计算脉冲在非线性耦合器中演化的Matlab 程序 i>i@r ;:| Se+sgw_" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
`sOCJ|rc5 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
EaGh`*"w(7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
szN`"Yi){ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$]EG|]"Ns G\& 4_MS %fid=fopen('e21.dat','w');
0TK+R43 _ N = 128; % Number of Fourier modes (Time domain sampling points)
8nw_Jatk1 M1 =3000; % Total number of space steps
o%X@Bz J =100; % Steps between output of space
XNkw9*IT T =10; % length of time windows:T*T0
ykc$B5* T0=0.1; % input pulse width
Tq[=&J MN1=0; % initial value for the space output location
K4N B# dt = T/N; % time step
xTNWT_d n = [-N/2:1:N/2-1]'; % Index
`!Ei
H<H} t = n.*dt;
y)o!F^ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
833K U_ N u20=u10.*0.0; % input to waveguide 2
6=a($s!
u1=u10; u2=u20;
.dwb@$ U1 = u1;
@1ZLr U2 = u2; % Compute initial condition; save it in U
ORk8^0\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
{^ 1s w=2*pi*n./T;
+[M5x[[$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ujsJ;\c L=4; % length of evoluation to compare with S. Trillo's paper
E8#RG-ci dz=L/M1; % space step, make sure nonlinear<0.05
V}(snG, for m1 = 1:1:M1 % Start space evolution
3OTq u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
HV ab14}E u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Cp(,+ dD ca1 = fftshift(fft(u1)); % Take Fourier transform
GY 4?}T^s ca2 = fftshift(fft(u2));
W#!![ JD c c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
\hv1" WaJ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
3D70`u u2 = ifft(fftshift(c2)); % Return to physical space
9^l_\:4 u1 = ifft(fftshift(c1));
pv8"E?9,k if rem(m1,J) == 0 % Save output every J steps.
Ag
QR"Nu6 U1 = [U1 u1]; % put solutions in U array
;Q>(%"z}; U2=[U2 u2];
A7SBm`XJ)p MN1=[MN1 m1];
L9[? qFp z1=dz*MN1'; % output location
.PBma/w
W end
M6U/.
n end
}
_Yk.@ J5 hg=abs(U1').*abs(U1'); % for data write to excel
1"{3v@yi ha=[z1 hg]; % for data write to excel
3Qmok@4e) t1=[0 t'];
/ ~*U'.V hh=[t1' ha']; % for data write to excel file
J'B6l#N %dlmwrite('aa',hh,'\t'); % save data in the excel format
Q|Uq.UjY figure(1)
w
A<JJ_R waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
|Z}uN!Jm figure(2)
{<%zcNKl^L waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Qag@#!&n e!wBN cG2 非线性超快脉冲耦合的数值方法的Matlab程序 O{hGh{y =;Gy"F1 dp 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。
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5 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
s8iJl+Jm ^50#R< Ny NidG|Yg~Z Un\h[m % This Matlab script file solves the nonlinear Schrodinger equations
-~T? xs0_ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
JK0L&t< % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3l"7 $B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J@'}lG 13(JW
C=1;
h7mJXS)t| M1=120, % integer for amplitude
f;M7y:A8q, M3=5000; % integer for length of coupler
1!<k-vt N = 512; % Number of Fourier modes (Time domain sampling points)
U{n< n8 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
z OkU R 9 T =40; % length of time:T*T0.
e(E6 t_ dt = T/N; % time step
~3 4Ly n = [-N/2:1:N/2-1]'; % Index
! Tuc#yFw t = n.*dt;
o<2 H~2/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)u~LzE]{_ w=2*pi*n./T;
9Cbf[\J!bq g1=-i*ww./2;
o =) hUr g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
l(|@ dp g3=-i*ww./2;
D/C,Q|Ya6 P1=0;
|KFR C)g P2=0;
.r!:` 6 P3=1;
sS#Lnj^`% P=0;
#MYhKySku for m1=1:M1
Z"rrbN1 p=0.032*m1; %input amplitude
IK Se X s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ImQ?<g8$ s1=s10;
!DFT}eu s20=0.*s10; %input in waveguide 2
v~i/e+.h>y s30=0.*s10; %input in waveguide 3
~ld qg2c s2=s20;
gE8p**LT+ s3=s30;
sp*_;h3' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
7N0V`&}T %energy in waveguide 1
#x Z7% p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
|4NH}XVYJ> %energy in waveguide 2
`PK1z S r p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
w7}m
T3p,) %energy in waveguide 3
;QbMVY for m3 = 1:1:M3 % Start space evolution
m }I@:s2 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
tpp. 9 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
td{M%D,R" s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
P wL]v. : sca1 = fftshift(fft(s1)); % Take Fourier transform
y\7 -! sca2 = fftshift(fft(s2));
kx=.K'd5H sca3 = fftshift(fft(s3));
3x2*K_A5:Q sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
]H8 ,} sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)Cl!, m)~ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
m ~a' s3 = ifft(fftshift(sc3));
{w*5uI%%e s2 = ifft(fftshift(sc2)); % Return to physical space
FWpcWmS`s s1 = ifft(fftshift(sc1));
9C[i#+_3M end
M]PH1 2O b p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
pj ?wQ' p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$w{!}U 2+- p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
FTvFtdY P1=[P1 p1/p10];
meQ>mW P2=[P2 p2/p10];
)`5k fj P3=[P3 p3/p10];
$o KT-G P=[P p*p];
tVJ}NI # end
?g*#l d () figure(1)
f4A evh: plot(P,P1, P,P2, P,P3);
1"k"<{% F&? &8. 转自：
http://blog.163.com/opto_wang/
