计算脉冲在非线性耦合器中演化的Matlab 程序 &s}sA +w Zos .W S# % This Matlab script file solves the coupled nonlinear Schrodinger equations of
-z J V(` % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
*q,nAL s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
m;rr 7{7X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
edcz%IOM( L>g6
9D ! %fid=fopen('e21.dat','w');
)CE]s)6+2 N = 128; % Number of Fourier modes (Time domain sampling points)
5bXpj86mY M1 =3000; % Total number of space steps
LH+ Bu%s J =100; % Steps between output of space
>?ar T =10; % length of time windows:T*T0
L >"O[ @ T0=0.1; % input pulse width
??P\v0E MN1=0; % initial value for the space output location
: *[mvF dt = T/N; % time step
5Uy *^C7M^ n = [-N/2:1:N/2-1]'; % Index
.{? ; #Cdn t = n.*dt;
"x$L 2>9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Q x|HvT2P u20=u10.*0.0; % input to waveguide 2
5%QYe]D u1=u10; u2=u20;
!T:7xEr U1 = u1;
=?+w5oI0 U2 = u2; % Compute initial condition; save it in U
qLxcr/fK ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m*jE\+)=^ w=2*pi*n./T;
B=^M& { g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
*>zOWocxD L=4; % length of evoluation to compare with S. Trillo's paper
K8-1?-W dz=L/M1; % space step, make sure nonlinear<0.05
eNi#% ?=WB for m1 = 1:1:M1 % Start space evolution
G,P
k3>I' u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
&FOq c u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Lk$Mfm5"M ca1 = fftshift(fft(u1)); % Take Fourier transform
mC\<fo-u ca2 = fftshift(fft(u2));
gp 11/ . c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
;@gI*i
N" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
bJ"2|VNH( u2 = ifft(fftshift(c2)); % Return to physical space
MNTVG&h u1 = ifft(fftshift(c1));
NRP) 'E if rem(m1,J) == 0 % Save output every J steps.
"%dENK U1 = [U1 u1]; % put solutions in U array
L7GNcV]c U2=[U2 u2];
}2*qv4},! MN1=[MN1 m1];
" 5 FP$o R z1=dz*MN1'; % output location
^qBm%R( end
|? ^N @ end
.=G3wox3 hg=abs(U1').*abs(U1'); % for data write to excel
Z[Iej:o5 ha=[z1 hg]; % for data write to excel
aL;zN%Tw t1=[0 t'];
Ge?DD,a c hh=[t1' ha']; % for data write to excel file
9fTl 6?x %dlmwrite('aa',hh,'\t'); % save data in the excel format
4, Vx3QFZ figure(1)
edpR x"_ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=^*EM<WG) figure(2)
H=WB6~8) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
iK1{SgXrFI 47*2QL^zj 非线性超快脉冲耦合的数值方法的Matlab程序 B>d49(jy 5S&Qj7kr 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ouo IbA9X Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fwzyCbks [9~ EH8 7TypzgXNe 7J$rA .tu % This Matlab script file solves the nonlinear Schrodinger equations
d_Zj W % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'
Gx\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
P@5-3]m= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Y Kp@ n8A G\k & s F C=1;
3^q9ll7Op M1=120, % integer for amplitude
.) ,9a , M3=5000; % integer for length of coupler
'h~IbP N = 512; % Number of Fourier modes (Time domain sampling points)
eW3?3l`fvt dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
\7xc*v [ T =40; % length of time:T*T0.
(~F}O dt = T/N; % time step
J?Q@f
n = [-N/2:1:N/2-1]'; % Index
sH1 ucZ>9Y t = n.*dt;
3&c'3y:b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
eD NY|}$}v w=2*pi*n./T;
\ E5kpm g1=-i*ww./2;
{LqYb:/C5U g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
4 PU@W o g3=-i*ww./2;
& n83 >Q P1=0;
!&@t P2=0;
" ~6&rt P3=1;
ix?Z :pIS0 P=0;
&lzCRRnvt for m1=1:M1
?aTC+\= p=0.032*m1; %input amplitude
VRY@}>W' s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ab)ckRC s1=s10;
Qch'C0u s20=0.*s10; %input in waveguide 2
6 9uDc s30=0.*s10; %input in waveguide 3
#Ak9f-pf s2=s20;
|r+hj<K s3=s30;
PT&qys 2k p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
XJS^{=/ %energy in waveguide 1
juM~X 5b p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Sv>CVp* %energy in waveguide 2
!@ AnwV] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
t0:~BYXu %energy in waveguide 3
=ty{ugM< for m3 = 1:1:M3 % Start space evolution
,~l4-x., s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
bsI?=lO s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
-I#<?=0B s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
wn<k "6x sca1 = fftshift(fft(s1)); % Take Fourier transform
%,Y^Tp sca2 = fftshift(fft(s2));
S|yDGT 1 sca3 = fftshift(fft(s3));
W7~OU(}[` sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
}ri7@ HCY4 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
NcSi %] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
6O l)SQE, s3 = ifft(fftshift(sc3));
%5Elj<eHZ s2 = ifft(fftshift(sc2)); % Return to physical space
$Nj'_G\} s1 = ifft(fftshift(sc1));
oVfRp.a end
t`V U< p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$"Ci{iE p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
|*]<*qnZt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
HGj[\kU ~ P1=[P1 p1/p10];
poi39B/Vt P2=[P2 p2/p10];
kCoEdQ_ P3=[P3 p3/p10];
\[B#dw# P=[P p*p];
BBl9<ne$ end
akgvV~5 figure(1)
SvQj'5~< plot(P,P1, P,P2, P,P3);
H3ob
8+J ET6}V"UD 转自：
http://blog.163.com/opto_wang/
