计算脉冲在非线性耦合器中演化的Matlab 程序 I #GsEhi V>B*_J,z. % This Matlab script file solves the coupled nonlinear Schrodinger equations of
B {- +1f 4 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
zK ir % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\
Q0-yNt % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Jkub|w#QH 0?\d%J!"S %fid=fopen('e21.dat','w');
]?j[P=\ N = 128; % Number of Fourier modes (Time domain sampling points)
Avo"jN*<d M1 =3000; % Total number of space steps
vV /fTO J =100; % Steps between output of space
a3(q;^v T =10; % length of time windows:T*T0
@P
xX]e T0=0.1; % input pulse width
>Wr MN1=0; % initial value for the space output location
UZ3oc[#D=] dt = T/N; % time step
te8lF{R n = [-N/2:1:N/2-1]'; % Index
jthGNVZ t = n.*dt;
Zmr*$,v<y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
jBnvu@K " u20=u10.*0.0; % input to waveguide 2
2:D1<z6RQ u1=u10; u2=u20;
CsW*E,|xyP U1 = u1;
qC$h~Epp4 U2 = u2; % Compute initial condition; save it in U
]2'{W]m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mp+lN: w=2*pi*n./T;
, K[}Bz g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Q.`O;D}x L=4; % length of evoluation to compare with S. Trillo's paper
o9D] \PdL> dz=L/M1; % space step, make sure nonlinear<0.05
qaN%&K9F8 for m1 = 1:1:M1 % Start space evolution
} l4d/I u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
4.0JgX u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
> aV
Q ca1 = fftshift(fft(u1)); % Take Fourier transform
K#oF=4_/| ca2 = fftshift(fft(u2));
UXN!iU) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
OBJk\j+Wi c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
LG3:V'| u2 = ifft(fftshift(c2)); % Return to physical space
)4/227b/( u1 = ifft(fftshift(c1));
dr8`;$;G* if rem(m1,J) == 0 % Save output every J steps.
Kg MW U1 = [U1 u1]; % put solutions in U array
4Js9 "<w U2=[U2 u2];
;*_U)th MN1=[MN1 m1];
Uq}-<q z1=dz*MN1'; % output location
K\]I@UTwq end
rezH5d6z62 end
C!r9+z)< hg=abs(U1').*abs(U1'); % for data write to excel
M,nLPHg K ha=[z1 hg]; % for data write to excel
.ko}m{ t1=[0 t'];
"vnWq=E 2 hh=[t1' ha']; % for data write to excel file
}n91aE3 v %dlmwrite('aa',hh,'\t'); % save data in the excel format
D/=
AU figure(1)
*K1GX waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
1Ev#[FOc figure(2)
drZ1D s waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
".R5K ? d 9n{jv| 非线性超快脉冲耦合的数值方法的Matlab程序 EO[U ezuU p| b&hgA 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。
MVpk/S%W 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;RQNhXh 8=h$6=1S 7f9i5E1 "L p"o % This Matlab script file solves the nonlinear Schrodinger equations
G~\ SI. % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
xRx8E;Q@h? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
H _%yh,L % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Ltt+BUJc /6%< 97/d C=1;
(YJ]}J^ M1=120, % integer for amplitude
>^Zyls M3=5000; % integer for length of coupler
>v DD . N = 512; % Number of Fourier modes (Time domain sampling points)
]% K 8 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
yb(zyGe T =40; % length of time:T*T0.
`RG_FS"v dt = T/N; % time step
4l~0LdYXKm n = [-N/2:1:N/2-1]'; % Index
>{dj6Wo t = n.*dt;
gZs UX^% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
faVR % w=2*pi*n./T;
+|w-1&- g1=-i*ww./2;
jJmg9&^R g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
1 JU1XQi g3=-i*ww./2;
nPj+mg P1=0;
@?GOO D_i P2=0;
|# zznT" P3=1;
.7HnWKUV P=0;
H lw0i a for m1=1:M1
E
Fx@O p=0.032*m1; %input amplitude
&x(^=sTHI s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Z-!W#
s1=s10;
79>8tOuo s20=0.*s10; %input in waveguide 2
7Lr}Y/1= s30=0.*s10; %input in waveguide 3
^'|\8 s2=s20;
1z\>>N$7B s3=s30;
MO{6B#(<F p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
`2Buf8|a, %energy in waveguide 1
N2"4dVV; p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
@42!\1YT %energy in waveguide 2
QcQ:hHF p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
% ` c?cB %energy in waveguide 3
X j\SJ* for m3 = 1:1:M3 % Start space evolution
S:UtmS+K s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
,'CDKzY s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
bm{L6D E s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
{GS7J sca1 = fftshift(fft(s1)); % Take Fourier transform
`3$S^|v sca2 = fftshift(fft(s2));
HgwL~vG sca3 = fftshift(fft(s3));
.>-`2 B*/ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
h<wF;g, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
L7 jMpz& sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
NC 0H5 s3 = ifft(fftshift(sc3));
SR#%gR_SC s2 = ifft(fftshift(sc2)); % Return to physical space
w@P c7$EP s1 = ifft(fftshift(sc1));
$+Hv5]/hb end
iz`u@QKc% p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
a$c7d~p$I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
KUfk5Y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Aa5IccR P1=[P1 p1/p10];
Zcg=a _ P2=[P2 p2/p10];
%$
^yot P3=[P3 p3/p10];
ms=I lz P=[P p*p];
?Rl?Pp=> end
8VLr*83~8 figure(1)
Z\E 3i plot(P,P1, P,P2, P,P3);
`@{qnCNQ m7 !Fb
转自：
http://blog.163.com/opto_wang/
