计算脉冲在非线性耦合器中演化的Matlab 程序 j'uz js[ {i<L<Y(3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Z!+n/ D-1 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
6fm oI K{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5E#8F % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%N #A1 l3Qt_I)L %fid=fopen('e21.dat','w');
!ra,HkU' N = 128; % Number of Fourier modes (Time domain sampling points)
&s8vmUt M1 =3000; % Total number of space steps
03 n+kh J =100; % Steps between output of space
g8R@ol 0 T =10; % length of time windows:T*T0
#e[S+a T0=0.1; % input pulse width
?!.L#]23f MN1=0; % initial value for the space output location
);/p[Fd2] dt = T/N; % time step
782 oXyD n = [-N/2:1:N/2-1]'; % Index
Z 5V_?bm$ t = n.*dt;
B un^EJ) u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8 4lT# ^q u20=u10.*0.0; % input to waveguide 2
_ G$21=
u1=u10; u2=u20;
?>1wZ U1 = u1;
Y1;jRIOA U2 = u2; % Compute initial condition; save it in U
P\y ZcL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
v'Pb x w=2*pi*n./T;
q:1n=i Ei g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
12V-EG i L=4; % length of evoluation to compare with S. Trillo's paper
* m8{yh dz=L/M1; % space step, make sure nonlinear<0.05
L=@8Z i!2< for m1 = 1:1:M1 % Start space evolution
6o1[fr u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
+V9 (4la u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
b5#Jo2C`AJ ca1 = fftshift(fft(u1)); % Take Fourier transform
z:8ieJ)C ca2 = fftshift(fft(u2));
]*X z~Ox2 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
k]9y+WC2 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
-;O" Y?ME u2 = ifft(fftshift(c2)); % Return to physical space
"H9q%S,FH u1 = ifft(fftshift(c1));
5`6U:MDq if rem(m1,J) == 0 % Save output every J steps.
u}?|d8$h\ U1 = [U1 u1]; % put solutions in U array
. )E1|U[L U2=[U2 u2];
q26 qY5D MN1=[MN1 m1];
NE><(02qW z1=dz*MN1'; % output location
Eb8~i_B- end
!TN)6e7`
end
Ekn3ODz, hg=abs(U1').*abs(U1'); % for data write to excel
sD9OV6^{?K ha=[z1 hg]; % for data write to excel
WQ9VcCY t1=[0 t'];
On(.(7sNc hh=[t1' ha']; % for data write to excel file
Q yhu=_& %dlmwrite('aa',hh,'\t'); % save data in the excel format
Rw<O%i5/d figure(1)
xS; tmc waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y~z&8XrH figure(2)
O[$XgPM waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ltv ~Kh )=!|^M 非线性超快脉冲耦合的数值方法的Matlab程序 {*"\6 8e e35 ")z~ 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。
4WPco"xH! 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
bduHYs+rq KuF>2KX~Y [sK'jQo-[1 Rl
( +TE % This Matlab script file solves the nonlinear Schrodinger equations
TCK#bJ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
4YXp ,U % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
"$3~):o % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~lbm^S}- xiVbVr#[ C=1;
%6x3 G M1=120, % integer for amplitude
F5H]$AjW M3=5000; % integer for length of coupler
J&L#^f *d N = 512; % Number of Fourier modes (Time domain sampling points)
+E+I.}sOB dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
U^Iq]L T =40; % length of time:T*T0.
`69xR[f dt = T/N; % time step
id)J;!^;J n = [-N/2:1:N/2-1]'; % Index
D 7 7$aCt t = n.*dt;
L?(m5u~b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
u}7r\MnwK, w=2*pi*n./T;
>}r
1A g1=-i*ww./2;
N.vkM`Z g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
R8|F qBs
g3=-i*ww./2;
/S9n!H:MT P1=0;
= j@8/ P2=0;
SJ lL!<i$ P3=1;
1 ]aya( P=0;
0L \v i for m1=1:M1
9 LUk [V p=0.032*m1; %input amplitude
~2UmX' s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
]_hXg*? s1=s10;
lWFm>DiLY s20=0.*s10; %input in waveguide 2
[bEm D s30=0.*s10; %input in waveguide 3
{sUc2vR s2=s20;
5 HN,y s3=s30;
6W'2w?qj?4 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
hOe$h,E'] %energy in waveguide 1
`nL^]i p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
lAAP V %energy in waveguide 2
zTze % p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
R/&C}6G n %energy in waveguide 3
>+S* Wtm5 for m3 = 1:1:M3 % Start space evolution
;_1 > nXh s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
mZ.E;X& ,* s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nVk ]Qe s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,]=Qg n sca1 = fftshift(fft(s1)); % Take Fourier transform
TzrU |D? sca2 = fftshift(fft(s2));
X6oY-4O sca3 = fftshift(fft(s3));
*4 Kc " M sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
HgRfMiC sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
e{,[\7nF sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
e0<L^|S s3 = ifft(fftshift(sc3));
DO ?
bJ01 s2 = ifft(fftshift(sc2)); % Return to physical space
u_ S>`I s1 = ifft(fftshift(sc1));
NAf u $7 end
uzL IllVX* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
|9
4xRC p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~wd~57i@ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
mW U*}-M P1=[P1 p1/p10];
(ZEDDV2 P2=[P2 p2/p10];
Zx,a j P3=[P3 p3/p10];
+,}CuF P=[P p*p];
~ {s7(^ P end
]TKM.[[ figure(1)
h9 3 plot(P,P1, P,P2, P,P3);
e7gWz~ I\ y>I?X 转自：
http://blog.163.com/opto_wang/
