计算脉冲在非线性耦合器中演化的Matlab 程序 jWNF3\ cl1>S 3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l:- <CbG % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
m4~>n( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/n-!dXi % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+b_o2'' _Qd CV` %fid=fopen('e21.dat','w');
~b;u1;ne N = 128; % Number of Fourier modes (Time domain sampling points)
WinwPn+9 M1 =3000; % Total number of space steps
L)yc_ d5 J =100; % Steps between output of space
7Q>bJ Ek7 T =10; % length of time windows:T*T0
>& `;@ZOH T0=0.1; % input pulse width
#Pr
w2u MN1=0; % initial value for the space output location
HyGu3 dt = T/N; % time step
_Y _v& n = [-N/2:1:N/2-1]'; % Index
2C[xrZa^ t = n.*dt;
X]+z:! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
w
tSX(LNY u20=u10.*0.0; % input to waveguide 2
4D=^24f`0 u1=u10; u2=u20;
!Y^3% B% U1 = u1;
%R m`+ U2 = u2; % Compute initial condition; save it in U
uRCZGg&V?# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1WUlBr/k w=2*pi*n./T;
hmp!|Q[) g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
x.kIzI5 L=4; % length of evoluation to compare with S. Trillo's paper
WWjc.A$ dz=L/M1; % space step, make sure nonlinear<0.05
XpIl-o&re for m1 = 1:1:M1 % Start space evolution
"(+p1
u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
KybrSa u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
n@_aTY ca1 = fftshift(fft(u1)); % Take Fourier transform
05s{Z.aK ca2 = fftshift(fft(u2));
Q/]t$ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$iMbtA5aQ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
2#)z%K6T u2 = ifft(fftshift(c2)); % Return to physical space
&ieb6@RO`Q u1 = ifft(fftshift(c1));
R
q9(<'F if rem(m1,J) == 0 % Save output every J steps.
SL5QhP U1 = [U1 u1]; % put solutions in U array
J. $U_k U2=[U2 u2];
Xv2Q8-}w MN1=[MN1 m1];
+<rWYF(ii/ z1=dz*MN1'; % output location
\V%l.P4>e end
pKkBAr, end
Ye]-RN/W hg=abs(U1').*abs(U1'); % for data write to excel
]US ha=[z1 hg]; % for data write to excel
JIU8~D t1=[0 t'];
s6(bTO. hh=[t1' ha']; % for data write to excel file
sh)[|?7z %dlmwrite('aa',hh,'\t'); % save data in the excel format
=58:e7(df figure(1)
_"h1#E waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
TrR=3_;.7 figure(2)
ZW%;"5uVm) waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
,d@FO|G#pt ^8V8,C) 非线性超快脉冲耦合的数值方法的Matlab程序 2g
HRfTF w)Z-, J 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
"'*Qq@!3? Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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%LU:WC 9a$ 7$4m w=kW~gg @M!nAQ8hY % This Matlab script file solves the nonlinear Schrodinger equations
iq<nuO % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
bY}:!aR<mK % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
|Ng}ZLBM % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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g se*!OiOt C=1;
EI8KK o * M1=120, % integer for amplitude
l5FKw;=K}: M3=5000; % integer for length of coupler
s(pNg?R N = 512; % Number of Fourier modes (Time domain sampling points)
N?v}\ PU dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{4>N2mP{M T =40; % length of time:T*T0.
Xk`' m[ dt = T/N; % time step
tvcM<
e20 n = [-N/2:1:N/2-1]'; % Index
"R^0eNv$ t = n.*dt;
qCy
SL lp0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
I78Q8W(5 w=2*pi*n./T;
W%@0Y m`7 g1=-i*ww./2;
-0>s`ruor g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
JYrOE"!h g3=-i*ww./2;
pcNpr`
P1=0;
?wpl
88z P2=0;
TEQs9-Uy P3=1;
n8Rsle`a P=0;
q$kx/6=k for m1=1:M1
:X 9_~ p=0.032*m1; %input amplitude
Odr<fvV,> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ODKHI\U
s1=s10;
{r?+PQQ# s20=0.*s10; %input in waveguide 2
6r)B|~,OA s30=0.*s10; %input in waveguide 3
_Lgi5B% s2=s20;
i|!W;2KL5 s3=s30;
sI`oz|$ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
`>u^Pm
%energy in waveguide 1
D2'J( p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
+6s6QeNS8 %energy in waveguide 2
thSXri?kl p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
d,E2l~s %energy in waveguide 3
9a]J Q for m3 = 1:1:M3 % Start space evolution
ONMR2J( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
DHVfb(H5e s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
eE" *c>I s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
l4AXjq2 sca1 = fftshift(fft(s1)); % Take Fourier transform
Zb:S
IJ sca2 = fftshift(fft(s2));
O'S9y sca3 = fftshift(fft(s3));
^%NjdZu DO sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ZM_-g4[H sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
;R7+6 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
grE'ySX0 s3 = ifft(fftshift(sc3));
d RHw]!. s2 = ifft(fftshift(sc2)); % Return to physical space
/ !aVv s1 = ifft(fftshift(sc1));
zO((FQ end
zcOG[- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
&W%fsy< p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&IP`j~b p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
#YK=e&da P1=[P1 p1/p10];
G$t:#2 P2=[P2 p2/p10];
}b+$S'`Bv P3=[P3 p3/p10];
Qn \=P*j P=[P p*p];
9>ML;$T& end
H,;9' *84 figure(1)
WD|pG;Gq plot(P,P1, P,P2, P,P3);
uo3o[H
QJ,~K&? 转自:
http://blog.163.com/opto_wang/