计算脉冲在非线性耦合器中演化的Matlab 程序 }uaFmXy3 {|<r7K1< % This Matlab script file solves the coupled nonlinear Schrodinger equations of
%yKcp5_ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?5lO1( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5"!K8
N
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
E#tfCM6 yH s9J1S f %fid=fopen('e21.dat','w');
y L XIjR N = 128; % Number of Fourier modes (Time domain sampling points)
%t1Z!xv_ M1 =3000; % Total number of space steps
Y:Lkh>S1Q J =100; % Steps between output of space
]w]BKpU= T =10; % length of time windows:T*T0
H|j]uLZ T0=0.1; % input pulse width
? ;5/"/i MN1=0; % initial value for the space output location
}7{( o- dt = T/N; % time step
:nqDX n = [-N/2:1:N/2-1]'; % Index
|FlB# t = n.*dt;
=Y!.0)t;* u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+:70vZc:V@ u20=u10.*0.0; % input to waveguide 2
ND=JpVkvZ? u1=u10; u2=u20;
iny/K/5bf U1 = u1;
~=HPqe8 U2 = u2; % Compute initial condition; save it in U
_Fv 6S}~Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.ty2! . w=2*pi*n./T;
(8o;Cm g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
J?Q@f
L=4; % length of evoluation to compare with S. Trillo's paper
sH1 ucZ>9Y dz=L/M1; % space step, make sure nonlinear<0.05
3&c'3y:b for m1 = 1:1:M1 % Start space evolution
eD NY|}$}v u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
3]'h (C u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
6wq%4RI0 ca1 = fftshift(fft(u1)); % Take Fourier transform
>nK ( ca2 = fftshift(fft(u2));
i^IL o,Q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
oHS Di c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
P&Xy6@%[Z u2 = ifft(fftshift(c2)); % Return to physical space
!rqs!-cCQ u1 = ifft(fftshift(c1));
R&P^rrC@B5 if rem(m1,J) == 0 % Save output every J steps.
9M|#X1r{%{ U1 = [U1 u1]; % put solutions in U array
3y:),;|5 U2=[U2 u2];
[6.<# _~{ MN1=[MN1 m1];
) 54cG z1=dz*MN1'; % output location
7pep\ end
z?`7g%Z?{ end
KiC,O7& < hg=abs(U1').*abs(U1'); % for data write to excel
L-q)48+^k ha=[z1 hg]; % for data write to excel
Z.aeE*Hs$ t1=[0 t'];
v6x jLP;O hh=[t1' ha']; % for data write to excel file
ci 22fw0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
~:_10g]r figure(1)
`r\/5|M waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
SwrzW'%A figure(2)
fbah~[5} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
QT1oU P#* q_> =| b 非线性超快脉冲耦合的数值方法的Matlab程序 4m~p(r 7( LB} 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。
we*E}U4 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
%/s+-j@s: P{2ED1T\ w5Ucj*A\ XwU1CejP0 % This Matlab script file solves the nonlinear Schrodinger equations
w0<1=;_% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
<
r b5' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>7W 8_6sC< % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/B{c L`< Ac
+fL C=1;
~"R;p}5 " M1=120, % integer for amplitude
O#vIn } M3=5000; % integer for length of coupler
/" &Jf}r N = 512; % Number of Fourier modes (Time domain sampling points)
`j.-hy>s dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-b
)~ T =40; % length of time:T*T0.
Fj <a;oV dt = T/N; % time step
v:9Vp{ ) n = [-N/2:1:N/2-1]'; % Index
{qH+S/ t = n.*dt;
bD 1IY1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
zj1_# =] w=2*pi*n./T;
+]C|y ,r g1=-i*ww./2;
:pP l|" g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
= o1 &.v2j g3=-i*ww./2;
*zX^Sg-[ P1=0;
dFnu&u" P2=0;
;,B $lgF P3=1;
vFgnb WxG P=0;
x$b Cbg for m1=1:M1
!T]bz+ p=0.032*m1; %input amplitude
9Fv VM9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Hwm] l`E] s1=s10;
c2f bqM~ s20=0.*s10; %input in waveguide 2
j_2yTz"G- s30=0.*s10; %input in waveguide 3
~^pV>>LX| s2=s20;
*# 2]`G) s3=s30;
pSlosv(6 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
a jyuk@ %energy in waveguide 1
xxC2F:Q?U p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Xeo2 < @[ %energy in waveguide 2
NU?05sF p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
2wki21oY %energy in waveguide 3
& e~g}7 for m3 = 1:1:M3 % Start space evolution
3BWYSJ| s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
PQFr4EY?i s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
z 7 'C;I s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ES&"zjr$ sca1 = fftshift(fft(s1)); % Take Fourier transform
^saH^kg1" sca2 = fftshift(fft(s2));
/MUa
b*h sca3 = fftshift(fft(s3));
nVVQ^i}`G sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Q-M"+ HO sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
x^ruPiH sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
.W)%*~ O!; s3 = ifft(fftshift(sc3));
P,/=c(5\} s2 = ifft(fftshift(sc2)); % Return to physical space
.Q^8 _'ZG s1 = ifft(fftshift(sc1));
r#CQCq end
P5^<c\Mr,Y p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
}b5If7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Z} Ld!Byz p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
y6*9, CF P1=[P1 p1/p10];
vUU)zZB ~ P2=[P2 p2/p10];
} JeP Emj P3=[P3 p3/p10];
- 'iV-]< P=[P p*p];
m $X0O_*A end
lQSKY}h figure(1)
k;bdzcMkQ plot(P,P1, P,P2, P,P3);
{!`0 i |6d0,muN 转自：
http://blog.163.com/opto_wang/
