计算脉冲在非线性耦合器中演化的Matlab 程序 .r\|9 *j< u{%dm5 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
>h{) 7Hv % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
D&!c7_ ^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u Xo? j kV 9$W0 %fid=fopen('e21.dat','w');
{B7${AE N = 128; % Number of Fourier modes (Time domain sampling points)
|wGmu&fY M1 =3000; % Total number of space steps
7&3 J =100; % Steps between output of space
bO+]1nZ. T =10; % length of time windows:T*T0
aXh~w<5F T0=0.1; % input pulse width
}}u16x}*n MN1=0; % initial value for the space output location
;2[ o>73F dt = T/N; % time step
XS=f>e1<W n = [-N/2:1:N/2-1]'; % Index
/|>?!; t = n.*dt;
#R*7y% cO u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
jhH&} d9 u20=u10.*0.0; % input to waveguide 2
Ox9M ![fC u1=u10; u2=u20;
}j;G `mV2 U1 = u1;
tX~ *.W: U2 = u2; % Compute initial condition; save it in U
_t?# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_@OS,A w=2*pi*n./T;
=hi{J
M g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=buarxk L=4; % length of evoluation to compare with S. Trillo's paper
rk
&ME#<r dz=L/M1; % space step, make sure nonlinear<0.05
V)A7q9Bum for m1 = 1:1:M1 % Start space evolution
IZ<Et/3H u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
4)?s? + u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
8, -U`. ca1 = fftshift(fft(u1)); % Take Fourier transform
]\ t20R{z ca2 = fftshift(fft(u2));
9xaieR c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
gubw&W c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
pMd!Jl#(N
u2 = ifft(fftshift(c2)); % Return to physical space
D-LQQ{!D5 u1 = ifft(fftshift(c1));
eL88lV]I if rem(m1,J) == 0 % Save output every J steps.
uSUog+i U1 = [U1 u1]; % put solutions in U array
(/KeGgkhv U2=[U2 u2];
~Z' /b|x<3 MN1=[MN1 m1];
{'sp8:$a z1=dz*MN1'; % output location
TlD^ EJG end
qyzH*#d=Cf end
\1<8'at hg=abs(U1').*abs(U1'); % for data write to excel
[xo-ZDIoG ha=[z1 hg]; % for data write to excel
WOi+y t1=[0 t'];
3v ~[kVhoG hh=[t1' ha']; % for data write to excel file
17#t 7Y k %dlmwrite('aa',hh,'\t'); % save data in the excel format
Nr?CZFN# figure(1)
M}]4tAyT waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
c!N#nt_< figure(2)
l'7' G$v waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
r6vI6|1 W:hTRq 非线性超快脉冲耦合的数值方法的Matlab程序 lJdrrR)wg '0v]?mM 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。
M)3'\x : 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
zMh`Uqid |f1Rh B <Vl`EfA( cCs@[D#O1 % This Matlab script file solves the nonlinear Schrodinger equations
P"+R:O\!g % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
o: `^1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8>`8p0I$+
gts09{"} Y C=1;
Kx02 2rgDU M1=120, % integer for amplitude
}Z)YK}_1 M3=5000; % integer for length of coupler
L@.Trso N = 512; % Number of Fourier modes (Time domain sampling points)
gfiFRwC`v dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`NfwW: T =40; % length of time:T*T0.
f.0HIc dt = T/N; % time step
<Ok7 -:OxA n = [-N/2:1:N/2-1]'; % Index
Q5]rc`}
5 t = n.*dt;
U/ax`_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mbH My[R w=2*pi*n./T;
F`>qg2wO g1=-i*ww./2;
~( :$c3\ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
@(IA:6 GN g3=-i*ww./2;
5t|$Yt[ P1=0;
\+Y5b} P2=0;
-$I$z o P3=1;
z{/#/,V5D4 P=0;
KQ0f2? for m1=1:M1
F~/~_9RJ p=0.032*m1; %input amplitude
mR~S$6cc s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
W9]0X
s1=s10;
D;z!C
ys s20=0.*s10; %input in waveguide 2
}(oWXwFb&W s30=0.*s10; %input in waveguide 3
|h6, .#n s2=s20;
|@VhR(^O$ s3=s30;
pZ]&M@Ijp p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=&PO_t5) z %energy in waveguide 1
JOyM#g9-? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
!Ej?9LHo %energy in waveguide 2
*VaQ\]:d p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(:R5"|]@<x %energy in waveguide 3
8 !
/ue.T for m3 = 1:1:M3 % Start space evolution
^4xl4nbx s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
GC|V>| tz# s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
n`! 6EaD s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Wu/:ES)C sca1 = fftshift(fft(s1)); % Take Fourier transform
!wC(
]Y sca2 = fftshift(fft(s2));
,+X:# $ sca3 = fftshift(fft(s3));
-s\R2_( sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
&'X gf!x sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
l ;@bs sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i=&]%T6Qk s3 = ifft(fftshift(sc3));
{asq[;] s2 = ifft(fftshift(sc2)); % Return to physical space
b5? k gY s1 = ifft(fftshift(sc1));
fcy4?SQ.<i end
;zd.KaS p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\+&)9 !K p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
5mZwg(si p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
'j! n
P1=[P1 p1/p10];
s[VYd:}se P2=[P2 p2/p10];
!_oR/) P3=[P3 p3/p10];
J&B5Ll
P=[P p*p];
@z:E]O} end
&8I*N6p:%/ figure(1)
,$ U~<Zd plot(P,P1, P,P2, P,P3);
uo ;m W$W w/mcl+ 转自：
http://blog.163.com/opto_wang/
