计算脉冲在非线性耦合器中演化的Matlab 程序 e ~3]/BL ^u3*hl}YKy % This Matlab script file solves the coupled nonlinear Schrodinger equations of
g %ZdIKj! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?vMK'" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
"oHp.$+K % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d3og?{i<}& ) sRN!~ %fid=fopen('e21.dat','w');
^)Smv\Md N = 128; % Number of Fourier modes (Time domain sampling points)
7,f:Qi@g M1 =3000; % Total number of space steps
Wux 0 RF& J =100; % Steps between output of space
`(P
"u T =10; % length of time windows:T*T0
3x P~~j;7 T0=0.1; % input pulse width
3\,MsoAl MN1=0; % initial value for the space output location
*3 !(*F@M, dt = T/N; % time step
vf6`s\6 n = [-N/2:1:N/2-1]'; % Index
DE'Xq6#PK t = n.*dt;
h|K\z{ A u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
:D DO= u20=u10.*0.0; % input to waveguide 2
K *TnUQ u1=u10; u2=u20;
*+NGi(N U1 = u1;
#,t2*tM U2 = u2; % Compute initial condition; save it in U
K1/
U
(A ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
L7X7Zt8% w=2*pi*n./T;
BQ).`f";d g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
j[_t6Z L=4; % length of evoluation to compare with S. Trillo's paper
yVT&rQ"{ dz=L/M1; % space step, make sure nonlinear<0.05
hJecCOA)' for m1 = 1:1:M1 % Start space evolution
mluW=fE u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
T:be 9 5!, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
3Wjq >\ ca1 = fftshift(fft(u1)); % Take Fourier transform
TViBCed40 ca2 = fftshift(fft(u2));
4s[`yV
c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
"(Mvl1^BT c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
o^8*aH)I>Y u2 = ifft(fftshift(c2)); % Return to physical space
ixIh
T u1 = ifft(fftshift(c1));
k&WUv 0 if rem(m1,J) == 0 % Save output every J steps.
5P-K *C& U1 = [U1 u1]; % put solutions in U array
pTc$+Z7 3 U2=[U2 u2];
{ k
kAqJ MN1=[MN1 m1];
r5D jCV" z1=dz*MN1'; % output location
O 5g}2 end
J>><o:~@ end
!>CE(;E>z hg=abs(U1').*abs(U1'); % for data write to excel
2O?Vr "
A ha=[z1 hg]; % for data write to excel
YI L'YNH t1=[0 t'];
F~tm`n8Z hh=[t1' ha']; % for data write to excel file
7h(HG ?2Y %dlmwrite('aa',hh,'\t'); % save data in the excel format
n/u i<&( figure(1)
CW.&Y?>Tv waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
}9{dR4hD figure(2)
K%98;e9 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?R dmKA `Af{H/qiI 非线性超快脉冲耦合的数值方法的Matlab程序 Gtj ( 83mlZ1jQz 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。
Y'tq m &} 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
OAmES;Ck$( r~8D\ _=s ^>3tYg&7 5x:Ift
* % This Matlab script file solves the nonlinear Schrodinger equations
lc\>DH\n6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
i}.{m Et % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Zkf 3t>[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
pem3G5
`g= qFvg}}^y C=1;
5F'%i;)oq M1=120, % integer for amplitude
It#h p,@e M3=5000; % integer for length of coupler
1"8Z
y6t N = 512; % Number of Fourier modes (Time domain sampling points)
f$:7A0 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
|pfhrwJp T =40; % length of time:T*T0.
{Q{lb(6Ba dt = T/N; % time step
#Tr;JAzVjG n = [-N/2:1:N/2-1]'; % Index
o?:;8]sr! t = n.*dt;
*>H M$.?Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
CBiU#h
q w=2*pi*n./T;
>w z ;}9v g1=-i*ww./2;
08<k'Oi] g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
@5{.K/s g3=-i*ww./2;
xi
'72 P1=0;
bBkm]
> P2=0;
! !?+M @ P3=1;
.`oJc J P=0;
4+ASw N9 for m1=1:M1
& /b? I ` p=0.032*m1; %input amplitude
@4 zi]v s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
&"U9X"8b s1=s10;
8zP :*|D s20=0.*s10; %input in waveguide 2
oV0LJ% s30=0.*s10; %input in waveguide 3
.Q=2WCv0 s2=s20;
DhtU]w} s3=s30;
&{-oA_@ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)GiFkG %energy in waveguide 1
eT7!a']x p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
m#5|J@] %energy in waveguide 2
;n( #b8r9 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
tnQR< %energy in waveguide 3
1 g~Dm}m for m3 = 1:1:M3 % Start space evolution
(cOND/S s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
'Z *\1Ci s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nUI63? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
uR 06&SaA> sca1 = fftshift(fft(s1)); % Take Fourier transform
_H~pH7WU sca2 = fftshift(fft(s2));
b aUEsg[~V sca3 = fftshift(fft(s3));
KKeb ioW sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Hrd 5p+j sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
H(5S K v5 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
]p4`7@@)* s3 = ifft(fftshift(sc3));
f7EIDFX>pt s2 = ifft(fftshift(sc2)); % Return to physical space
x'E' jh% s1 = ifft(fftshift(sc1));
rh:s
7 end
2]of SdM p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8{}Pj p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
fWtb mUq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
?/`C~e<J P1=[P1 p1/p10];
p`E|SNt/W P2=[P2 p2/p10];
J[j/aDdP P3=[P3 p3/p10];
~6@ c]: P=[P p*p];
p^pQZ6- end
EuKrYY] g figure(1)
#hy5c,}> plot(P,P1, P,P2, P,P3);
TnvHO_P, _/QKWk&j 转自：
http://blog.163.com/opto_wang/
