计算脉冲在非线性耦合器中演化的Matlab 程序 hL(zVkYI T0F!0O ` % This Matlab script file solves the coupled nonlinear Schrodinger equations of
p J #<e % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
j%TcW!D-_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
>6\rhx> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cd-; ?/ /2jw]ekQ' %fid=fopen('e21.dat','w');
<}z, !w8 N = 128; % Number of Fourier modes (Time domain sampling points)
>}|Vmy[/ M1 =3000; % Total number of space steps
#>[5NQ;$' J =100; % Steps between output of space
#CcWsI>+w> T =10; % length of time windows:T*T0
S1Ql%Yk-( T0=0.1; % input pulse width
kE*OjywN MN1=0; % initial value for the space output location
Xx;4 dt = T/N; % time step
r!W XD9# n = [-N/2:1:N/2-1]'; % Index
zSM;N^X 8? t = n.*dt;
$9In\ x
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
jxdxIkAHZc u20=u10.*0.0; % input to waveguide 2
hrZ=8SrW u1=u10; u2=u20;
Q4!6|%n8v U1 = u1;
^a?H " U2 = u2; % Compute initial condition; save it in U
+:D90p$e ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/GDG E } w=2*pi*n./T;
cUPC8k. 1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
(;1Pgh L=4; % length of evoluation to compare with S. Trillo's paper
0oU;Cmw. dz=L/M1; % space step, make sure nonlinear<0.05
#fTP o:*t for m1 = 1:1:M1 % Start space evolution
Ljq !\D u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
7]&ouT u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Zyx92z9Y ca1 = fftshift(fft(u1)); % Take Fourier transform
c =Y8R/G< ca2 = fftshift(fft(u2));
TexSUtx@$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
cN] ]J c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
ZA! yw7~ u2 = ifft(fftshift(c2)); % Return to physical space
Or9`E( u1 = ifft(fftshift(c1));
x O gUX6n if rem(m1,J) == 0 % Save output every J steps.
oyt#C HX U1 = [U1 u1]; % put solutions in U array
r@ 9qjva U2=[U2 u2];
:!nBTw MN1=[MN1 m1];
KfkE'_ F z1=dz*MN1'; % output location
%J%ZoptY: end
++ZtL\h{7 end
V {H/>>k7 hg=abs(U1').*abs(U1'); % for data write to excel
)VoQ/ch< ha=[z1 hg]; % for data write to excel
n "P29" t1=[0 t'];
ujMics( hh=[t1' ha']; % for data write to excel file
F')f i0= %dlmwrite('aa',hh,'\t'); % save data in the excel format
g-cC&)0Q figure(1)
Ag#o&Y waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
8 ta`sNy9 figure(2)
/H m), 9NN waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
|4tnG& = 5Rc^5Nv 非线性超快脉冲耦合的数值方法的Matlab程序 UvPD/qu$8D zEu15!~ 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。
Tl2e?El; 4 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
.o!z:[IPY Q*h%'oc` SFd SA4D" `OP?[
f d % This Matlab script file solves the nonlinear Schrodinger equations
X|3l*FL % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
yxpDQ O~x % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^3:y<{J % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5|^{t00T ~ $F,& 7{^ C=1;
pHpHvSI M1=120, % integer for amplitude
OYC\+
= M3=5000; % integer for length of coupler
n$S`NNO{] N = 512; % Number of Fourier modes (Time domain sampling points)
Q|+g= |%^ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
!R/- |Kjy T =40; % length of time:T*T0.
FYtf<C+ dt = T/N; % time step
_a e&@s1 n = [-N/2:1:N/2-1]'; % Index
9^5D28y t = n.*dt;
[=xJ h?*P ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ju= +!nGUa w=2*pi*n./T;
zJJ6"9sl g1=-i*ww./2;
{g7[3WRy g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
W18I"lHeh g3=-i*ww./2;
H^e0fm
P1=0;
$^1L|KgXp P2=0;
.{@aQ wN P3=1;
W 6>SYa P=0;
*xl930y for m1=1:M1
`Rc7*2I)l p=0.032*m1; %input amplitude
;N FTdP s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Wveba)"$ s1=s10;
/K WR08ftp s20=0.*s10; %input in waveguide 2
ctzaqsr s30=0.*s10; %input in waveguide 3
;Q0WCm\5 s2=s20;
Qf }^x9' s3=s30;
A,2dK}\> p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
u
VZouw# %energy in waveguide 1
O73 /2=1V p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
xq2
,S %energy in waveguide 2
/
hl:p p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-q-/0d<l %energy in waveguide 3
}uTe(Rf for m3 = 1:1:M3 % Start space evolution
<%2A,
Vz" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
X@[)j Ws s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
rkW2_UTZE s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
q Pc"A!-i sca1 = fftshift(fft(s1)); % Take Fourier transform
4&+; n[ D sca2 = fftshift(fft(s2));
aB(6yBBoxj sca3 = fftshift(fft(s3));
> WsRCBA sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
E|aP kq]
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
/<Doe SDJ| sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
<$\En[u0 s3 = ifft(fftshift(sc3));
;BR`}~m s2 = ifft(fftshift(sc2)); % Return to physical space
N~%F/`Z<+ s1 = ifft(fftshift(sc1));
gDmw Jr end
Z !qH L$ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
ET&Q}UO E p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@?w8XHEa| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
a^*@j :[ P1=[P1 p1/p10];
e (^\0 =u< P2=[P2 p2/p10];
& m'ttUG? P3=[P3 p3/p10];
)cMW, P=[P p*p];
_TRO2 p0 end
CS:mO | figure(1)
U se`E plot(P,P1, P,P2, P,P3);
D &xb tJd 9\|n2$H: 转自：
http://blog.163.com/opto_wang/
