计算脉冲在非线性耦合器中演化的Matlab 程序 q 2HYiH^L <dyewy*.L % This Matlab script file solves the coupled nonlinear Schrodinger equations of
tabT0 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
HF|oBX$_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fnx-s{c? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[qsEUc+Z.' \EseGgd21 %fid=fopen('e21.dat','w');
0!v ->Dk N = 128; % Number of Fourier modes (Time domain sampling points)
@cU&n6C@ M1 =3000; % Total number of space steps
% `Z! 4L J =100; % Steps between output of space
G
"P4- T =10; % length of time windows:T*T0
ybp -$e T0=0.1; % input pulse width
E*i#?u MN1=0; % initial value for the space output location
&/,|+U[ dt = T/N; % time step
r'gOVi4t1* n = [-N/2:1:N/2-1]'; % Index
F;^F+H t = n.*dt;
`~eUee3b.~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
|7x\m t u20=u10.*0.0; % input to waveguide 2
K98i[,rP u1=u10; u2=u20;
gv5*!eI U1 = u1;
^n0]dizB U2 = u2; % Compute initial condition; save it in U
@JdZ5Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
YJ$1N!rG w=2*pi*n./T;
q+,Q <2J g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
^pHq66d%Z L=4; % length of evoluation to compare with S. Trillo's paper
Sp@-p9# dz=L/M1; % space step, make sure nonlinear<0.05
G @j0rnn>B for m1 = 1:1:M1 % Start space evolution
T0]MuIJ). u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
-_$$ Te u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
cu+FM ca1 = fftshift(fft(u1)); % Take Fourier transform
](|\whI ca2 = fftshift(fft(u2));
nB .G c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
[`
sL?&a c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
nT2)E&U6% u2 = ifft(fftshift(c2)); % Return to physical space
ToYAW,U[d u1 = ifft(fftshift(c1));
/ *0K92NB if rem(m1,J) == 0 % Save output every J steps.
Bj7gQ%>H4 U1 = [U1 u1]; % put solutions in U array
T
Q,?>6n U2=[U2 u2];
@IXsy MN1=[MN1 m1];
v$^Z6>v VI z1=dz*MN1'; % output location
%.Q
!oYehj end
6Cp]NbNrq end
>t7x>_~
hg=abs(U1').*abs(U1'); % for data write to excel
K(aJi,e> ha=[z1 hg]; % for data write to excel
y|wc ,n%L> t1=[0 t'];
{s;U~!3aY hh=[t1' ha']; % for data write to excel file
*g^x*|f6 %dlmwrite('aa',hh,'\t'); % save data in the excel format
Z(Jt~a3o figure(1)
@V!r"Bkg. waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
_o8 ?E&d figure(2)
1@$K o5 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ZRYEqSm ++E 3] X| 非线性超快脉冲耦合的数值方法的Matlab程序 V*~Zs'L'E }u1O#L}F5 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。
&4_qF^9J 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
3 h< , 0 bo/XUpi v hhC>
7 o6p98Dpg % This Matlab script file solves the nonlinear Schrodinger equations
]LM-@G+Jz % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
`jOX6_z?I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}1r m % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
bcupo:N 4ni3kmvX C=1;
#^ ]n0! M1=120, % integer for amplitude
Si~vDQ7" M3=5000; % integer for length of coupler
G%Lt.?m[ N = 512; % Number of Fourier modes (Time domain sampling points)
B-r0"MX & dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
1x,tu}<u^ T =40; % length of time:T*T0.
h\'n**f_x dt = T/N; % time step
SCTA=l. n = [-N/2:1:N/2-1]'; % Index
#BS T lz t = n.*dt;
L31|\x] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
D$x_o!JT w=2*pi*n./T;
zL J/5& g1=-i*ww./2;
3 g6j?yYqb g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
y8DhOlewQ g3=-i*ww./2;
jQ)T6 7 P1=0;
+}a ]GTBgA P2=0;
1</kTm/Qa P3=1;
.(WQYOMl0 P=0;
%!1Q P[}K for m1=1:M1
}C|dyyr p=0.032*m1; %input amplitude
B2O} 1. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
!3ctB3eJ s1=s10;
-!
K-Htb- s20=0.*s10; %input in waveguide 2
[VWUqlNt> s30=0.*s10; %input in waveguide 3
kTvd+TP4 s2=s20;
Lup kr xV s3=s30;
,f&5pw
= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
7t*"%]o %energy in waveguide 1
1w&!H ]%{ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
9rA=pH%<>B %energy in waveguide 2
_H/8_[xk p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
'f?$"U JF %energy in waveguide 3
S1?-I_t+] for m3 = 1:1:M3 % Start space evolution
',S'.U s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
rX1QMR7? s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
YSe.t_ K2C s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
;"m ,:5% sca1 = fftshift(fft(s1)); % Take Fourier transform
&sd}ulEg` sca2 = fftshift(fft(s2));
~T89_L sca3 = fftshift(fft(s3));
P $-X)c$& sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
n9xAPB } sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
,zT y?OQ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Zg .& V s3 = ifft(fftshift(sc3));
[r[ =W! s2 = ifft(fftshift(sc2)); % Return to physical space
Pp5 ^ @A s1 = ifft(fftshift(sc1));
@ W9x$ end
xagBORg+Bd p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
a 7,C>%I p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
z.I9wQ]X[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
pLzk P1=[P1 p1/p10];
Kc^;vT >3 P2=[P2 p2/p10];
*VZ5B<I c P3=[P3 p3/p10];
oo.2Dn6z P=[P p*p];
0a "c2J end
Xqm::1(-( figure(1)
I2nhqJy^ plot(P,P1, P,P2, P,P3);
D= h)& L;f!.FX# 转自：
http://blog.163.com/opto_wang/
