计算脉冲在非线性耦合器中演化的Matlab 程序 ~ 3k& =3d] H:9Z.|{Gv % This Matlab script file solves the coupled nonlinear Schrodinger equations of
!<9sOvka{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
1 o< l;: % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
CNwYQe-i % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x1:#rb ' a^yBtb~,P %fid=fopen('e21.dat','w');
Ki#({~ N = 128; % Number of Fourier modes (Time domain sampling points)
#hinb[fQ M1 =3000; % Total number of space steps
J6 x#c`Y J =100; % Steps between output of space
dre@V(\;hQ T =10; % length of time windows:T*T0
=%u\x=u| T0=0.1; % input pulse width
8`bQ,E+2 MN1=0; % initial value for the space output location
f8]Qn8 dt = T/N; % time step
-TnvX(ok4 n = [-N/2:1:N/2-1]'; % Index
uK6_H vHuy t = n.*dt;
qyXx`'e u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
t;BvKH77 u20=u10.*0.0; % input to waveguide 2
q^{Z"ifL u1=u10; u2=u20;
? f1PQ U1 = u1;
BR8W8nRb U2 = u2; % Compute initial condition; save it in U
e">$[IhXtV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\BB(0Ah+t w=2*pi*n./T;
4%l
@ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
O6rrv,+_L L=4; % length of evoluation to compare with S. Trillo's paper
*"rgK|CM$ dz=L/M1; % space step, make sure nonlinear<0.05
1d4 9z9F for m1 = 1:1:M1 % Start space evolution
yX: A?U u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
"=~P &Mi_ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
.ZSG nbJ ca1 = fftshift(fft(u1)); % Take Fourier transform
.<`W2*1 ca2 = fftshift(fft(u2));
-$pS
{q; c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&cj/8 A5- c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
y/' ^r? u2 = ifft(fftshift(c2)); % Return to physical space
a
}6Fj&hj u1 = ifft(fftshift(c1));
L||_Js u if rem(m1,J) == 0 % Save output every J steps.
u3{ gX{ so U1 = [U1 u1]; % put solutions in U array
1_JxDT,=> U2=[U2 u2];
+ -e8MvP MN1=[MN1 m1];
1$,t:/'-4 z1=dz*MN1'; % output location
5j(3pV`_ end
]:* 8
Mb# end
Qxds]5WB/ hg=abs(U1').*abs(U1'); % for data write to excel
aQa x85 ha=[z1 hg]; % for data write to excel
Q;O\tl t1=[0 t'];
F",] *> r hh=[t1' ha']; % for data write to excel file
,#^<0u+zrF %dlmwrite('aa',hh,'\t'); % save data in the excel format
W":is" figure(1)
,e"A9ik # waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wv,,# P figure(2)
oo\0X waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
KMz\h2X bH7[6#y$ 非线性超快脉冲耦合的数值方法的Matlab程序 T-7'#uB.m U\ S%Jq* 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。
1j*I`xZ 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
s PNX) %gd=d 0vm I\R5Cb<p V43pZ]YZ> % This Matlab script file solves the nonlinear Schrodinger equations
ld1t1'I' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
7Dy\-9:v % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+Ux)m4}j % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
9IL#\:d1 S=O/W(ZB C=1;
&]~z-0`$! M1=120, % integer for amplitude
LV:oNK( M3=5000; % integer for length of coupler
.vRLK N = 512; % Number of Fourier modes (Time domain sampling points)
STgl{# dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
8$avPD3jx T =40; % length of time:T*T0.
mwFI89 J' dt = T/N; % time step
jY-i`rJN n = [-N/2:1:N/2-1]'; % Index
ZTG*| t = n.*dt;
1Giy|;2/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
fys@%PZq w=2*pi*n./T;
[Kk LpZG g1=-i*ww./2;
6 G"AP~|0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Eg t;Bj#% g3=-i*ww./2;
c L*D_)?8 P1=0;
/U<-N'| P2=0;
_<5 o1 P3=1;
(]0$^!YK P=0;
|0(Z)s, for m1=1:M1
F#_7m C p=0.032*m1; %input amplitude
lj.z> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
DLE|ctzj[7 s1=s10;
aKaqi}IT s20=0.*s10; %input in waveguide 2
JGIN<J85e s30=0.*s10; %input in waveguide 3
NFGC.< s2=s20;
JnCY O^Qj s3=s30;
[ (t goh/ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
w5jH#ja %energy in waveguide 1
UuxWP\~2 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
T3['6% %energy in waveguide 2
ro37H2^Ty p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
s)yEVh %energy in waveguide 3
1rC8] M.N for m3 = 1:1:M3 % Start space evolution
q
/|<>s s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
n6WSTh s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
}j TE gog s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
WX
79V sca1 = fftshift(fft(s1)); % Take Fourier transform
ltt %X].[ sca2 = fftshift(fft(s2));
mBc;^8I?23 sca3 = fftshift(fft(s3));
?7G?uk]3,@ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
c[< lr sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~=%eOoZP;c sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$c0SWz s3 = ifft(fftshift(sc3));
iAf, :g s2 = ifft(fftshift(sc2)); % Return to physical space
oypq3V=5 s1 = ifft(fftshift(sc1));
T~ Jl{(s9) end
<PW*vo9v p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
e`R*6^e p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>;o^qi_$ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
EBw}/y{Kt P1=[P1 p1/p10];
-'{ioHt&X/ P2=[P2 p2/p10];
.)})8csl.d P3=[P3 p3/p10];
({ ![ P=[P p*p];
8nES=<rz end
| IH-a" figure(1)
)rhKWg plot(P,P1, P,P2, P,P3);
?`\<t$M +Qu~UK\ 转自：
http://blog.163.com/opto_wang/
