计算脉冲在非线性耦合器中演化的Matlab 程序 8U\ +b?} a&Z|3+ZA % This Matlab script file solves the coupled nonlinear Schrodinger equations of
C"0gAN % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
~Bu~?ZJmd % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
JziMjR % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Fb-NG.Z# tx5@r; %fid=fopen('e21.dat','w');
NPf,9c; N = 128; % Number of Fourier modes (Time domain sampling points)
Z39^nGO M1 =3000; % Total number of space steps
gB
kb0 J =100; % Steps between output of space
w(mn@Qc T =10; % length of time windows:T*T0
p&ow\A O T0=0.1; % input pulse width
^!kv gm<{$ MN1=0; % initial value for the space output location
drb_GT dt = T/N; % time step
7a@V2cr@ n = [-N/2:1:N/2-1]'; % Index
%iJ6;V 4 t = n.*dt;
h ]MSjC.X u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
?$r+#'asd( u20=u10.*0.0; % input to waveguide 2
U ][.ioc u1=u10; u2=u20;
HjV^6oP U1 = u1;
>n` OLHg; U2 = u2; % Compute initial condition; save it in U
Ea P#~x ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ODEy2). w=2*pi*n./T;
X)nOY* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
CQ v
[Od L=4; % length of evoluation to compare with S. Trillo's paper
%*jpQOw
dz=L/M1; % space step, make sure nonlinear<0.05
L;BYPZR for m1 = 1:1:M1 % Start space evolution
w)!(@}vd u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
RA\H?1;8C u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
n.7 $*9)# ca1 = fftshift(fft(u1)); % Take Fourier transform
y`(z_ 5ClT ca2 = fftshift(fft(u2));
:mg#&MZj< c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
d(]LRIn~1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
4@8i,q> u2 = ifft(fftshift(c2)); % Return to physical space
}i/{8Ou W u1 = ifft(fftshift(c1));
?B h} if rem(m1,J) == 0 % Save output every J steps.
v $ pA Rt U1 = [U1 u1]; % put solutions in U array
3QXGbu}:h! U2=[U2 u2];
;M'R/JlUN MN1=[MN1 m1];
kWoy%?|RRa z1=dz*MN1'; % output location
tX)]ZuEi$ end
xR aYm end
^[ id8 hg=abs(U1').*abs(U1'); % for data write to excel
x,p|n ha=[z1 hg]; % for data write to excel
kxf'_Nzy t1=[0 t'];
H;$w^Tr hh=[t1' ha']; % for data write to excel file
+;*])N%q %dlmwrite('aa',hh,'\t'); % save data in the excel format
F92n)* [ figure(1)
F htf4 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
7Y!^88,f. figure(2)
("{AY?{{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<BO|.(ys Wt4!XV 非线性超快脉冲耦合的数值方法的Matlab程序 ,xR^8G 8 G`)I _uO 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。
4vy!'r@ 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
'nCBLc8 Dn d ZZe qOu7^ Gt 2rJ<> % This Matlab script file solves the nonlinear Schrodinger equations
M8 g=t[\ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
HVk3F| ]V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
n
P 69W % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^U`[P@T 8:0l5cZE C=1;
>\>H Ryt% M1=120, % integer for amplitude
*1elUI2Rg M3=5000; % integer for length of coupler
[IHT)%>E8& N = 512; % Number of Fourier modes (Time domain sampling points)
QDgOprha dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
>\@ 6i
s T =40; % length of time:T*T0.
vn
kktD'n dt = T/N; % time step
?j $z[_K n = [-N/2:1:N/2-1]'; % Index
@c{Z?>dUc# t = n.*dt;
yJKezIL\z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9VP|a- w=2*pi*n./T;
NIYAcLa@n8 g1=-i*ww./2;
*^NC5=A(d g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
S&R~* g3=-i*ww./2;
qed;
UyN P1=0;
) W c#?K P2=0;
~ xXB
!K~C P3=1;
Xbap' /t
P=0;
YjsaTdZ!& for m1=1:M1
&[kwM3 95 p=0.032*m1; %input amplitude
nkG 6. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
^@tn+ '. s1=s10;
}~A-ELe: s20=0.*s10; %input in waveguide 2
0 "<g g5 s30=0.*s10; %input in waveguide 3
al" 1T- s2=s20;
JBg",2w |C s3=s30;
MiRMjQ2 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
-@i2]o %energy in waveguide 1
:v&GA s6H p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
QtX ->6P> %energy in waveguide 2
;GvyL>|-~ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
hz )L+ %energy in waveguide 3
(6.0gB$aTu for m3 = 1:1:M3 % Start space evolution
ss-B e s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
N5~g:([k s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
;((gmg7, s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
7OW;o mT` sca1 = fftshift(fft(s1)); % Take Fourier transform
O >'o; 0 sca2 = fftshift(fft(s2));
Q_@
Z.{ sca3 = fftshift(fft(s3));
\DfvNeF sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
q A G0t{K sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
M/B_-8B_D sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{k maMP s3 = ifft(fftshift(sc3));
.4?M.Z4[ s2 = ifft(fftshift(sc2)); % Return to physical space
G19FSLrtA s1 = ifft(fftshift(sc1));
{Y
IVHl end
;rk}\M$+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
=D 3Y
q? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
W]rXt,{ & p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
FUHa"$Bg P1=[P1 p1/p10];
=0 m[ P2=[P2 p2/p10];
3 :f5xF P3=[P3 p3/p10];
[*50Ng>P` P=[P p*p];
nY(jN D end
t CA |sN figure(1)
*d(wO l5[ plot(P,P1, P,P2, P,P3);
u8o!ncy 0w(<pNA 转自：
http://blog.163.com/opto_wang/
