计算脉冲在非线性耦合器中演化的Matlab 程序 p l nH &/WM:]^?0) % This Matlab script file solves the coupled nonlinear Schrodinger equations of
;F"!$Z/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Cj8&wz}ez % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
W34xrm % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
H
u;"TG !2Nk %fid=fopen('e21.dat','w');
B-C$>H^ N = 128; % Number of Fourier modes (Time domain sampling points)
05FGfnq.8 M1 =3000; % Total number of space steps
/ "g Ryv J =100; % Steps between output of space
xyGwYv>*KO T =10; % length of time windows:T*T0
e`qrafa T0=0.1; % input pulse width
O0qG
6 a MN1=0; % initial value for the space output location
bzNnEH`^] dt = T/N; % time step
Z2$_9 . n = [-N/2:1:N/2-1]'; % Index
<x^$Fu t = n.*dt;
fI)XV7,X u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
3s!6rT_=)d u20=u10.*0.0; % input to waveguide 2
1PwtzH .w u1=u10; u2=u20;
dw <i)P^
U1 = u1;
s0?'mC+p U2 = u2; % Compute initial condition; save it in U
DPzW,aIgv ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
r V%6 8x9 w=2*pi*n./T;
C{J5:ak g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
hUl Rtt L=4; % length of evoluation to compare with S. Trillo's paper
gS +X% dz=L/M1; % space step, make sure nonlinear<0.05
pKc!sd C for m1 = 1:1:M1 % Start space evolution
G7 UUx+ X u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Ah F@ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_h-agn 4[i ca1 = fftshift(fft(u1)); % Take Fourier transform
j V sH ca2 = fftshift(fft(u2));
`}),wBq c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
; CCg]hX c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
k2D*`\
D u2 = ifft(fftshift(c2)); % Return to physical space
*m"9F'(Sd u1 = ifft(fftshift(c1));
ta)gOc)r
R if rem(m1,J) == 0 % Save output every J steps.
gFTU9k< U1 = [U1 u1]; % put solutions in U array
]%6%rq%9C U2=[U2 u2];
)4ek!G]Rb MN1=[MN1 m1];
oDA'$]UL z1=dz*MN1'; % output location
V|'@D#\ end
SiaNL: end
0v qH-)} hg=abs(U1').*abs(U1'); % for data write to excel
u;q
Q/Ftb ha=[z1 hg]; % for data write to excel
MeBTc&S< t1=[0 t'];
]vQa~ } hh=[t1' ha']; % for data write to excel file
aH6j, R% %dlmwrite('aa',hh,'\t'); % save data in the excel format
daKZ *B| figure(1)
#'&-S@/nQs waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
CB#2XS>V figure(2)
: g|.x waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
6- wpR ' bl9fO4v 非线性超快脉冲耦合的数值方法的Matlab程序 ;I*t5{ 1!1JT;gG^9 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
jv~#'= T' Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
M$EF 8 m-O*t$6 jI8`trD PL = v,NB % This Matlab script file solves the nonlinear Schrodinger equations
K` N$nOw % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
bD vGFSAH % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g&g:H H : % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
viG= Ap.Th AJ/Hw>>$?m C=1;
h/\v+xiF M1=120, % integer for amplitude
VjWJx^ZL# M3=5000; % integer for length of coupler
^N<aHFF N = 512; % Number of Fourier modes (Time domain sampling points)
[s^p P2 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
e W8cI)wU T =40; % length of time:T*T0.
.$-;`&0cZ dt = T/N; % time step
9mD dX n = [-N/2:1:N/2-1]'; % Index
@M\JzV4 A[ t = n.*dt;
a^&"gGg ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Jzf+"%lv w=2*pi*n./T;
DL,R~ g1=-i*ww./2;
z!6_u@^- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
I '0[ g3=-i*ww./2;
X{#^O/ P1=0;
\/1~5mQ+ P2=0;
`S((F|Ty=; P3=1;
9q?knMt P=0;
AIOGa<^ for m1=1:M1
YTTy6*\,_ p=0.032*m1; %input amplitude
s>G6/TTH6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
g=D]=& H s1=s10;
,$Fh^KN o] s20=0.*s10; %input in waveguide 2
RbUir185Y s30=0.*s10; %input in waveguide 3
-aJ(-Np$f s2=s20;
C3 "EZe[R s3=s30;
aN"YEL>w p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Z6gwAvf< %energy in waveguide 1
`{YOl\d_ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]Qe~|9I %energy in waveguide 2
AT
t.}- p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
D 7pQWlN\ %energy in waveguide 3
eW.qMx#:od for m3 = 1:1:M3 % Start space evolution
wOL%otEf s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
5L6.7}B s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
aEdMZ+P. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Jy: @&c sca1 = fftshift(fft(s1)); % Take Fourier transform
Q']'KU. sca2 = fftshift(fft(s2));
){GJgk|P sca3 = fftshift(fft(s3));
fQ~~%#z1 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
BpA7
z / sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
9hK8dJw sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
IJ.H/l}h s3 = ifft(fftshift(sc3));
WClprSl8 s2 = ifft(fftshift(sc2)); % Return to physical space
v0WB.`rO s1 = ifft(fftshift(sc1));
a. u{b&+9 end
L'
_%zO p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
bL<H$DB6 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Us ht\<{ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
(Ajhf}zJ P1=[P1 p1/p10];
<2 j$P Y9 P2=[P2 p2/p10];
Z D50-w; P3=[P3 p3/p10];
J8FzQ2 P=[P p*p];
mn1!A`$ end
:fX61S6) figure(1)
++w{)Io Z plot(P,P1, P,P2, P,P3);
Pi[]k]XA\ 0F!Uai1 转自：
http://blog.163.com/opto_wang/
