计算脉冲在非线性耦合器中演化的Matlab 程序 1)u
3 (yE?)s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
FG7}MUu % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?eT^gWX % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/-<S F T` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`G\uTC pk nBL7LocvR %fid=fopen('e21.dat','w');
|")}p=
N = 128; % Number of Fourier modes (Time domain sampling points)
i 8I%}8 M1 =3000; % Total number of space steps
^~0Mw;n& J =100; % Steps between output of space
z 8M^TV T =10; % length of time windows:T*T0
>2`)S{pBD T0=0.1; % input pulse width
S#qd#Zk|Y MN1=0; % initial value for the space output location
goi.'8M|/b dt = T/N; % time step
,#&lNQ'I n = [-N/2:1:N/2-1]'; % Index
@(PYeXdV6& t = n.*dt;
`h12 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
$ud5bT{n u20=u10.*0.0; % input to waveguide 2
S =q.Y u1=u10; u2=u20;
<OF7:f U1 = u1;
ys:1%D,,_ U2 = u2; % Compute initial condition; save it in U
Mn $TWhg' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_{&znXf>?6 w=2*pi*n./T;
^AMcZ6!\ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
> /1N#S#9 L=4; % length of evoluation to compare with S. Trillo's paper
6}
!n0 dz=L/M1; % space step, make sure nonlinear<0.05
ZA zn-n for m1 = 1:1:M1 % Start space evolution
CJk$o K{Q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`@ULG> u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
|$#u~<r_
w ca1 = fftshift(fft(u1)); % Take Fourier transform
4H8vB^ ca2 = fftshift(fft(u2));
K+ xiov-r? c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Wm4@+ } c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
T5NO}bz u2 = ifft(fftshift(c2)); % Return to physical space
7
2ux3D u1 = ifft(fftshift(c1));
"JAYTatO7H if rem(m1,J) == 0 % Save output every J steps.
oabc=N!7r U1 = [U1 u1]; % put solutions in U array
@jO3+ U2=[U2 u2];
!7@IWz(, " MN1=[MN1 m1];
tYiK#N 7 z1=dz*MN1'; % output location
2V _C_5)1 end
-0PT(gx end
U .hV1 hg=abs(U1').*abs(U1'); % for data write to excel
+Z tqR ha=[z1 hg]; % for data write to excel
V(1Ldl'a t1=[0 t'];
vG O- a2Z hh=[t1' ha']; % for data write to excel file
(;P)oB"`C %dlmwrite('aa',hh,'\t'); % save data in the excel format
BKfcK>%g figure(1)
Bp 6jF2 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
jDI O,XuF figure(2)
8s pGDg\g waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
!! 4_x VdQ}G!d 非线性超快脉冲耦合的数值方法的Matlab程序
]p:x,%nm br+{23&1R# 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
%)8`(9J* Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5#s?rA% u (Mhj-0xf$ .2/(G{}U g
!w7Yv % This Matlab script file solves the nonlinear Schrodinger equations
5i7,s % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
G+
PBV%gE[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!YSAQi ;I % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~F^=7oq -}@3,G C=1;
048BQ M1=120, % integer for amplitude
E{sTxO I$ M3=5000; % integer for length of coupler
F=yrqRS= N = 512; % Number of Fourier modes (Time domain sampling points)
|Y|{9Osus dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
RS!~5nk 5 T =40; % length of time:T*T0.
AJ` b- $Q dt = T/N; % time step
l b5Y$ZC n = [-N/2:1:N/2-1]'; % Index
xz[a3In+ t = n.*dt;
e@*Gnh <& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
w' K\}G~ w=2*pi*n./T;
VS@o_fUx) g1=-i*ww./2;
{ ^>m3 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
(o)nN8 g3=-i*ww./2;
@4Z>; P1=0;
yd[}? P2=0;
#qT 97NQ P3=1;
dbSIC[q P=0;
2+
F34 for m1=1:M1
}MW*xtGV p=0.032*m1; %input amplitude
P\KP )bkC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
, fFB.q"
s1=s10;
nzE 4P3 C+ s20=0.*s10; %input in waveguide 2
o{pQDI {R s30=0.*s10; %input in waveguide 3
PF*<_p" j s2=s20;
.9+"rK}u s3=s30;
wQWokpP;T7 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
& F9 BaJ %energy in waveguide 1
01}az~&;35 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
DhV( $&*M %energy in waveguide 2
))cL+ r p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
~V[pu %energy in waveguide 3
:,%~rR for m3 = 1:1:M3 % Start space evolution
FFb`4. s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Ypo O: s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6 /gh_'& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
eWS[|' dl sca1 = fftshift(fft(s1)); % Take Fourier transform
.pNWpWL. sca2 = fftshift(fft(s2));
c-3AzB#[ sca3 = fftshift(fft(s3));
)Q9m,/F sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
h2ewYe<87` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4YM!S E-I sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Or=
[2@Wg s3 = ifft(fftshift(sc3));
5p}Y6Lc\j s2 = ifft(fftshift(sc2)); % Return to physical space
u$ $@Hw s1 = ifft(fftshift(sc1));
D% } ?l end
f @l$52f3D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
m5Q,RwJ!xK p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
<8yzBp4gZ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
>[B}eS> P1=[P1 p1/p10];
v Ic 0V P2=[P2 p2/p10];
asb-syqU P3=[P3 p3/p10];
JO\Tf."a \ P=[P p*p];
oGx OJyD end
`G&W%CHB figure(1)
]+;1) plot(P,P1, P,P2, P,P3);
.^j #gE &B *gfx'$ 转自：
http://blog.163.com/opto_wang/
