计算脉冲在非线性耦合器中演化的Matlab 程序 - o$S= `9B xDp]I % This Matlab script file solves the coupled nonlinear Schrodinger equations of
pMM-LY7%{ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
H6 ( ~6Bp5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
'\ H {Y[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?u` ?_us lb2m Wsg" %fid=fopen('e21.dat','w');
,G S8Gu N = 128; % Number of Fourier modes (Time domain sampling points)
\K9 XG/XIx M1 =3000; % Total number of space steps
oOy@X =cw J =100; % Steps between output of space
)p4o4 aM T =10; % length of time windows:T*T0
^ ]SS\=7 T0=0.1; % input pulse width
V=I au_ MN1=0; % initial value for the space output location
&_HS rU dt = T/N; % time step
=\e}fyuK n = [-N/2:1:N/2-1]'; % Index
[Maon.t!l t = n.*dt;
7=0uG u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
T D].*9 u20=u10.*0.0; % input to waveguide 2
FjRJSMwO, u1=u10; u2=u20;
(P~Jzp9u U1 = u1;
Wz nz U2 = u2; % Compute initial condition; save it in U
38b%km# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Qzw ~\KY: w=2*pi*n./T;
*E+2E ^B g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
+ _rjA_ L=4; % length of evoluation to compare with S. Trillo's paper
GeWB "(t dz=L/M1; % space step, make sure nonlinear<0.05
> ~ _y\ for m1 = 1:1:M1 % Start space evolution
9E)*X u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
+2O('}t u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
} >b4s!k, ca1 = fftshift(fft(u1)); % Take Fourier transform
d%Jl9!u ca2 = fftshift(fft(u2));
^LaI{UDw%h c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
'Sppm;? c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
5s8S;Pb]< u2 = ifft(fftshift(c2)); % Return to physical space
A3*ti!X<6 u1 = ifft(fftshift(c1));
*>V 6KW if rem(m1,J) == 0 % Save output every J steps.
$"0 t 1 U1 = [U1 u1]; % put solutions in U array
U2 < *BRJ U2=[U2 u2];
9m0`;~! MN1=[MN1 m1];
&eQzfx=|km z1=dz*MN1'; % output location
x 9xb4ZW end
bI TOA end
{/uBZ( hg=abs(U1').*abs(U1'); % for data write to excel
n{d} ]V@ ha=[z1 hg]; % for data write to excel
0{F"b'h t1=[0 t'];
e
&^BPzg hh=[t1' ha']; % for data write to excel file
}X$vriW %dlmwrite('aa',hh,'\t'); % save data in the excel format
fO [X<|9 figure(1)
3H%R`ha waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ly I
rO"o figure(2)
@;qC % +^ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
! CtY.Lp {R
`IA|T#k 非线性超快脉冲耦合的数值方法的Matlab程序 Wy@Z)z? /D` M? nD7 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。
Ev0GAc1 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
$_k'!/ 5 Wa
#,> gGw6c" FRQ y$r^UjJEO % This Matlab script file solves the nonlinear Schrodinger equations
)&1yt4
x6% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
nT` NfN % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;!, ]}2w*X % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6?Q&>V26Y Fe.Y4\xz C=1;
> C+0LF`U M1=120, % integer for amplitude
yiQke M3=5000; % integer for length of coupler
K~<p D:s N = 512; % Number of Fourier modes (Time domain sampling points)
Qc;`n ck dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
_DMj )enH" T =40; % length of time:T*T0.
P{)H7B> dt = T/N; % time step
SW (7!` n = [-N/2:1:N/2-1]'; % Index
7IBm(# t = n.*dt;
,r{*o6 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
n}
GIf& w=2*pi*n./T;
AJ2Xq*fk g1=-i*ww./2;
_bqiS]: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Fly@"W4a g3=-i*ww./2;
0(Y$x g P1=0;
&YO5N4X~o P2=0;
HQ7-,!XO P3=1;
j$T2ff6 P=0;
MVjc.^ for m1=1:M1
LnZ*,>1 Z p=0.032*m1; %input amplitude
-Hh$3U v s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
}1TfKS]m> s1=s10;
D4s*J21)D s20=0.*s10; %input in waveguide 2
?Ee?Ol?i2 s30=0.*s10; %input in waveguide 3
'Vy$d<@s[ s2=s20;
fbB(W E+ s3=s30;
/AJ ^wY p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
t"2WJ-1k } %energy in waveguide 1
<3P?rcd,5K p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
7$x@;%xd %energy in waveguide 2
5U|f"3&8 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
ZgtW %energy in waveguide 3
\>cZ = for m3 = 1:1:M3 % Start space evolution
lcJ`OLG s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
a: iIfdd4' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
3Aa j+=]W s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
S#jH2fRo sca1 = fftshift(fft(s1)); % Take Fourier transform
}n 6BI}n sca2 = fftshift(fft(s2));
zVxiCyU sca3 = fftshift(fft(s3));
x?:WR*5w sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
o1Mb HBb sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Br]VCp sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
~IE:i-K z s3 = ifft(fftshift(sc3));
o|] xj' s2 = ifft(fftshift(sc2)); % Return to physical space
aC]~ s1 = ifft(fftshift(sc1));
<$UMMA end
s? ~Abj_ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!aa^kcEjnL p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
RduA0@g0 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
i= ~HXr} P1=[P1 p1/p10];
zq4,%$y8| P2=[P2 p2/p10];
7*'_& 0 P3=[P3 p3/p10];
3tnY K& P=[P p*p];
W} Nd3 end
&wNN| fH figure(1)
Zx}=c4I(y plot(P,P1, P,P2, P,P3);
1Na CGD" IZJV6clM 转自：
http://blog.163.com/opto_wang/
