计算脉冲在非线性耦合器中演化的Matlab 程序 )#0Llx! `XK+Y % This Matlab script file solves the coupled nonlinear Schrodinger equations of
|W;EPQ+< % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ibxtrt= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
x-Fl|kwX.5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?t"bF :! &Tn7 %fid=fopen('e21.dat','w');
MtXd}/ N = 128; % Number of Fourier modes (Time domain sampling points)
Mb\[` 4z M1 =3000; % Total number of space steps
q,fk@GI'2 J =100; % Steps between output of space
:qxd
s>Xm T =10; % length of time windows:T*T0
kOLS<>. T0=0.1; % input pulse width
#e5*Dr8 MN1=0; % initial value for the space output location
ghVxcK dt = T/N; % time step
}<
m@82\ n = [-N/2:1:N/2-1]'; % Index
r57rH^Hc t = n.*dt;
TM$Ek^fQ. u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
*h Bo,
u20=u10.*0.0; % input to waveguide 2
5%%A2FrB.S u1=u10; u2=u20;
DOGg=`XK1 U1 = u1;
#7dM % U2 = u2; % Compute initial condition; save it in U
!Z`xwk"! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Nk/Ms:57y w=2*pi*n./T;
2apQ4)6#[H g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
oQ_n:<3X L=4; % length of evoluation to compare with S. Trillo's paper
*l\vqgv.Z dz=L/M1; % space step, make sure nonlinear<0.05
'P,F)*kh for m1 = 1:1:M1 % Start space evolution
Ykt(%2L u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$jKeJn8, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
bmu<V1[W ca1 = fftshift(fft(u1)); % Take Fourier transform
G##^xFx ca2 = fftshift(fft(u2));
xrky5[XoD c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Gj(UA1~1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
||vQW\g u2 = ifft(fftshift(c2)); % Return to physical space
js8GK u1 = ifft(fftshift(c1));
;3k6_ub if rem(m1,J) == 0 % Save output every J steps.
tmf=1M U1 = [U1 u1]; % put solutions in U array
DU:
sQS4 U2=[U2 u2];
Zjh9jvsW MN1=[MN1 m1];
DozC> z1=dz*MN1'; % output location
!B\[Q$ end
)#n>))
end
%D:5 S?{ hg=abs(U1').*abs(U1'); % for data write to excel
>5!/&D.q ha=[z1 hg]; % for data write to excel
Cb/?hT t1=[0 t'];
m
K@a7fF? hh=[t1' ha']; % for data write to excel file
|~3$L\X %dlmwrite('aa',hh,'\t'); % save data in the excel format
.+cYzS]! figure(1)
3((53@s98 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*>XY' -;2e figure(2)
6lc/_&0 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^. i;, 07dUBoq 非线性超快脉冲耦合的数值方法的Matlab程序 i|Y_X umWZ]8 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
"yCek Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
tKUy&]T T\h_8 B<Ynx_95 2)^[SpZ % This Matlab script file solves the nonlinear Schrodinger equations
SEXLi8;/ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
r6-'p0| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
UVD:: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
9/k?Lv !u#o"e<qh C=1;
s=nE'/q1| M1=120, % integer for amplitude
q[3b i!Q M3=5000; % integer for length of coupler
pPG@_9qf N = 512; % Number of Fourier modes (Time domain sampling points)
" lf_`4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
(A*r&Ak[ T =40; % length of time:T*T0.
rS
4'@a dt = T/N; % time step
&xqe8!FeA n = [-N/2:1:N/2-1]'; % Index
#:68}f"$ t = n.*dt;
NOa.K)^k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
XabrX|B# w=2*pi*n./T;
F*d{< g1=-i*ww./2;
IfZaK([ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
CW=-@W7 g3=-i*ww./2;
>gr6H1 P1=0;
j1>77C3 P2=0;
| ~G;M*q P3=1;
~^"cq
S( P=0;
.6E7 R for m1=1:M1
Ac.z6]p p=0.032*m1; %input amplitude
XY|-qd}A s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
5Wi5`8m s1=s10;
R^F99L s20=0.*s10; %input in waveguide 2
/d >fp s30=0.*s10; %input in waveguide 3
8}Y(
@
%4 s2=s20;
nu$LWC- s3=s30;
r DY q]` p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
j86s[Dty %energy in waveguide 1
%'* |N[ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
JPUDnPr %energy in waveguide 2
,[bcyf p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
SAG)vmm %energy in waveguide 3
-JZl?hY( for m3 = 1:1:M3 % Start space evolution
!*|CIxk( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
G-n`X":$DT s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
7B%@f9g s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
#OWwg`AWv sca1 = fftshift(fft(s1)); % Take Fourier transform
r+0)l:{. sca2 = fftshift(fft(s2));
YQN=.Wtc sca3 = fftshift(fft(s3));
.(S,dG0P sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@;<w"j`r sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&r<<4J(t sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
}C#YR(] s3 = ifft(fftshift(sc3));
NE9e brK s2 = ifft(fftshift(sc2)); % Return to physical space
v&XG4 & s1 = ifft(fftshift(sc1));
!gf&l ^) end
p]+W1 v}V! p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
&9s6p6eb p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
hkU#
lt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
il-&d]AP P1=[P1 p1/p10];
Vn/6D[}Tu P2=[P2 p2/p10];
XY4s P3=[P3 p3/p10];
}UGPEf\ P=[P p*p];
i]$d3J3 end
(Z,,H1L figure(1)
K.z}%a plot(P,P1, P,P2, P,P3);
:za!!^ W: ?-d{ 转自:
http://blog.163.com/opto_wang/