计算脉冲在非线性耦合器中演化的Matlab 程序 {j%'EJ5 ;eYm+e^?. % This Matlab script file solves the coupled nonlinear Schrodinger equations of
aw
z(W > % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
i
v7^ ! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
q V^Z@N+, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&S/@i|_ +Tnn'^4 %fid=fopen('e21.dat','w');
`Pa z N = 128; % Number of Fourier modes (Time domain sampling points)
GAK!qLy 9 M1 =3000; % Total number of space steps
sTx23RJ9 J =100; % Steps between output of space
R"NR-iU T =10; % length of time windows:T*T0
k WVa HZr T0=0.1; % input pulse width
.!yXto: MN1=0; % initial value for the space output location
K.k%Tg [ ~ dt = T/N; % time step
Bf37/kkf( n = [-N/2:1:N/2-1]'; % Index
$j? zEz t = n.*dt;
SJ(<u2J] u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
+AGI)uQQ u20=u10.*0.0; % input to waveguide 2
N#(p_7M u1=u10; u2=u20;
V/C":!; U1 = u1;
)erI3?k U2 = u2; % Compute initial condition; save it in U
b 4o`eR ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
M`6rI w=2*pi*n./T;
B(+J?0Dj g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
.wj?}Fr?97 L=4; % length of evoluation to compare with S. Trillo's paper
^Ec);Z dz=L/M1; % space step, make sure nonlinear<0.05
6M({T2e for m1 = 1:1:M1 % Start space evolution
0s >ozAJ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D?yiK=:08` u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
UVND1XV^f ca1 = fftshift(fft(u1)); % Take Fourier transform
=ELl86=CG ca2 = fftshift(fft(u2));
-:mT8'.F - c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
WvV!F?uqZ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
8UY[ $lc u2 = ifft(fftshift(c2)); % Return to physical space
Aj9<4N u1 = ifft(fftshift(c1));
AUZ^XiK if rem(m1,J) == 0 % Save output every J steps.
vumA W* U1 = [U1 u1]; % put solutions in U array
$9LI v U2=[U2 u2];
3[*E>:)qh MN1=[MN1 m1];
;onhc*{lv z1=dz*MN1'; % output location
qX,T X
3 end
AmSrc. end
X8l|^ [2F hg=abs(U1').*abs(U1'); % for data write to excel
Qq,w6ekr ha=[z1 hg]; % for data write to excel
$CT 2E t1=[0 t'];
oT=XCa5 hh=[t1' ha']; % for data write to excel file
){~]-VK %dlmwrite('aa',hh,'\t'); % save data in the excel format
U]!~C 1cmw figure(1)
Q]n a_'_ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
B !>hHQ2
figure(2)
{,kA'Px) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
M$@Do nx t@hE}R 非线性超快脉冲耦合的数值方法的Matlab程序 >M `ryM2=D NT3Ti
?J, 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。
?< 3wks|C 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
$F^p5EXkc6 ~hx__^]d ak_&\'P 6 ;JlA}) % This Matlab script file solves the nonlinear Schrodinger equations
aaa6R|>0 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
_Vv XE572 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B)^uGS W % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
(g>8!Gl {`X O3 C=1;
R]Iv?) Y M1=120, % integer for amplitude
5;:P^[cH9 M3=5000; % integer for length of coupler
VB(S]N)F^ N = 512; % Number of Fourier modes (Time domain sampling points)
y9/x:n&] dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
AE UXdMo T =40; % length of time:T*T0.
5!tiu4LU dt = T/N; % time step
},tN{() n = [-N/2:1:N/2-1]'; % Index
#.Q8q t = n.*dt;
-FxE!K ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1-!q,q w=2*pi*n./T;
,m"0Bu2 g1=-i*ww./2;
-c_}^j g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
CVk.Ez6 g3=-i*ww./2;
O4l] Q P1=0;
ZSs)AB_Pe/ P2=0;
()[j<KX{. P3=1;
948 lL& P=0;
=Su~i Oa for m1=1:M1
F4o)6+YM p=0.032*m1; %input amplitude
aC2cyUuaN s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
| mHxkd s1=s10;
7QnQ=gu s20=0.*s10; %input in waveguide 2
i,3[0* ge s30=0.*s10; %input in waveguide 3
-n>JlfCd2 s2=s20;
0q4E^}iR s3=s30;
j$%uip{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
FF} A_ZFY %energy in waveguide 1
x{|`q9V~ N p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
{(00,6M)i %energy in waveguide 2
K0YUN^St p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
. #7B10 %energy in waveguide 3
<E&[sQ |3 for m3 = 1:1:M3 % Start space evolution
#<4/ * < 5 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
E <O :
s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Ho_ 2zx:8b s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,xhB sca1 = fftshift(fft(s1)); % Take Fourier transform
jO5R0^w sca2 = fftshift(fft(s2));
$$GmundqB sca3 = fftshift(fft(s3));
X~#jx(0_ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
7?[{/`k~? sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
0Na/3cz|zg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
XH"-sZt s3 = ifft(fftshift(sc3));
@a[Y[F S s2 = ifft(fftshift(sc2)); % Return to physical space
N.l\2S} s1 = ifft(fftshift(sc1));
qR X:e o end
8*-N@j8 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
sy
s6 V? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l7p*: :(9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
uyfH;9L5$ P1=[P1 p1/p10];
`H#G/zOr P2=[P2 p2/p10];
4!3mS WNV P3=[P3 p3/p10];
Z: e|~# P=[P p*p];
3P&K<M#\ end
; DG&H O figure(1)
~"t33U6 plot(P,P1, P,P2, P,P3);
.&Q'aOg Cnv M>] 转自：
http://blog.163.com/opto_wang/
