZ3E %energy in waveguide 3
` Axn for m3 = 1:1:M3 % Start space evolution
Yg7C"3;Vt s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(OK;*ZH+T@ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
oxm3R8 S s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Hb *&& sca1 = fftshift(fft(s1)); % Take Fourier transform
n|iO)L\9aB sca2 = fftshift(fft(s2));
;i&'va$ sca3 = fftshift(fft(s3));
g TP0: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
G&*2h2,] sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
*FUb Kr0 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
[< {+tAdn) s3 = ifft(fftshift(sc3));
ny~~xQ" s2 = ifft(fftshift(sc2)); % Return to physical space
AA,n.;zy< s1 = ifft(fftshift(sc1));
}" 'l8t0? end
V`"A|Y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Y;XEC;PXD p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
fL&bN[XA"$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
%,*{hhfu P1=[P1 p1/p10];
g g%OOvaj5 P2=[P2 p2/p10];
;/Dp P3=[P3 p3/p10];
Dx27 s P=[P p*p];
.qBf`T; end
HI30 -$9 figure(1)
1e#}+i!a plot(P,P1, P,P2, P,P3);
t1YVE%`w * 7 o ( 转自：
http://blog.163.com/opto_wang/
