计算脉冲在非线性耦合器中演化的Matlab 程序 Pvv7|AV
+|oLS_ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
\Rt> U|% % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
7!o#pt7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
D}{]5R % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O d6'bO;G 3 ?gfDJfE %fid=fopen('e21.dat','w');
-'oxenu N = 128; % Number of Fourier modes (Time domain sampling points)
MD;,O3Ge M1 =3000; % Total number of space steps
Z 5wDf+ J =100; % Steps between output of space
<vs*aFq T =10; % length of time windows:T*T0
&a >UVs?= T0=0.1; % input pulse width
7
mA3&<&q MN1=0; % initial value for the space output location
4*n1Xu 7^x dt = T/N; % time step
/a$Zzs&xs n = [-N/2:1:N/2-1]'; % Index
b
V_<5PHP t = n.*dt;
_M>S =3w u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
F_}y[Yn^ u20=u10.*0.0; % input to waveguide 2
IAmMO[9H u1=u10; u2=u20;
e'v_eD T^ U1 = u1;
!t)uRJ U2 = u2; % Compute initial condition; save it in U
X)TZ S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fA V.Mj- w=2*pi*n./T;
EN>a ^B+! g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
su60j^e* L=4; % length of evoluation to compare with S. Trillo's paper
j9%vw.3b dz=L/M1; % space step, make sure nonlinear<0.05
rJp9ut'FEz for m1 = 1:1:M1 % Start space evolution
] RVme^= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
]G!
APE u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
E_z,%aD[ ca1 = fftshift(fft(u1)); % Take Fourier transform
d.>O`.Mu)} ca2 = fftshift(fft(u2));
za.^vwkBk2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&` "uKO] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
\u /=?b u2 = ifft(fftshift(c2)); % Return to physical space
d|
{<SRAI u1 = ifft(fftshift(c1));
JV;VR9-l if rem(m1,J) == 0 % Save output every J steps.
2{ h G",JL U1 = [U1 u1]; % put solutions in U array
lP(<4mdP U2=[U2 u2];
85H*Xm?d# MN1=[MN1 m1];
s BuXw a z1=dz*MN1'; % output location
hz 2f7g end
v`jFWq8I, end
A~a7/N6s; hg=abs(U1').*abs(U1'); % for data write to excel
p|r>tBv?x ha=[z1 hg]; % for data write to excel
> LU !Z t1=[0 t'];
4 tt=u]: hh=[t1' ha']; % for data write to excel file
@<S'f<>g %dlmwrite('aa',hh,'\t'); % save data in the excel format
61b<6 r0o figure(1)
k a8=`cn waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
M%eTNsbNm figure(2)
?`SB GN; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
]V"B`ip[2 <U /r U9O 非线性超快脉冲耦合的数值方法的Matlab程序 :y!{=[>M( $yZP"AsA R 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
)B^T7{ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y= 1(o3( BQ~\ p\ Nu; 9 m?)F@4] % This Matlab script file solves the nonlinear Schrodinger equations
"L)?dlb6T % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
|y]8gL^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`7
J4h9K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x1`Jlzrp, V#PT.,Xa. C=1;
Ed"p|5~ M1=120, % integer for amplitude
=co6.Il M3=5000; % integer for length of coupler
o PA m* N = 512; % Number of Fourier modes (Time domain sampling points)
h`:gMhn dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
qEPC]es|T T =40; % length of time:T*T0.
`9VRT`e dt = T/N; % time step
T!H }^v n = [-N/2:1:N/2-1]'; % Index
s9?H#^Y5u t = n.*dt;
eOd'i{f@F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Ar$ Am w=2*pi*n./T;
z`y^o*qc] g1=-i*ww./2;
R ?kyJ4S g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]*AQT 7PH g3=-i*ww./2;
v}"DW? P1=0;
TP)}1 @ P2=0;
!*-|s}e P3=1;
LZ~}*}jy P=0;
?w "zW6U for m1=1:M1
, *Z!Bd8 p=0.032*m1; %input amplitude
5q.)K
f+ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
.u 9,w s1=s10;
ncij)7c)u s20=0.*s10; %input in waveguide 2
)L7h:%h# s30=0.*s10; %input in waveguide 3
~@VyJT% s2=s20;
$)M 5@KT s3=s30;
< SNu`,/I p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
$[*<e~ ? %energy in waveguide 1
s `
+cQ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
,tHV
H7[ %energy in waveguide 2
s\
YHT.O? p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
iXuSFman %energy in waveguide 3
vHx[:vuq: for m3 = 1:1:M3 % Start space evolution
b(: U]>J s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
kt hy9<!$ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
-Y/c]g s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V3> JZH` sca1 = fftshift(fft(s1)); % Take Fourier transform
Wr\A ->+ sca2 = fftshift(fft(s2));
.d%CD`8! sca3 = fftshift(fft(s3));
i~EFRI@ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
2G BE=T sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
8A2 _4q@34 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
5g;i{T/6~x s3 = ifft(fftshift(sc3));
F]KAnEf s2 = ifft(fftshift(sc2)); % Return to physical space
nHF%PH#|o s1 = ifft(fftshift(sc1));
&X
OFc.u end
/~;om\7r p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
59M\uVWR p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@ZGD'+zd? p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
o",J { P1=[P1 p1/p10];
rE$=~s P2=[P2 p2/p10];
o)
,1R: P3=[P3 p3/p10];
J`d;I#R%c P=[P p*p];
JWvL end
}w/6"MJ[n figure(1)
yk&PJ;%O< plot(P,P1, P,P2, P,P3);
#hF(`oX}4K &`Ek-b!7 转自：
http://blog.163.com/opto_wang/
