计算脉冲在非线性耦合器中演化的Matlab 程序 !f+H,]D" `6xkf&Kt % This Matlab script file solves the coupled nonlinear Schrodinger equations of
"UJ
S5[7$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
dp* u9z~NA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~'CE[G5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/Dj=iBO Q{l pKe0 %fid=fopen('e21.dat','w');
a,WICv0E N = 128; % Number of Fourier modes (Time domain sampling points)
| ]X M1 =3000; % Total number of space steps
> b{q. J =100; % Steps between output of space
Bjz P z T =10; % length of time windows:T*T0
XnWr5-; T0=0.1; % input pulse width
z=3\Ab MN1=0; % initial value for the space output location
x"
L20} dt = T/N; % time step
Aw5HF34J n = [-N/2:1:N/2-1]'; % Index
M%kO7>h8 t = n.*dt;
G8Y<1%`< u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
p$3sME$L u20=u10.*0.0; % input to waveguide 2
ftF@Wq1f u1=u10; u2=u20;
+P`*kj-P\ U1 = u1;
`.Qi?* ^ U2 = u2; % Compute initial condition; save it in U
Evjj"h&0J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\hEN4V[ w=2*pi*n./T;
Nu?-0> g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
n4#;k=mA L=4; % length of evoluation to compare with S. Trillo's paper
d!
LE{ dz=L/M1; % space step, make sure nonlinear<0.05
+y3%3EKs1~ for m1 = 1:1:M1 % Start space evolution
d5gR"ja u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
S_IU V) u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
cZ2kYn 8 ca1 = fftshift(fft(u1)); % Take Fourier transform
L$E{ycn ca2 = fftshift(fft(u2));
T"DlT/\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
-K3^BZ H I c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
*=I}Qh( 1 u2 = ifft(fftshift(c2)); % Return to physical space
|='z{WS u1 = ifft(fftshift(c1));
c5D) if rem(m1,J) == 0 % Save output every J steps.
@8pp EFw U1 = [U1 u1]; % put solutions in U array
5E zw
~hn U2=[U2 u2];
\S! e![L/ MN1=[MN1 m1];
]X ?7Z I^ z1=dz*MN1'; % output location
zIu
E9l end
2 vWx)Drb6 end
zM(vr"U hg=abs(U1').*abs(U1'); % for data write to excel
!~rY1T~ ha=[z1 hg]; % for data write to excel
n4R(.N 00 t1=[0 t'];
sWc*5Rt hh=[t1' ha']; % for data write to excel file
Yd=>K HVD %dlmwrite('aa',hh,'\t'); % save data in the excel format
r'HtZo$^R figure(1)
Xy$3V U* waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
li}1S figure(2)
)E-inHD / waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
uJC~ LC N |w<H!lGe!$ 非线性超快脉冲耦合的数值方法的Matlab程序 Ne[7gxpu
G(G{RAk> 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。
UVd 7 JGR 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
Z: sg} 4hTMbS_; K k-S}.E x"gd8j]s % This Matlab script file solves the nonlinear Schrodinger equations
JS CZ{v J$ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
?7.7`1m !v % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
IpcNuZo9& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;
Q3n "2) H'< C=1;
0+kH:dP{ M1=120, % integer for amplitude
hp 5|@ M3=5000; % integer for length of coupler
C (#u[8 N = 512; % Number of Fourier modes (Time domain sampling points)
a!"$~y $* dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
@M_oH:GV T =40; % length of time:T*T0.
0 Tx{3# dt = T/N; % time step
LH kc7 X$ n = [-N/2:1:N/2-1]'; % Index
%'s>QF]' t = n.*dt;
3TY5 ;6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
gT0BkwIV w=2*pi*n./T;
m
g4nrr\ g1=-i*ww./2;
w~"KA 6 ^ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
6/r)y+H g3=-i*ww./2;
w&o&jAb-M P1=0;
N D(/uyI P2=0;
-ZRO@&tMD P3=1;
S||}nJ0 P=0;
-- %N8L;e for m1=1:M1
$_o-~F2i5 p=0.032*m1; %input amplitude
\KQ71yqY s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
@Z\,q's s1=s10;
V C2 4sU s20=0.*s10; %input in waveguide 2
{f2S/$q s30=0.*s10; %input in waveguide 3
clL2k8VS s2=s20;
g!?:Ye`5 s3=s30;
tG9BfGF p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@` 1Ds %energy in waveguide 1
QxVq^H p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Q@<S[Qh[. %energy in waveguide 2
@|63K)Xy p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
$JJ rSwR<h %energy in waveguide 3
f78An 8 for m3 = 1:1:M3 % Start space evolution
jr /pj? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
q_g+Jf
P-D s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Y2ZT.l s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
pb
~u E sca1 = fftshift(fft(s1)); % Take Fourier transform
b F"G[pD sca2 = fftshift(fft(s2));
aW WU4xe sca3 = fftshift(fft(s3));
UEM(@zD] sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#LL?IRH9^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Mc09ES sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
%l}D. ml s3 = ifft(fftshift(sc3));
g X ]-\ s2 = ifft(fftshift(sc2)); % Return to physical space
wsIW
|@ s1 = ifft(fftshift(sc1));
aT)BR?OYSJ end
4'`{H@]tb p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vY }A p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
bx{$Y_L+p p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
p?7v$ev_ P1=[P1 p1/p10];
9`I _Et P2=[P2 p2/p10];
zR1^I~
% P3=[P3 p3/p10];
2ORNi,_I P=[P p*p];
6:Ch^c+IZ end
] >LhkA@V figure(1)
5!D BmAB plot(P,P1, P,P2, P,P3);
P9 ^-6;'Y p^%YBY#,H 转自：
http://blog.163.com/opto_wang/
