计算脉冲在非线性耦合器中演化的Matlab 程序 |V Bt:dd< 3[YG
BM( % This Matlab script file solves the coupled nonlinear Schrodinger equations of
=kjKK % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\iuR +I % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
zC?' Qiuh* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_Cmmx`ln tcD7OC:"6 %fid=fopen('e21.dat','w');
(m ~>W"x/ N = 128; % Number of Fourier modes (Time domain sampling points)
88g3<& M1 =3000; % Total number of space steps
jk Aj YR . J =100; % Steps between output of space
S$6|K Y u T =10; % length of time windows:T*T0
D!<F^mtl T0=0.1; % input pulse width
`zd,^.i5~ MN1=0; % initial value for the space output location
|.<_$[v[x dt = T/N; % time step
(I[_}l n = [-N/2:1:N/2-1]'; % Index
a:kAo0@":j t = n.*dt;
*Rgr4-eS u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xEb>6+-F@ u20=u10.*0.0; % input to waveguide 2
)H 8_.]| u1=u10; u2=u20;
h<9 s&
p U1 = u1;
pu-HEv}]a| U2 = u2; % Compute initial condition; save it in U
j]u!;] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4>JSZ6i#n w=2*pi*n./T;
E
C?}iP g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F' bwXb** L=4; % length of evoluation to compare with S. Trillo's paper
dbp \tWaW dz=L/M1; % space step, make sure nonlinear<0.05
!`69.v for m1 = 1:1:M1 % Start space evolution
E$ d #4x u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
+C( -f u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
YEL0h0gn ca1 = fftshift(fft(u1)); % Take Fourier transform
L*@`i ]jl ca2 = fftshift(fft(u2));
?Oyo /?/ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%xt9k9=vZ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
LC%o coc u2 = ifft(fftshift(c2)); % Return to physical space
|23F@s1 u1 = ifft(fftshift(c1));
fr17|#L+s if rem(m1,J) == 0 % Save output every J steps.
j\2Qe %d U1 = [U1 u1]; % put solutions in U array
2qM iX|Y U2=[U2 u2];
#M,&g{ MN1=[MN1 m1];
F%OP,>zl z1=dz*MN1'; % output location
0w?da~ end
tKbxC>w end
'Wlbh:=$ hg=abs(U1').*abs(U1'); % for data write to excel
!fh (k ha=[z1 hg]; % for data write to excel
F O! Td t1=[0 t'];
bA;OphO( hh=[t1' ha']; % for data write to excel file
X! d-"[ %dlmwrite('aa',hh,'\t'); % save data in the excel format
N*Y[[ N( figure(1)
+m=b
"g waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
$)lkiA&; figure(2)
mm/\\my waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
,Qj G|P K'A+V 非线性超快脉冲耦合的数值方法的Matlab程序 W .a>K$ ^y<^hKjV 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。
L/k35 x8 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
M xTJgY ]'.qRTz'\t -&+:7t r,5e/X % This Matlab script file solves the nonlinear Schrodinger equations
m=l >8 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
T:^. ; ZY % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Wu>]R'C % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'L /)9.29 _3/u#'m0 C=1;
2/-m-5A M1=120, % integer for amplitude
x Idb9hm< M3=5000; % integer for length of coupler
G[ 64qhTC N = 512; % Number of Fourier modes (Time domain sampling points)
xUJ(tG3 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.K
C*
(}- T =40; % length of time:T*T0.
_i =*0Q dt = T/N; % time step
TTf
j 5 n = [-N/2:1:N/2-1]'; % Index
WQ|Ufl; t = n.*dt;
V@'Xj .ze ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>a;a8EA<O w=2*pi*n./T;
"4b{YWv g1=-i*ww./2;
5'! fi] Z g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
z)Rkd0/X g3=-i*ww./2;
Kz'GAm\ P1=0;
ak 7% P2=0;
D#GuF~-F!R P3=1;
vo/x`F'ib P=0;
kQ\GVI11? for m1=1:M1
ib,`0=0= O p=0.032*m1; %input amplitude
qq)5)S s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
+17! v_4^ s1=s10;
+3,7 Apj s20=0.*s10; %input in waveguide 2
F|%PiC,,qO s30=0.*s10; %input in waveguide 3
G|c jI* s2=s20;
,xwiJfG;
] s3=s30;
\VPw3 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Fe8X@63 %energy in waveguide 1
'4,?YcZ?S p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
z,Xj$wl %energy in waveguide 2
*q}yfa35eR p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
P| NGAd %energy in waveguide 3
a1,)1 y~ for m3 = 1:1:M3 % Start space evolution
\`. v8C>vG s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Y3@+a A s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%! ` %21 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
FM]clC;X? sca1 = fftshift(fft(s1)); % Take Fourier transform
:7{GOx sca2 = fftshift(fft(s2));
RHsVG &<j sca3 = fftshift(fft(s3));
%YVPm*J ~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
|=5zI6pT sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
8UB2 du@? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}$)~HmZw s3 = ifft(fftshift(sc3));
J;sQvPHV8 s2 = ifft(fftshift(sc2)); % Return to physical space
lhM5a
\ s1 = ifft(fftshift(sc1));
Q g/Rw4[ end
Xl=RaV^X" p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
fhi}x( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
w,hm_aDq p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
&D<6Go/)_* P1=[P1 p1/p10];
6+=_p$crMx P2=[P2 p2/p10];
k7uX!} P3=[P3 p3/p10];
2K4Xu9-i:b P=[P p*p];
Boj R" end
rL<N:@HL figure(1)
(~Z &U plot(P,P1, P,P2, P,P3);
Zx8$M5 e;v7!X 转自：
http://blog.163.com/opto_wang/
