计算脉冲在非线性耦合器中演化的Matlab 程序 _ n4ma =Gz>ZWF % This Matlab script file solves the coupled nonlinear Schrodinger equations of
j]O[I^5 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
#%"TU,[+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/exl9Ilt] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
d<? :Q F$ p*G][ %fid=fopen('e21.dat','w');
^3o8F N = 128; % Number of Fourier modes (Time domain sampling points)
m (:qZW M1 =3000; % Total number of space steps
K0=E4>z,`q J =100; % Steps between output of space
wLe &y4 T =10; % length of time windows:T*T0
\<x_96jt!\ T0=0.1; % input pulse width
xH#a|iT?( MN1=0; % initial value for the space output location
@zF:{=+]+ dt = T/N; % time step
VDjIs UUX n = [-N/2:1:N/2-1]'; % Index
B^~Bv!tHWr t = n.*dt;
vcU\xk") u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@~G`~8 u20=u10.*0.0; % input to waveguide 2
Atq2pL" u1=u10; u2=u20;
GSnHxs) U1 = u1;
\1C!,C U2 = u2; % Compute initial condition; save it in U
S_VncTIO ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7d8qs%nA w=2*pi*n./T;
c$:=d4t5$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
R bc2g"] L=4; % length of evoluation to compare with S. Trillo's paper
|Umfq:W`y_ dz=L/M1; % space step, make sure nonlinear<0.05
KqUSTR1e[ for m1 = 1:1:M1 % Start space evolution
nL 07^6( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
{59VS
Nl u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
:42;c:8 5 ca1 = fftshift(fft(u1)); % Take Fourier transform
y"L`bl A9} ca2 = fftshift(fft(u2));
O rJlHMz c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
lT!$\E$1
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
0QH3,Ps1C u2 = ifft(fftshift(c2)); % Return to physical space
)u/
^aK53^ u1 = ifft(fftshift(c1));
`Mp7 }) if rem(m1,J) == 0 % Save output every J steps.
D 4 ]B> U1 = [U1 u1]; % put solutions in U array
J K]tcP U2=[U2 u2];
MGKeD+=5 MN1=[MN1 m1];
seU^IC< z1=dz*MN1'; % output location
o ]jP3
$t; end
JP,(4h * end
53*, f hg=abs(U1').*abs(U1'); % for data write to excel
15T[J%7f ha=[z1 hg]; % for data write to excel
v[DbhIX U t1=[0 t'];
p't :bR hh=[t1' ha']; % for data write to excel file
q;0&idYC %dlmwrite('aa',hh,'\t'); % save data in the excel format
!v4j` A;% figure(1)
^pV>b(?qw waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
RHl=$Hm .% figure(2)
zpr@!76 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
jo3}]KC ! H?(S SL 非线性超快脉冲耦合的数值方法的Matlab程序 A1t~&? akCo+ @ 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。
Z MMo6; 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
X8SRQO^ O:=|b ]t |}p}`Mb)a ZIL|
.<8I % This Matlab script file solves the nonlinear Schrodinger equations
._MAHBx+G % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
:Ip:sRz % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!+DJhw&c, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
< R PoQ'.^ XZdr`$z f C=1;
-0VA!3l M1=120, % integer for amplitude
TFYT vUn M3=5000; % integer for length of coupler
LUDJPIk N = 512; % Number of Fourier modes (Time domain sampling points)
8u'O` j dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
'bI ~61{A T =40; % length of time:T*T0.
'uf\.F dt = T/N; % time step
w Al}:|+n n = [-N/2:1:N/2-1]'; % Index
=i^<a7M~ t = n.*dt;
e_~ fJ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
^ ?7dOW w=2*pi*n./T;
Tq\~<rEo g1=-i*ww./2;
X:``{!~geo g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Ph +X{| g3=-i*ww./2;
it\DZGsg P1=0;
]dbSa1? P2=0;
:E mQ_?( ^ P3=1;
d=Df.H+3 P=0;
T<f\*1~^ for m1=1:M1
:9F''f$AP p=0.032*m1; %input amplitude
ey\m)6A$ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
%t`SSW7I s1=s10;
$ ~,}yh; s20=0.*s10; %input in waveguide 2
%t~SO kx s30=0.*s10; %input in waveguide 3
Q 1nDl s2=s20;
:`U yn!w s3=s30;
)o9Q5Lq p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
P w B g %energy in waveguide 1
"\/^/vn? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
6v gB qn[ %energy in waveguide 2
~3bZ+*H> p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
H\| ]!8w5Z %energy in waveguide 3
hH1lgc for m3 = 1:1:M3 % Start space evolution
Wyq~:vU.S s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
MZ5Y\-nq\ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Cl6m$YUt s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
@1qdd~B} sca1 = fftshift(fft(s1)); % Take Fourier transform
Jh43)#G- sca2 = fftshift(fft(s2));
!0ce kSesr sca3 = fftshift(fft(s3));
l 70,Jo?78 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
&v$,pg%-: sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
v. Xoq sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
-*|:v67C& s3 = ifft(fftshift(sc3));
(rr}Pv%yb s2 = ifft(fftshift(sc2)); % Return to physical space
w!WRa8 C s1 = ifft(fftshift(sc1));
/}w#Jk4pD end
zUs ~V`0 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
4O`6h)!NQ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
bR`r T4.F p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
T0`"kjE P1=[P1 p1/p10];
]am~aJ|L
P2=[P2 p2/p10];
?h!t$QQ!M P3=[P3 p3/p10];
,\o<y|+`S P=[P p*p];
T~%H%O(F end
BrJ
o!@< figure(1)
aXdf>2c{JD plot(P,P1, P,P2, P,P3);
i s L{9^ S~0JoCeo 转自：
http://blog.163.com/opto_wang/
