计算脉冲在非线性耦合器中演化的Matlab 程序 :/y1yM 8* 8Zc/{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
.^N/peU q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GMMp|W V| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
A~Y^V En % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
D<|qaHB= }xBc0g r %fid=fopen('e21.dat','w');
1v,Us5s<"6 N = 128; % Number of Fourier modes (Time domain sampling points)
j2Tr $gx< M1 =3000; % Total number of space steps
@|<<H3I J =100; % Steps between output of space
!xP8# |1 T =10; % length of time windows:T*T0
OC1I&",Ai| T0=0.1; % input pulse width
-M%_\;"de MN1=0; % initial value for the space output location
I([!]z dt = T/N; % time step
Z^V6K3GSz- n = [-N/2:1:N/2-1]'; % Index
? z}=B t = n.*dt;
=3q/F7- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Wm_4avXtO u20=u10.*0.0; % input to waveguide 2
x\F,SEj u1=u10; u2=u20;
VS9`{ U1 = u1;
5nv<^>[J U2 = u2; % Compute initial condition; save it in U
>2~+.WePu ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"
Om[~-31 w=2*pi*n./T;
hJwC~HG5 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
%FXfqF9 L=4; % length of evoluation to compare with S. Trillo's paper
NLS%S q dz=L/M1; % space step, make sure nonlinear<0.05
cs T2B[f9D for m1 = 1:1:M1 % Start space evolution
j;s"q]"x] u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*:>" q ej u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
qY~`8
x ca1 = fftshift(fft(u1)); % Take Fourier transform
L !=4N!j ca2 = fftshift(fft(u2));
QA 2borfy c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Sl-v W c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Jj,U RD&0R u2 = ifft(fftshift(c2)); % Return to physical space
._8K suJG u1 = ifft(fftshift(c1));
4D[ '^q if rem(m1,J) == 0 % Save output every J steps.
4 !+pc-}- U1 = [U1 u1]; % put solutions in U array
[
j3&/ U2=[U2 u2];
vr0WS3 MN1=[MN1 m1];
~.A)bp z1=dz*MN1'; % output location
&krwf
]| end
/rq VB|M end
ox:[f9.5 hg=abs(U1').*abs(U1'); % for data write to excel
6b %WHLUeT ha=[z1 hg]; % for data write to excel
j'% $XvI t1=[0 t'];
8'<-:KG hh=[t1' ha']; % for data write to excel file
FL(6?8zK %dlmwrite('aa',hh,'\t'); % save data in the excel format
\"CZI<=TB figure(1)
}e2(T waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Q -MQ9' figure(2)
?*?R P)V waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
tj Gd ) 9Xl`pEhC 非线性超快脉冲耦合的数值方法的Matlab程序 %^I88,$&L JNkwEZhHyg 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。
#ggf' QIHp 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
/%0<p,T C0S^h<iSe* %=?cZfFqO 9:`(Q3Ei % This Matlab script file solves the nonlinear Schrodinger equations
F%i^XA]a* % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
-8 r % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
TJ: ]SB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Ku\Y'ub ,$'])A? $ C=1;
;QW3CEaUq M1=120, % integer for amplitude
dxZ u2&gi M3=5000; % integer for length of coupler
9cEv&3 N = 512; % Number of Fourier modes (Time domain sampling points)
TjQvAkT dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
uq,
{ tV T =40; % length of time:T*T0.
~4s'0 w^ dt = T/N; % time step
nBHnkbKoy n = [-N/2:1:N/2-1]'; % Index
A5i :x$ww t = n.*dt;
s< 9RKfm ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
DXa=|T w=2*pi*n./T;
Q$:! [}[( g1=-i*ww./2;
EL8NZ%:v: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
&v"3*.org@ g3=-i*ww./2;
G:pEE:W[ P1=0;
z I+\Oll#Q P2=0;
AX= 1b,s P3=1;
4O;OjUI0a P=0;
mt5KbA>nU for m1=1:M1
M/):e$S p=0.032*m1; %input amplitude
ep=qf/vd< s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1j :Wh s1=s10;
i&vaeP25) s20=0.*s10; %input in waveguide 2
\0mb
3Q' s30=0.*s10; %input in waveguide 3
[5u RS}! s2=s20;
TQ {Han! s3=s30;
Kx=4~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
$KLD2BAL %energy in waveguide 1
N nk@h p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Ea?XT&, %energy in waveguide 2
* P 3V p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/}Lt,9 %energy in waveguide 3
D K=cVpN%s for m3 = 1:1:M3 % Start space evolution
+ +aL4: s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
x7vctjM| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
FL8g5I s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
om |"S sca1 = fftshift(fft(s1)); % Take Fourier transform
TYlbU< sca2 = fftshift(fft(s2));
"Ae@lINn[y sca3 = fftshift(fft(s3));
$uap8nN sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
^':! 1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
N.4q. sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
B 9T!j]' s3 = ifft(fftshift(sc3));
,o NOC3 U s2 = ifft(fftshift(sc2)); % Return to physical space
/;tPNp{!dw s1 = ifft(fftshift(sc1));
FJ % end
p|Q*5TO p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f m(e 3] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
=xsTDjH> p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ZkIg L P1=[P1 p1/p10];
# [ e P2=[P2 p2/p10];
<L{(M j%Z P3=[P3 p3/p10];
wtT}V=_ P=[P p*p];
8 a_[B~ end
{
.*y figure(1)
;L|uIg;.s plot(P,P1, P,P2, P,P3);
2_ :n r}0\}~'?c 转自：
http://blog.163.com/opto_wang/
