计算脉冲在非线性耦合器中演化的Matlab 程序 $rySz7NI lxRzyx % This Matlab script file solves the coupled nonlinear Schrodinger equations of
* 6)u5 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.bOueB- % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#_+T@|r % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R0y@#}JH :zC'jceO %fid=fopen('e21.dat','w');
{. N" 6P N = 128; % Number of Fourier modes (Time domain sampling points)
Qhnz7/a9 M1 =3000; % Total number of space steps
c?0uv2*Yh J =100; % Steps between output of space
]]s_ 8u 3 T =10; % length of time windows:T*T0
j~ G ^J T0=0.1; % input pulse width
G6zFCgFJ^y MN1=0; % initial value for the space output location
mmXLGLMd dt = T/N; % time step
C61KY7iyR n = [-N/2:1:N/2-1]'; % Index
$ J #} 3;a t = n.*dt;
.~ a) u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Q^v8 n1 u20=u10.*0.0; % input to waveguide 2
j\nnx8`7 u1=u10; u2=u20;
rb nu:+! U1 = u1;
<?P UF, U2 = u2; % Compute initial condition; save it in U
N1Y*IkW" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fV3!x,H w=2*pi*n./T;
_[V.%k g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
0>-l {4srs L=4; % length of evoluation to compare with S. Trillo's paper
_tQ= ASe0 dz=L/M1; % space step, make sure nonlinear<0.05
Nh41o0 for m1 = 1:1:M1 % Start space evolution
J-fU ,*Bk u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
/D_8uTS>d[ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
0.nS30 6
ca1 = fftshift(fft(u1)); % Take Fourier transform
&_&])V)<\S ca2 = fftshift(fft(u2));
y^zVb\"4 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
P _t8=d c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
fPHv|_XM> u2 = ifft(fftshift(c2)); % Return to physical space
O'm&S?> u1 = ifft(fftshift(c1));
F 5%-6@= if rem(m1,J) == 0 % Save output every J steps.
'TV^0D" U1 = [U1 u1]; % put solutions in U array
<27B*C M U2=[U2 u2];
-,96Qg4vI MN1=[MN1 m1];
IgC)YI hd z1=dz*MN1'; % output location
eF"7[_+D end
kT UQ8U end
(@M=W.M# hg=abs(U1').*abs(U1'); % for data write to excel
+= MO6}5T ha=[z1 hg]; % for data write to excel
ap\2={u^| t1=[0 t'];
T~%5^+[h hh=[t1' ha']; % for data write to excel file
7(~^6Ql! %dlmwrite('aa',hh,'\t'); % save data in the excel format
V/|Ln*rm figure(1)
M!=v"C# waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
<HG~#oBRq figure(2)
tF&%7(EU3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
~MO'%'@ 5Zn3s() 非线性超快脉冲耦合的数值方法的Matlab程序 wH!]B-hn h|%d=`P, 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。
]-)qL[ Q 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
M.d{:&@`% *NDLGdQqz b_Ba0 h= [ O [ N _z % This Matlab script file solves the nonlinear Schrodinger equations
7G%`zi Z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+U+c] Xgt % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
a| 5GC p p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
yN~=3b> c.&vWmLSGE C=1;
8c__ U< M1=120, % integer for amplitude
9A 3Q&@, M3=5000; % integer for length of coupler
3 %dbfT j N = 512; % Number of Fourier modes (Time domain sampling points)
ClV MZ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
H:9(
XW T =40; % length of time:T*T0.
| fTQ\q]W dt = T/N; % time step
0,m*W?^31 n = [-N/2:1:N/2-1]'; % Index
AGCqJ 8`|T t = n.*dt;
G~4 ^`[elB ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
zK:/
1 w=2*pi*n./T;
v 1 oS f g1=-i*ww./2;
#) >>f g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
f*5=, $0 g3=-i*ww./2;
e@0wF59 P1=0;
[ Q= ) f P2=0;
s/sH", P3=1;
Q6%m}R P=0;
Ylt[Ks<2 for m1=1:M1
3u{[(W} 08 p=0.032*m1; %input amplitude
O:lD>A4{ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
9KXp0Q ?-$ s1=s10;
_E' M(.B< s20=0.*s10; %input in waveguide 2
Di-"y, [ s30=0.*s10; %input in waveguide 3
z0g]nYN% s2=s20;
1 oX"}YY1 s3=s30;
s o ~p+] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
-+Q, xxu %energy in waveguide 1
W11_ M TIU p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
VWfrcSZg6M %energy in waveguide 2
X dB#+"[ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Q
`E{Oo, %energy in waveguide 3
eX _}KH-Q for m3 = 1:1:M3 % Start space evolution
\3)%p(' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
h.2!d0j] s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{_[l,tdZ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Ubn5tN
MK sca1 = fftshift(fft(s1)); % Take Fourier transform
!0Q(x sca2 = fftshift(fft(s2));
`$@1NL7> sca3 = fftshift(fft(s3));
y-sQ"HPN sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
"_#%W
oo sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Qr0JJoHT sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
sU bZVPDr s3 = ifft(fftshift(sc3));
'a"<uk3DT s2 = ifft(fftshift(sc2)); % Return to physical space
3\D jV2t s1 = ifft(fftshift(sc1));
wau81rSd end
9=<
Z> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
S~6<'N&[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
j*xe ns$) p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
%&gx@ \v P1=[P1 p1/p10];
kN]#;R 6 P2=[P2 p2/p10];
^x/0*t5};z P3=[P3 p3/p10];
e2B~j3- ?z P=[P p*p];
o@pM??&x end
9w0 ^= figure(1)
] L &_R^ plot(P,P1, P,P2, P,P3);
2d3wQ)2 *VRFs= 转自：
http://blog.163.com/opto_wang/
