计算脉冲在非线性耦合器中演化的Matlab 程序 a/ uo}[Y 2`= 6 %s
% This Matlab script file solves the coupled nonlinear Schrodinger equations of
D=)f
)- u' % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
'?yCq$& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
t=#Pya % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5Z Ab]F90 41 vL"P
K %fid=fopen('e21.dat','w');
AP\ofLmq N = 128; % Number of Fourier modes (Time domain sampling points)
VZIR4J[\. M1 =3000; % Total number of space steps
\BI/G J =100; % Steps between output of space
=BZ?- mIU T =10; % length of time windows:T*T0
mEuHl> T0=0.1; % input pulse width
Yp4c'Zk MN1=0; % initial value for the space output location
5H:@ 8,B dt = T/N; % time step
"MiD8wX- n = [-N/2:1:N/2-1]'; % Index
)DUL)S t = n.*dt;
fH8!YQG8$ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Gr(|R a . u20=u10.*0.0; % input to waveguide 2
uC]Z8&+obb u1=u10; u2=u20;
g9my=gY U1 = u1;
ELh3 ^ U2 = u2; % Compute initial condition; save it in U
n`;R p r& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
i3
)xX@3 w=2*pi*n./T;
- &[z\"T g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
*,\` o~ L=4; % length of evoluation to compare with S. Trillo's paper
.%0ne:5 dz=L/M1; % space step, make sure nonlinear<0.05
$rG< uO for m1 = 1:1:M1 % Start space evolution
YJ2ro-X u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
pyW u9 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
? 4)v`* ca1 = fftshift(fft(u1)); % Take Fourier transform
s([Wn)I ca2 = fftshift(fft(u2));
twk&-:' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$~'Tf>e c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
=J |sbY"] u2 = ifft(fftshift(c2)); % Return to physical space
M>_ = "atI u1 = ifft(fftshift(c1));
p#_ [ if rem(m1,J) == 0 % Save output every J steps.
I*1S/o_xI U1 = [U1 u1]; % put solutions in U array
%TK&)Q% h5 U2=[U2 u2];
G"S5ki`o MN1=[MN1 m1];
C 7n Kk/r z1=dz*MN1'; % output location
;>2#@QP end
mT_ GrIl[ end
U 0ZB^` hg=abs(U1').*abs(U1'); % for data write to excel
|tG+iF@4 ha=[z1 hg]; % for data write to excel
`% E9xcD% t1=[0 t'];
Uk-HP\C"7 hh=[t1' ha']; % for data write to excel file
@%@zH% b %dlmwrite('aa',hh,'\t'); % save data in the excel format
j.QHkI1. figure(1)
R.7#zhC`4 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
.T3=Eq&"W figure(2)
TvrwVL) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
=%h~/, FpkXOj?* 非线性超快脉冲耦合的数值方法的Matlab程序 "]]q} O? WaYO1*= 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。
bx(w :]2 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
_F8T\f | }h~'AM AQci,j" J`Oy .Qu) % This Matlab script file solves the nonlinear Schrodinger equations
Sa}D.SBg % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{of]/ 3= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
pVOI5>f\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
-fux2?8M +?e}<#vd'? C=1;
Yh gUCF# M1=120, % integer for amplitude
ULvVD6RQ47 M3=5000; % integer for length of coupler
Y MAQ+A ! N = 512; % Number of Fourier modes (Time domain sampling points)
`45d"B
I dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Y(GW0\< T =40; % length of time:T*T0.
VC=6uB dt = T/N; % time step
<PD|_nZT n = [-N/2:1:N/2-1]'; % Index
q$^<zY t = n.*dt;
uiK:*[ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Jn,w)El s w=2*pi*n./T;
{aJz. `u\ g1=-i*ww./2;
kGD |c=K} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!3KPwI, g3=-i*ww./2;
*o |p)lH P1=0;
R ]=SWE}U P2=0;
J<_ 1z':W) P3=1;
b]dxlj}
< P=0;
? -{IsF^ for m1=1:M1
NS 5 4 9S p=0.032*m1; %input amplitude
|E|T%i^}./ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
l\U*sro< s1=s10;
3"B+xbe= s20=0.*s10; %input in waveguide 2
3*\8p6G s30=0.*s10; %input in waveguide 3
k6g| 7^es2 s2=s20;
e3rfXhp s3=s30;
nh|EZp] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
-4`sqv ] %energy in waveguide 1
2))t*9;h p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
'WzUu MCx %energy in waveguide 2
u~)% tL p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
y7;
5xF?q %energy in waveguide 3
s7Qyfe&> for m3 = 1:1:M3 % Start space evolution
Wy," cT s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
*cy.*@d s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
;q&Z9 lm s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,^!Zm^4, sca1 = fftshift(fft(s1)); % Take Fourier transform
$Q,n+ / sca2 = fftshift(fft(s2));
'Ix5,^M}B sca3 = fftshift(fft(s3));
+cw{aI`a8 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
;;6\q!7` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
r UvwpP"k sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
KPg[-d s3 = ifft(fftshift(sc3));
;<VR2U` s2 = ifft(fftshift(sc2)); % Return to physical space
bN4d:0 Y s1 = ifft(fftshift(sc1));
Wb'*lT0= end
m^c%]5$ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
}*OD M6 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
j>V"hf p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
AYYR xhv_, P1=[P1 p1/p10];
0c-QI r}m P2=[P2 p2/p10];
yx 7loy$[ P3=[P3 p3/p10];
3v G P=[P p*p];
=G[ H,;W end
wz)m{:b< figure(1)
cnC _#kp plot(P,P1, P,P2, P,P3);
`lvh\[3^ \c FAxL( 转自：
http://blog.163.com/opto_wang/
