计算脉冲在非线性耦合器中演化的Matlab 程序 h83 ho /<:9NP' ^ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
6}iIK,Om % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%h|z) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
K'?ab 0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ccD+o$7LT `m2F.^qrr %fid=fopen('e21.dat','w');
JS(KCY 9 N = 128; % Number of Fourier modes (Time domain sampling points)
"vLqYc4$ M1 =3000; % Total number of space steps
x?CjRvT $ J =100; % Steps between output of space
VPN@q<BV T =10; % length of time windows:T*T0
O.rk!&N T0=0.1; % input pulse width
{h9#JMIA MN1=0; % initial value for the space output location
!YJdi~q
dt = T/N; % time step
o\|dm. "f n = [-N/2:1:N/2-1]'; % Index
nt;A7pI` t = n.*dt;
0?p_|X'_ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8.-P Q u20=u10.*0.0; % input to waveguide 2
-HoPECe u1=u10; u2=u20;
pbqa U1 = u1;
$,i:#KT` U2 = u2; % Compute initial condition; save it in U
&)s
A( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
=Rb, `% w=2*pi*n./T;
xmiF!R g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
$6y1';A L=4; % length of evoluation to compare with S. Trillo's paper
;uoH+`pf dz=L/M1; % space step, make sure nonlinear<0.05
][G<CO`k for m1 = 1:1:M1 % Start space evolution
B/5C jHz u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
I*lq0& u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
~ S-x-cZ ca1 = fftshift(fft(u1)); % Take Fourier transform
I5x/N. ca2 = fftshift(fft(u2));
2A`EFk7_X c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
PI?-gc ?[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
dDpe$N u2 = ifft(fftshift(c2)); % Return to physical space
6 Dg [ b u1 = ifft(fftshift(c1));
)3)L if rem(m1,J) == 0 % Save output every J steps.
*3 9sh[*} U1 = [U1 u1]; % put solutions in U array
=z=Guvcn` U2=[U2 u2];
d+&V^qLJ MN1=[MN1 m1];
#mllVQ z1=dz*MN1'; % output location
4 uNcp0 end
v 11mu2 end
G uDus2#+ hg=abs(U1').*abs(U1'); % for data write to excel
h+Q == ha=[z1 hg]; % for data write to excel
'| FM|0~-J t1=[0 t'];
3[V|C=u0 hh=[t1' ha']; % for data write to excel file
u |QfCwQ %dlmwrite('aa',hh,'\t'); % save data in the excel format
;OdUH figure(1)
(9cIU2e waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
L3<XWpv figure(2)
Qy6A vw/$ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
#Jm_~k CS"p[-0 非线性超快脉冲耦合的数值方法的Matlab程序 t S!~> X sW X 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。
C62<pLJf 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
"V9!srIC ]AHUo;(f% pnqjAT GU z4f5@ % This Matlab script file solves the nonlinear Schrodinger equations
,#c-"x Y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
jM7}LV1Ck % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
DG:=E/ @ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y !v $5wi g:2/!tujL C=1;
Aga7X@fV( M1=120, % integer for amplitude
MiSFT5$v6 M3=5000; % integer for length of coupler
u@gYEx} N = 512; % Number of Fourier modes (Time domain sampling points)
nEGku]pCH{ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
3)3'-wu T =40; % length of time:T*T0.
G4RsH/ dt = T/N; % time step
k~q[qKb8y: n = [-N/2:1:N/2-1]'; % Index
m.^6e f t = n.*dt;
F(XWnfUv ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|2oB3 \)/ w=2*pi*n./T;
3[e@mcO g1=-i*ww./2;
R 7{ r Y g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
KK] >0QAY g3=-i*ww./2;
PkVXn
P1=0;
BFEo:!'F P2=0;
SjJUhTb P3=1;
d@w
I:
7 P=0;
D^TKv;%d for m1=1:M1
Lte\;Se.tu p=0.032*m1; %input amplitude
WYh7Y s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
8bK}& *z< s1=s10;
'8Gw{&& s20=0.*s10; %input in waveguide 2
3; M!]9ms s30=0.*s10; %input in waveguide 3
8WyG49eic s2=s20;
XG [%oL s3=s30;
@e Myq1ZU p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
-!}1{ %energy in waveguide 1
<y'ttxe S p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
!PQRlgcG %energy in waveguide 2
$"UAJ - p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
;{ezK8FJ}@ %energy in waveguide 3
(*;u{m= for m3 = 1:1:M3 % Start space evolution
AVJF[t , s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?Z!KV= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Jg Xbs+. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
^Gy l:hN sca1 = fftshift(fft(s1)); % Take Fourier transform
Zn^E sca2 = fftshift(fft(s2));
rcbixOT sca3 = fftshift(fft(s3));
vIG,!^*3 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
MUo?ajbqOd sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
bc"{ZL!C sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
@%TQ/L^| s3 = ifft(fftshift(sc3));
\vT8
)\ s2 = ifft(fftshift(sc2)); % Return to physical space
dKMuo'H'% s1 = ifft(fftshift(sc1));
bHMlh^{`% end
iKK=A.g p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
K)v(Z" p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
!uZ +r% p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
8jZYy! P1=[P1 p1/p10];
J )-owu; P2=[P2 p2/p10];
Z/I!\ P3=[P3 p3/p10];
U-k;kmaj P=[P p*p];
8t^"1ND end
f>'7~69 figure(1)
"2h#i nS plot(P,P1, P,P2, P,P3);
2KG j !w ZD<,h`
lZ 转自：
http://blog.163.com/opto_wang/
