计算脉冲在非线性耦合器中演化的Matlab 程序 K5lp -F Q=8
cBRe % This Matlab script file solves the coupled nonlinear Schrodinger equations of
q': wSu u % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
TfVD'HAN;l % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`[&2K@ u % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\G@6jn1G( d"UW38K{ %fid=fopen('e21.dat','w');
,]mwk~HeF N = 128; % Number of Fourier modes (Time domain sampling points)
| dwxea M1 =3000; % Total number of space steps
n4 @a`lN5g J =100; % Steps between output of space
jZ!JXmVV T =10; % length of time windows:T*T0
'5U$`Xe1 T0=0.1; % input pulse width
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l$E MN1=0; % initial value for the space output location
Y(z N dt = T/N; % time step
jTr 4A-" n = [-N/2:1:N/2-1]'; % Index
PuJ{!S\T7 t = n.*dt;
!f-o,RJ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
He!!oKK> u20=u10.*0.0; % input to waveguide 2
H@ms43v\ u1=u10; u2=u20;
bl?%:qb.V U1 = u1;
\2xBOe-a] U2 = u2; % Compute initial condition; save it in U
&'b }N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7y Te]O w=2*pi*n./T;
O97bgj] g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1qe^rz| L=4; % length of evoluation to compare with S. Trillo's paper
mN
6`8
[ dz=L/M1; % space step, make sure nonlinear<0.05
c$kb0VR for m1 = 1:1:M1 % Start space evolution
^&H=dYcV>/ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
i q:Q$z& u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Sp,Q,Q4 ca1 = fftshift(fft(u1)); % Take Fourier transform
E$Pjp oQTf ca2 = fftshift(fft(u2));
BpG'e-2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
`;CU[Ps?] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
y9li<u<PF u2 = ifft(fftshift(c2)); % Return to physical space
D!a5#+\C u1 = ifft(fftshift(c1));
&AcFa<U if rem(m1,J) == 0 % Save output every J steps.
|u r~s$8y- U1 = [U1 u1]; % put solutions in U array
s; 7qNwYO U2=[U2 u2];
F ^ t?*
MN1=[MN1 m1];
@:9fS z1=dz*MN1'; % output location
-Q PWi2:k end
(mIJI,[xn end
.Pes{uHg hg=abs(U1').*abs(U1'); % for data write to excel
qd ~98FS ha=[z1 hg]; % for data write to excel
n
E}<e: t1=[0 t'];
NJf(,Mr*| hh=[t1' ha']; % for data write to excel file
-5v.1y=!L %dlmwrite('aa',hh,'\t'); % save data in the excel format
uQ]]]Z(H' figure(1)
6//FZ:q waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4t
Nv q figure(2)
L1kM~M waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
E97+GJ3 nQ17E {^pR 非线性超快脉冲耦合的数值方法的Matlab程序 iEVA[xy=D pJIE@Q|hi 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Vt=(2d5:p Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ob0 8x Gj b]<Hh U 3E}NiD\V} `XSc > % This Matlab script file solves the nonlinear Schrodinger equations
(:- Jl"&R@ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
aXbNDj
][ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
:~3{oZGX& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
H<Kk j 2U v3_i< C=1;
d&T6p&V$ M1=120, % integer for amplitude
[AX"ne# M* M3=5000; % integer for length of coupler
gJ5wAK+? N = 512; % Number of Fourier modes (Time domain sampling points)
Q
A) 9 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2PR7M.V 7 T =40; % length of time:T*T0.
i<wU.JX&h dt = T/N; % time step
'"w}gx n = [-N/2:1:N/2-1]'; % Index
$FQcDo|[ t = n.*dt;
+*_fN ]M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_TO i
[G T w=2*pi*n./T;
5+bFy.UW g1=-i*ww./2;
?S@R~y0K g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
S -6"f / g3=-i*ww./2;
<F)w= _%& P1=0;
)y`TymM[F P2=0;
6<s(e_ 5f P3=1;
+t>*l>[ P=0;
<,@H;|mZ for m1=1:M1
<DXmZ1 p=0.032*m1; %input amplitude
KIKq9 * s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
4aN+}TkH@G s1=s10;
0n*rs=\V G s20=0.*s10; %input in waveguide 2
L8:]`M Q0 s30=0.*s10; %input in waveguide 3
0Q$~k s2=s20;
V9zywM s3=s30;
2~M;L&9- p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
AJ\VY;m7F %energy in waveguide 1
niYz9YX p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
i'!jx. %energy in waveguide 2
CO:*x,6au p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
t}]9V D9
%energy in waveguide 3
|I}A> XG for m3 = 1:1:M3 % Start space evolution
0):uF_t< s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
TZh\#dp4l s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
TwM1M["3 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
d<^_w!4X} sca1 = fftshift(fft(s1)); % Take Fourier transform
7 MO sca2 = fftshift(fft(s2));
U~{Sa+ sca3 = fftshift(fft(s3));
.'5'0lR5 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
l5=u3r9WYC sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
O1?B{F/ e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}c`
?0FQ s3 = ifft(fftshift(sc3));
e(}oq"'z s2 = ifft(fftshift(sc2)); % Return to physical space
(| g").L s1 = ifft(fftshift(sc1));
C~ZE95 g end
VLh%XoQx[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
t7|MkX1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"JzfL(yt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
7szls71/= P1=[P1 p1/p10];
>oft :7p P2=[P2 p2/p10];
[as-3&5S P3=[P3 p3/p10];
d[Rb:Y w P=[P p*p];
20r N,@2< end
<G\
<QV8W figure(1)
+"YTCzv;t plot(P,P1, P,P2, P,P3);
3D
9N: c F~z_>1lpP& 转自：
http://blog.163.com/opto_wang/
