计算脉冲在非线性耦合器中演化的Matlab 程序 x %`YV):* KDb j
C'3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
g%Tokl % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
cY5;~lO % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Rd7U5MBEF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'k]~Q{K$ b-/QZvg %fid=fopen('e21.dat','w');
h STcL:b
N = 128; % Number of Fourier modes (Time domain sampling points)
st* sv} M1 =3000; % Total number of space steps
ML'y`S J =100; % Steps between output of space
DzMg^Kp T =10; % length of time windows:T*T0
UUDHknm" T0=0.1; % input pulse width
C{$iuus0 MN1=0; % initial value for the space output location
K"VcPDK dt = T/N; % time step
uvJHkAi n = [-N/2:1:N/2-1]'; % Index
J*b Je"8 t = n.*dt;
&xB*Shp,B u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
LI@BB:)[ u20=u10.*0.0; % input to waveguide 2
sgP{A}4 W u1=u10; u2=u20;
D'u7"^= U1 = u1;
$ c-O+~ U2 = u2; % Compute initial condition; save it in U
Z8Ig, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
O>+=cg w=2*pi*n./T;
,ja!OZ0$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
pTi7Xy!Cw L=4; % length of evoluation to compare with S. Trillo's paper
^%zhj3# dz=L/M1; % space step, make sure nonlinear<0.05
L,.~VNy- for m1 = 1:1:M1 % Start space evolution
, d $"`W2 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$365VTh" u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
8#JX#<HEo ca1 = fftshift(fft(u1)); % Take Fourier transform
pl3ap(/ ca2 = fftshift(fft(u2));
#S9J9k c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
UL}wGWaoG c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
O!nS3%De u2 = ifft(fftshift(c2)); % Return to physical space
J;Z2<x/H u1 = ifft(fftshift(c1));
?ckV 2
if rem(m1,J) == 0 % Save output every J steps.
;AJQ2 U1 = [U1 u1]; % put solutions in U array
dq.U#Rhrx U2=[U2 u2];
17?YN< MN1=[MN1 m1];
d/yF}%0QI z1=dz*MN1'; % output location
~Z/,o) end
}R16WY_' end
Jn=;gtD-* hg=abs(U1').*abs(U1'); % for data write to excel
1|4,jm $ ha=[z1 hg]; % for data write to excel
v.<mrI#? t1=[0 t'];
oDu6W9 + hh=[t1' ha']; % for data write to excel file
P#!N %dlmwrite('aa',hh,'\t'); % save data in the excel format
5C1EdQ4S0 figure(1)
1UJ rPM% waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
aR6F%7gvz figure(2)
5z0VMt waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
PlH~um[J h-1?c\Qq: 非线性超快脉冲耦合的数值方法的Matlab程序 T4wk$R
L 8O]`3oa> 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
:!g|pd[{ag Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?110} [jw y(QFf*J }r@dZBp: e^\e;>Dh> % This Matlab script file solves the nonlinear Schrodinger equations
hm73Zy % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~5&4s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]87BP%G % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
xA(z/% ~C%I'z' C=1;
SC~k4&xy M1=120, % integer for amplitude
an"~n`g M3=5000; % integer for length of coupler
O_1[KiZ N = 512; % Number of Fourier modes (Time domain sampling points)
3:nBl?G< dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
FiiDmhu T =40; % length of time:T*T0.
HQm_ K0$ dt = T/N; % time step
A/<u>cCW n = [-N/2:1:N/2-1]'; % Index
;9OhK71} t = n.*dt;
-:ucp2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
At:8+S<?A w=2*pi*n./T;
]w6Q? %'9 g1=-i*ww./2;
.c-a$39 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
U)bv,{-q g3=-i*ww./2;
wUCxa>h' P1=0;
\PE;R.v_: P2=0;
IANSpWea? P3=1;
T3P9 P=0;
fYUV[Gm for m1=1:M1
(|^m9v0: p=0.032*m1; %input amplitude
sRD
fA4/TF s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
O<cP1TF s1=s10;
Gf\h7)T\ s20=0.*s10; %input in waveguide 2
hNN[dj R s30=0.*s10; %input in waveguide 3
bOj)Wu s2=s20;
z;S-Q, s3=s30;
DD$>3` p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
!}TsFa %energy in waveguide 1
d{4;qM# p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
AVpg %energy in waveguide 2
mcez3gH p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
e7U\gtZ. %energy in waveguide 3
v~Q'm1!O4\ for m3 = 1:1:M3 % Start space evolution
uAPVR s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7l69SQo]? s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
vt#;j;liG s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
S\TXx79PhC sca1 = fftshift(fft(s1)); % Take Fourier transform
en< $.aY sca2 = fftshift(fft(s2));
06pvI} sca3 = fftshift(fft(s3));
bGWfMu=n sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
l\s!A&L sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
X@`a_XAfd sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
p'
>i3T( s3 = ifft(fftshift(sc3));
W91yj: s2 = ifft(fftshift(sc2)); % Return to physical space
GF ux?8A:% s1 = ifft(fftshift(sc1));
lv
8EfN end
B`}um;T#~, p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f,HUr% @ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
5Ml=<^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
G|g^yaq> P1=[P1 p1/p10];
B'}?cG] P2=[P2 p2/p10];
?mg@z q8 P3=[P3 p3/p10];
f4f2xe7\Q P=[P p*p];
O_:l;D#i end
lxhb)]c
^> figure(1)
Z4VFfGCTL plot(P,P1, P,P2, P,P3);
jn2=)KBa_ *1dDs^D#| 转自:
http://blog.163.com/opto_wang/