计算脉冲在非线性耦合器中演化的Matlab 程序 2& l~8, 8 3wa{m: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
]D;X"2I2'b % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
t:G6 7^<3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^s p+ sr : % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
VY5/C;0^h 1c}
%_Z/ %fid=fopen('e21.dat','w');
[l2 ds: N = 128; % Number of Fourier modes (Time domain sampling points)
.*s1d)\: M1 =3000; % Total number of space steps
Ol~j q;75 J =100; % Steps between output of space
OA_Bz" T =10; % length of time windows:T*T0
?m?DAd~ZY T0=0.1; % input pulse width
bI,gNVN= MN1=0; % initial value for the space output location
*c+Kqz- dt = T/N; % time step
/{';\?w n = [-N/2:1:N/2-1]'; % Index
2 %'iTXF t = n.*dt;
^$7Lmd.qI u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-4&SYC w u20=u10.*0.0; % input to waveguide 2
L"akV,w4p u1=u10; u2=u20;
pUs s_3 U1 = u1;
^hhJ6E_W U2 = u2; % Compute initial condition; save it in U
&ESE?{of) ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rVx%"_'*- w=2*pi*n./T;
+|N! (H g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|[ tlR`A $ L=4; % length of evoluation to compare with S. Trillo's paper
RY(\/W#$ dz=L/M1; % space step, make sure nonlinear<0.05
hDp
-,ag{ for m1 = 1:1:M1 % Start space evolution
,&;#$ b5 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$\|$ ekil4 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
?X1vU0 c
ca1 = fftshift(fft(u1)); % Take Fourier transform
@"9^U_Qf1z ca2 = fftshift(fft(u2));
4|Dxyb>pS c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
tTT./-*0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
MjAF&bD^ u2 = ifft(fftshift(c2)); % Return to physical space
{jX
h/` u1 = ifft(fftshift(c1));
o!`.LL% if rem(m1,J) == 0 % Save output every J steps.
ckXJ9 > U1 = [U1 u1]; % put solutions in U array
<m"yPi3TY U2=[U2 u2];
q^
{ Xn-G MN1=[MN1 m1];
dsKEWZ
= z1=dz*MN1'; % output location
#HD$=ECcw end
30(O]@f~ end
6OJ`R.DM` hg=abs(U1').*abs(U1'); % for data write to excel
W_N Qi ha=[z1 hg]; % for data write to excel
NJG- ~ w t1=[0 t'];
AR i_ m hh=[t1' ha']; % for data write to excel file
}xx[=t=nUf %dlmwrite('aa',hh,'\t'); % save data in the excel format
9Z,vpTE figure(1)
#:{Bd8PS waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
p m+_s]s, figure(2)
b]v.jgD waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
}|rnyYA
o *2TH2 非线性超快脉冲耦合的数值方法的Matlab程序 ~V Z)LQ'7 8}3dwr;- 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
i]:T{2 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_ECWS fZ aVI/x5p~ ?\dY! @| :_ ? % This Matlab script file solves the nonlinear Schrodinger equations
)GDP?Nc<Ik % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
HhN;&67~Z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w(O/mUDX % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U^tr Z]) %oas IiO C=1;
<0OZ9?,dm M1=120, % integer for amplitude
eHCLENLmB M3=5000; % integer for length of coupler
M),i4a?2 N = 512; % Number of Fourier modes (Time domain sampling points)
CA7 ZoMB# dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
@EZ@X/8{& T =40; % length of time:T*T0.
1$Rua dt = T/N; % time step
D2 o,K&V n = [-N/2:1:N/2-1]'; % Index
1ID0 'j$ t = n.*dt;
$;1#gq% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Zgt:ZO w=2*pi*n./T;
) -+u8# g1=-i*ww./2;
29DYL g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
X}.y-X#v5J g3=-i*ww./2;
T/DKT 1P- P1=0;
rPoPs@CBD P2=0;
l +BJh1^ P3=1;
iUl5yq P=0;
8 RJXY:% for m1=1:M1
0|g|k7c{rF p=0.032*m1; %input amplitude
( H/JB\~r s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
3+mC96wN s1=s10;
3.M<A Te^ s20=0.*s10; %input in waveguide 2
lP *_dt 9 s30=0.*s10; %input in waveguide 3
%$/t`'&o- s2=s20;
7%C6hEP/*W s3=s30;
rQ -pD p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
',L>UIXw %energy in waveguide 1
E/mp.f2! p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
5gnNgt~ %energy in waveguide 2
Z?k4Kb p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
!Z978Aub3& %energy in waveguide 3
j4j %r( for m3 = 1:1:M3 % Start space evolution
uMl.}t2uYu s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
UR|UGldt_T s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
J-t5kU;L{ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
= h,6/cs sca1 = fftshift(fft(s1)); % Take Fourier transform
fHTqLYd- sca2 = fftshift(fft(s2));
tZlz0BY! sca3 = fftshift(fft(s3));
h|h-< G?> sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
LaL .C^K sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
v a \ 5
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
DC4,*a~ s3 = ifft(fftshift(sc3));
]O'dwC s2 = ifft(fftshift(sc2)); % Return to physical space
nN!/ s1 = ifft(fftshift(sc1));
\ . H X7v end
VT1Nd p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
t2Dx$vT*& p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
`2 X~ 3im p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
E)liuu! qI P1=[P1 p1/p10];
'EF Sr!+ P2=[P2 p2/p10];
K7 >Z)21 P3=[P3 p3/p10];
<Z %iP{ P=[P p*p];
ZS 51QB end
C2RR(n=N^ figure(1)
!e?;f=1+E plot(P,P1, P,P2, P,P3);
jQjtO"\JG N yT|=`; 转自：
http://blog.163.com/opto_wang/
