计算脉冲在非线性耦合器中演化的Matlab 程序 2Q bCH} zDK"Y{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
(zIW JJw % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
'tJb(X!]q % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>~+qU&'2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$0[t<4K`yn rl/]Ym4j %fid=fopen('e21.dat','w');
"+dByaY N = 128; % Number of Fourier modes (Time domain sampling points)
bf4QW JZD M1 =3000; % Total number of space steps
G!<-9HA5 J =100; % Steps between output of space
6j 2mr6o T =10; % length of time windows:T*T0
4CH/ ~b1 ( T0=0.1; % input pulse width
PNgdWf3 MN1=0; % initial value for the space output location
*@+E82D dt = T/N; % time step
m7 $t$/g n = [-N/2:1:N/2-1]'; % Index
V'iT> t = n.*dt;
Q0j4 c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ov$ S u20=u10.*0.0; % input to waveguide 2
#ULjK*)R u1=u10; u2=u20;
@sPuc. U1 = u1;
_48@o^{ U2 = u2; % Compute initial condition; save it in U
Kry^ 47" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#_p QS}$ w=2*pi*n./T;
<>71;%e;' g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
H*KZZTKd L=4; % length of evoluation to compare with S. Trillo's paper
+"?O2PX dz=L/M1; % space step, make sure nonlinear<0.05
+{b3A@f |F for m1 = 1:1:M1 % Start space evolution
:iEIo7B u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^l8&y;-T u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
dTTC6?yPXf ca1 = fftshift(fft(u1)); % Take Fourier transform
goje4; ca2 = fftshift(fft(u2));
0wE)1w<C~ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
1}/ 37\ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
-\I".8"YE u2 = ifft(fftshift(c2)); % Return to physical space
8M6wc394 u1 = ifft(fftshift(c1));
Sv>bU4LHf if rem(m1,J) == 0 % Save output every J steps.
) RCva3Ul U1 = [U1 u1]; % put solutions in U array
N~!
G AaD U2=[U2 u2];
XF Cwa MN1=[MN1 m1];
{ b,#l]v z1=dz*MN1'; % output location
#+ai G52+ end
>c30k pGg end
C j5=UUnO hg=abs(U1').*abs(U1'); % for data write to excel
GOU>j "5}2 ha=[z1 hg]; % for data write to excel
[}Z!hq t1=[0 t'];
@Wl2E.)K; hh=[t1' ha']; % for data write to excel file
{8e4TD9E0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
V2oXg figure(1)
H[J5A2b waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
tO~o-R figure(2)
A Ac*\K waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
w|[{xn^R L7"B`oa(p 非线性超快脉冲耦合的数值方法的Matlab程序 .T*89cEu q]rqFP0C 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。
IfzW%UL 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
;=lQMKx0 J`'wprSBb 2 q}lSa7r S]g`Ds< % This Matlab script file solves the nonlinear Schrodinger equations
c.{t +OR % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
$*qQ/h i % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
HLb`'TC3r+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
W8N__ Wu@v%!0 C=1;
KYM%U" j D M1=120, % integer for amplitude
XJ6=Hg4_O M3=5000; % integer for length of coupler
(_n U}<y_i N = 512; % Number of Fourier modes (Time domain sampling points)
8T"8C dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
XF i!= |F T =40; % length of time:T*T0.
vT; ~\,M dt = T/N; % time step
\}:;kO4f n = [-N/2:1:N/2-1]'; % Index
'q7&MM'oS^ t = n.*dt;
tk66Ggi[K ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Q=?YY-*$ w=2*pi*n./T;
<o: O<p@6 g1=-i*ww./2;
/c!@ H(^) g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
JLh{>_Rr g3=-i*ww./2;
2'-o'z< P1=0;
WKB
K)= P2=0;
cIQ e^C
P3=1;
I!u fw \[ P=0;
It8s#o q8 for m1=1:M1
`2a7y]? p=0.032*m1; %input amplitude
O)D+u@RhH s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-:|t^RM;FT s1=s10;
D[Kq` s20=0.*s10; %input in waveguide 2
H|s,; 1# s30=0.*s10; %input in waveguide 3
!~-@p?kW/ s2=s20;
!CUX13/0 s3=s30;
(
P\oLr9 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
gT#hF]c: %energy in waveguide 1
@2/ xu p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
^-g-]?q %energy in waveguide 2
|*JMCI@Mz p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
>slGicZ0 %energy in waveguide 3
m98w0D@Ee for m3 = 1:1:M3 % Start space evolution
!BEl6h s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
>"<<hjKJ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
@!,W] ?{ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
T3In0LQ sca1 = fftshift(fft(s1)); % Take Fourier transform
uU!}/mbo sca2 = fftshift(fft(s2));
=S< E[D{V` sca3 = fftshift(fft(s3));
@
Br? sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
C
o," sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
!w{ (}n2Wq sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
[z r 2\( s3 = ifft(fftshift(sc3));
J9q[u[QZ9O s2 = ifft(fftshift(sc2)); % Return to physical space
VL/KC -6 s1 = ifft(fftshift(sc1));
gi
JjE end
{LqahO* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
a
n|bzG p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
f;]C8/ W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
0<u (!iL P1=[P1 p1/p10];
#8i9@w P2=[P2 p2/p10];
0jMS!"k
P3=[P3 p3/p10];
bI+ TFOP P=[P p*p];
6a4-V X5 end
MOIMW+n figure(1)
Kpf Q=~' plot(P,P1, P,P2, P,P3);
^-dhz88wV df7 xpV 转自：
http://blog.163.com/opto_wang/
