计算脉冲在非线性耦合器中演化的Matlab 程序 k2<VUeW5 ; '} 1 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
(IIOKx _ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
}v0oFY$u`H % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
GZXUB0W\@) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
A37Z;/H~k B:qZh$YN %fid=fopen('e21.dat','w');
_
97F N = 128; % Number of Fourier modes (Time domain sampling points)
zJ3{!E}`v M1 =3000; % Total number of space steps
/ta-jOcRH& J =100; % Steps between output of space
hP`3Ao T =10; % length of time windows:T*T0
b&H A_G4 T0=0.1; % input pulse width
-g;iMqh# MN1=0; % initial value for the space output location
w; }P<K dt = T/N; % time step
[% |i n = [-N/2:1:N/2-1]'; % Index
,U],Wu) t = n.*dt;
3UslVj1u u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
RA>xol~xy u20=u10.*0.0; % input to waveguide 2
E:&=A 4 % u1=u10; u2=u20;
]*%0CDY6`N U1 = u1;
7$Bq.Lc#z U2 = u2; % Compute initial condition; save it in U
k
U*\Fa*E ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3PpycJ} w=2*pi*n./T;
%$`pD
I ) g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
~BrERUk L=4; % length of evoluation to compare with S. Trillo's paper
$kh Wu>b dz=L/M1; % space step, make sure nonlinear<0.05
HS ="t3 for m1 = 1:1:M1 % Start space evolution
Wl;F]_|* ( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
'r(}7>~fC u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
xo6-Y=c8 ca1 = fftshift(fft(u1)); % Take Fourier transform
S,n*1&ogj ca2 = fftshift(fft(u2));
qI^6}PB c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
DFVaZN?~
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$;@^coz9U u2 = ifft(fftshift(c2)); % Return to physical space
Dx 4?6 u1 = ifft(fftshift(c1));
(] (:0H if rem(m1,J) == 0 % Save output every J steps.
hG
uRV| ` U1 = [U1 u1]; % put solutions in U array
~>k<I:BtrT U2=[U2 u2];
&]ts*qCEL MN1=[MN1 m1];
#=OKY@z/ z1=dz*MN1'; % output location
zy end
%g kR G66 end
1bYc^(z0 hg=abs(U1').*abs(U1'); % for data write to excel
['tGc{4 ha=[z1 hg]; % for data write to excel
?`u Y*+u t1=[0 t'];
VI74{='= hh=[t1' ha']; % for data write to excel file
rNO'0Ck= %dlmwrite('aa',hh,'\t'); % save data in the excel format
QPg
QM6 figure(1)
eL0 U5># waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
vf K^^S figure(2)
SBzJQt@Hs waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ltwX- #:3ca] k 非线性超快脉冲耦合的数值方法的Matlab程序 i!*w'[G->Y g`d5OHvO o 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。
<wW#Wnc ] 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
8uP,#D<wZ #OqQD6 E<:XH j m M`q >i B % This Matlab script file solves the nonlinear Schrodinger equations
Dw j!B;AZ_ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
9 ]c2ub7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&-:ZM0Fl % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Yev ] Lp 2RFY nDN C=1;
T4]/w|?G M1=120, % integer for amplitude
:r k=(=@8` M3=5000; % integer for length of coupler
='`z N = 512; % Number of Fourier modes (Time domain sampling points)
a:r8Jzr dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-+Axa[,5= T =40; % length of time:T*T0.
EeIV6ug dt = T/N; % time step
9.{u2a\ n = [-N/2:1:N/2-1]'; % Index
}3E@]"<cVR t = n.*dt;
E/v.+m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
E2 Q[ w=2*pi*n./T;
q6bi{L@/R g1=-i*ww./2;
GbUw:I g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
R9A8)dDz g3=-i*ww./2;
IDQ@h`"B P1=0;
$sT bFY P2=0;
;PCnEs P3=1;
\T `InBbf P=0;
eee77.@y-p for m1=1:M1
(OwAhjHE p=0.032*m1; %input amplitude
wzVx16Rvc s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2&MIt(\- s1=s10;
Jr$,w7tQn@ s20=0.*s10; %input in waveguide 2
ROlef;/A s30=0.*s10; %input in waveguide 3
~b}a|K s2=s20;
NRN3*YGo s3=s30;
d[E~ }Dq3# p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
c7UmR?m %energy in waveguide 1
4[m})X2( p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
tS!Fn Qg4 %energy in waveguide 2
m5m}RWZ# p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Aslh}'$}- %energy in waveguide 3
%sxLxx_x! for m3 = 1:1:M3 % Start space evolution
sU! h^N$ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}(k#,&Fv` s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
d3-F?i
5d s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
1/X@~ sca1 = fftshift(fft(s1)); % Take Fourier transform
=r"- Pm{ sca2 = fftshift(fft(s2));
,cZhkXd
sca3 = fftshift(fft(s3));
C))5,aX sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,5!&} sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
_&V%idz!0 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2;Vss<hR4A s3 = ifft(fftshift(sc3));
vUm#^/#I s2 = ifft(fftshift(sc2)); % Return to physical space
vT/e&8w s1 = ifft(fftshift(sc1));
Z/ -9 G end
rQmDpoy = p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
jz,Mm,Gi p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=1Nz*
c p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
j/.$ (E P1=[P1 p1/p10];
p]h;M P2=[P2 p2/p10];
-#<6 P3=[P3 p3/p10];
}L
mhM P=[P p*p];
f@S n1c,Mk end
Yc~( W ue figure(1)
%Ms "LoK plot(P,P1, P,P2, P,P3);
5Ku=Xzvq O2i7w1t 转自：
http://blog.163.com/opto_wang/
