计算脉冲在非线性耦合器中演化的Matlab 程序 jn+NX)9 ppcuMcR{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
)3O0:]<H % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
{ bjK(| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
NXhQdf % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
C^Jf&a T*"15ppfk %fid=fopen('e21.dat','w');
$,+'|_0yM N = 128; % Number of Fourier modes (Time domain sampling points)
/($!("b M1 =3000; % Total number of space steps
o* qF"xG J =100; % Steps between output of space
\VW&z:/*pZ T =10; % length of time windows:T*T0
p)M\q fZ T0=0.1; % input pulse width
VKa- MN1=0; % initial value for the space output location
{4\hxyw dt = T/N; % time step
H]:z:AAvX n = [-N/2:1:N/2-1]'; % Index
TF %8pIg>Z t = n.*dt;
m#[tY>Q[b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
z?~W]PWiZ u20=u10.*0.0; % input to waveguide 2
s(yV E u1=u10; u2=u20;
!6:q#B* U1 = u1;
%\=oy=f U2 = u2; % Compute initial condition; save it in U
p_hljgOV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
s
}P-4Sg w=2*pi*n./T;
%y
zFWDg g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
1c=Roiq L=4; % length of evoluation to compare with S. Trillo's paper
I0\}S [+H dz=L/M1; % space step, make sure nonlinear<0.05
'TPRGX~& for m1 = 1:1:M1 % Start space evolution
j[/'`1tOe u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Q>gU( u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
{Kp<T ca1 = fftshift(fft(u1)); % Take Fourier transform
iR-MuDM ca2 = fftshift(fft(u2));
!x9j~D'C` c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
%]9
<a c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
y%T5"p$, u2 = ifft(fftshift(c2)); % Return to physical space
:j/PtNT@ u1 = ifft(fftshift(c1));
yVPkJ if rem(m1,J) == 0 % Save output every J steps.
7#Qa/[? D U1 = [U1 u1]; % put solutions in U array
1m-"v:fT5D U2=[U2 u2];
_`!@ MN1=[MN1 m1];
zT}Q rf~
z1=dz*MN1'; % output location
UV>^[/^O end
C~M~2@Iori end
A%u@xL,_ hg=abs(U1').*abs(U1'); % for data write to excel
]y6`9p ha=[z1 hg]; % for data write to excel
M%7H-^{ t1=[0 t'];
mY9u/;dK hh=[t1' ha']; % for data write to excel file
t`{^gt %dlmwrite('aa',hh,'\t'); % save data in the excel format
|Iy55~hK` figure(1)
R6 wK' waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y^gK^?K figure(2)
=+gp~RR, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
zO>N 3pMv 1Oo^ 非线性超快脉冲耦合的数值方法的Matlab程序 vx=I3o P[{w23`4 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
^o't& Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+P6#7.p`Z 4ei
.- [|{yr 5Ah-aDBj % This Matlab script file solves the nonlinear Schrodinger equations
:=04_5 z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
U'LO;s04m % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
A"Rzn1/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
I=hgfo kP%W:4l0 C=1;
@6GM)N\{[ M1=120, % integer for amplitude
*Kt7"J M3=5000; % integer for length of coupler
*Rshzv[ N = 512; % Number of Fourier modes (Time domain sampling points)
6__@?XzJ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0c1}?$f[?% T =40; % length of time:T*T0.
) iy>sa{ dt = T/N; % time step
'O`jV0aa' n = [-N/2:1:N/2-1]'; % Index
]^gD@]. t = n.*dt;
p)tac*US ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&F\J%#{ w=2*pi*n./T;
nvD"_.K rJ g1=-i*ww./2;
;JFE7\-mC g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
,@!8jar@w} g3=-i*ww./2;
nx=#QLi P1=0;
S^)r,cC P2=0;
*D<S \6= P3=1;
UVu"meZX P=0;
<Xy8}Z`s for m1=1:M1
s~/]nz]"J p=0.032*m1; %input amplitude
p%IR4f s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
.mDqZOpf=4 s1=s10;
&7Ixf?e!K s20=0.*s10; %input in waveguide 2
~N[hY1}X[ s30=0.*s10; %input in waveguide 3
O(
he s2=s20;
TFxb\ s3=s30;
q22cp&gmX p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
R)cns7oW %energy in waveguide 1
'! 1ts @ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
-f9M*7O<gf %energy in waveguide 2
'n:Ft p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
RW(AjDM %energy in waveguide 3
Q77qrx3 for m3 = 1:1:M3 % Start space evolution
kTiQO2H s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
xOT'4v&. s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
*,
*"G? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
42p6l sca1 = fftshift(fft(s1)); % Take Fourier transform
(dMFYL>YP sca2 = fftshift(fft(s2));
0*3 <} sca3 = fftshift(fft(s3));
--.j&w sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
3jS= sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
IU$bP#< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
C2<y(GU[Bh s3 = ifft(fftshift(sc3));
f=K1ZD s2 = ifft(fftshift(sc2)); % Return to physical space
+crAkb}i s1 = ifft(fftshift(sc1));
I J4"X#Q/ end
MCh8Q|Yx4 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
a+{g~/z;,Q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
WP]<\_r2 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=AD/5E,3 P1=[P1 p1/p10];
)sV#
b P2=[P2 p2/p10];
T@yH.4D P3=[P3 p3/p10];
(la<X<w P=[P p*p];
\=N
tbBL$[ end
~Y'e1w$` figure(1)
2jhVmK plot(P,P1, P,P2, P,P3);
$,aU"'D p1?}"bHk 转自:
http://blog.163.com/opto_wang/