计算脉冲在非线性耦合器中演化的Matlab 程序 B&<5VjZ\ ~4Mz:h^ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
V~Z)^.6 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
' o*\N% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
j]`hy" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
a=x&sz\x 'tcve2Tt %fid=fopen('e21.dat','w');
m-+>h:1b|9 N = 128; % Number of Fourier modes (Time domain sampling points)
VS_\bIC M1 =3000; % Total number of space steps
]YfG`0eK< J =100; % Steps between output of space
_qpIdQBo T =10; % length of time windows:T*T0
j9GKz1 T0=0.1; % input pulse width
.*xO/pn MN1=0; % initial value for the space output location
7GG`9!l]D dt = T/N; % time step
#3eI4KJ4+l n = [-N/2:1:N/2-1]'; % Index
mG\9Qkom| t = n.*dt;
;]=@;? 9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
[eBt Dc*w u20=u10.*0.0; % input to waveguide 2
R>1oF]w u1=u10; u2=u20;
#7]>ozKm U1 = u1;
="f-I9y U2 = u2; % Compute initial condition; save it in U
vpOGyvI ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6W3."}; w=2*pi*n./T;
~E_irzOFP g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
p_e x L=4; % length of evoluation to compare with S. Trillo's paper
/v|b]Ji dz=L/M1; % space step, make sure nonlinear<0.05
;=E}PbZt2 for m1 = 1:1:M1 % Start space evolution
RBg2iG$8| u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
*CAz_s< u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
C8YStT ca1 = fftshift(fft(u1)); % Take Fourier transform
&gJ@"`r4 ca2 = fftshift(fft(u2));
k.Gt}\6zP c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Y5B!*+h c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
SB5qm?pT8< u2 = ifft(fftshift(c2)); % Return to physical space
odJE~\\hw u1 = ifft(fftshift(c1));
Zm|il9y4m if rem(m1,J) == 0 % Save output every J steps.
1=E}X5 U1 = [U1 u1]; % put solutions in U array
DYC2bs> U2=[U2 u2];
z|Xt'?9&n MN1=[MN1 m1];
,zH\P+* z1=dz*MN1'; % output location
]W%rhppC end
!U(KQ:j end
:D>flZi hg=abs(U1').*abs(U1'); % for data write to excel
{ehYE ^%N ha=[z1 hg]; % for data write to excel
bNtOqhi t1=[0 t'];
eb,QT\/G hh=[t1' ha']; % for data write to excel file
iEy2z+/"^ %dlmwrite('aa',hh,'\t'); % save data in the excel format
#)#'^MZX figure(1)
IM[=]j.? waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
I\rjw$V# figure(2)
`/wXx5n5< waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
A)d0Z6G` glKPjL * 非线性超快脉冲耦合的数值方法的Matlab程序 N[O_}_ <S;YNHLC 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。
h"}F3E 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
}v?l0Gk( Z3ODZfu> 3O2vY1Y2 IBNb!mPu% % This Matlab script file solves the nonlinear Schrodinger equations
NcX-*o % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
a{%EHL,F % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
20` XklV % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vt5>>rl W&Xi&[Ux C=1;
rEU1
VvE M1=120, % integer for amplitude
6Q+VW_~ M3=5000; % integer for length of coupler
"/UPq6 N = 512; % Number of Fourier modes (Time domain sampling points)
|L-- j dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
zx"0^r} T =40; % length of time:T*T0.
gq~`!tW' dt = T/N; % time step
kjQI=:i= n = [-N/2:1:N/2-1]'; % Index
tEibxE t = n.*dt;
o(t`XE['< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
CaoQPb* w=2*pi*n./T;
5VfpeA` g1=-i*ww./2;
X\<a|/{V A g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
~wGjr7Wt g3=-i*ww./2;
2Y=Q% P1=0;
HDu|KW$o1 P2=0;
lb"T'}q P3=1;
.Dr7YquW P=0;
)_kEy>YscZ for m1=1:M1
*t={9h p=0.032*m1; %input amplitude
AJzm/,H s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
W^3'9nYU s1=s10;
jd
8g0^ s20=0.*s10; %input in waveguide 2
'XSHl?+q s30=0.*s10; %input in waveguide 3
7FP"]\x s2=s20;
)%!X, s3=s30;
mj9]M?] p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
%U1HvmyK %energy in waveguide 1
~i}/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
9@*4^Ks p %energy in waveguide 2
A+3=OBpkW0 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
%u]>K(tU %energy in waveguide 3
xlW>3'uHfa for m3 = 1:1:M3 % Start space evolution
FOcDBCrOe s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
,-Lv3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
i l%9j s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
EkN>5). sca1 = fftshift(fft(s1)); % Take Fourier transform
V<REcII. sca2 = fftshift(fft(s2));
^$lsmF]^ sca3 = fftshift(fft(s3));
er !+QD,EM sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_)#~D*3 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
[|HQfTp$ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
):Ekf2 s3 = ifft(fftshift(sc3));
`7',RUj|D s2 = ifft(fftshift(sc2)); % Return to physical space
jqoU;u` s1 = ifft(fftshift(sc1));
HsK52< end
/ pR,l5 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9x9E+DG#( p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
uQW d1> p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
b55G1w P1=[P1 p1/p10];
%,) Xi P2=[P2 p2/p10];
8ZO~=e P3=[P3 p3/p10];
j7HOh|q P=[P p*p];
%E2C4UbY end
ra\|c>[% figure(1)
i{>YQ plot(P,P1, P,P2, P,P3);
WF<*rl Q9t.*+ 转自:
http://blog.163.com/opto_wang/