计算脉冲在非线性耦合器中演化的Matlab 程序 k?`Q\ ;-d2~1$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
uV\~2#o$_ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
>IEc4 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
?Y'r=Q{w % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Rq,Fp/ e\WG-zi/ %fid=fopen('e21.dat','w');
V2BsvR` N = 128; % Number of Fourier modes (Time domain sampling points)
*vP:+] M1 =3000; % Total number of space steps
_v +At;Y J =100; % Steps between output of space
gtJCvVj>g T =10; % length of time windows:T*T0
_0!<iN L T0=0.1; % input pulse width
-< }#ImTN MN1=0; % initial value for the space output location
4<y|SI! dt = T/N; % time step
E9#.!re|^ n = [-N/2:1:N/2-1]'; % Index
[A46WF>L t = n.*dt;
!AFii:# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
apd"p{ u20=u10.*0.0; % input to waveguide 2
c%x.cbu> u1=u10; u2=u20;
a 8.Xy])! U1 = u1;
%tZ[wwt U2 = u2; % Compute initial condition; save it in U
S<nbNSu6+ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~)%DiGW& w=2*pi*n./T;
;%Rp=&J g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
<hzuPi@ L=4; % length of evoluation to compare with S. Trillo's paper
T8\%+3e. dz=L/M1; % space step, make sure nonlinear<0.05
#u$ Z/, for m1 = 1:1:M1 % Start space evolution
D[bPm:\0M u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
uoe>T: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
(5&l<u"K~ ca1 = fftshift(fft(u1)); % Take Fourier transform
-`d(>ok ca2 = fftshift(fft(u2));
I oFtfb[ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
LAPCL&Z c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
]]lM) u2 = ifft(fftshift(c2)); % Return to physical space
F >co# u1 = ifft(fftshift(c1));
}I
^e:,{ if rem(m1,J) == 0 % Save output every J steps.
XaR(~2 U1 = [U1 u1]; % put solutions in U array
{pM3f U2=[U2 u2];
Cswa5l`af MN1=[MN1 m1];
egy#8U)Z z1=dz*MN1'; % output location
R4Si{J*O end
P<s:dH" end
kH>^3(Q\ hg=abs(U1').*abs(U1'); % for data write to excel
WDQw)EUl& ha=[z1 hg]; % for data write to excel
u}BN)%`B t1=[0 t'];
oLz9mqp2% hh=[t1' ha']; % for data write to excel file
`%Uz0h F %dlmwrite('aa',hh,'\t'); % save data in the excel format
C;.+ kE figure(1)
?,Zc{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
aFV d}RO0 figure(2)
3:G94cp5 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
9Qhk~^ngg HP*AN@>Kw 非线性超快脉冲耦合的数值方法的Matlab程序 NZ?| #53 {GM8}M~D& 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。
/dt'iai~l 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
~L=Idt!9 Ax"I$6n> 8et.A DsH`I%w{ % This Matlab script file solves the nonlinear Schrodinger equations
7z4u?>pne* % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{;j@-=pV % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
sKuPV % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+jpC%o}C Il,^/qvIY C=1;
9\[A%jp#K@ M1=120, % integer for amplitude
"J (.dg]" M3=5000; % integer for length of coupler
n*U+jc N = 512; % Number of Fourier modes (Time domain sampling points)
W_z?t; dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
b1`(f"&l T =40; % length of time:T*T0.
hg=BXe4: dt = T/N; % time step
{ei,>5K n = [-N/2:1:N/2-1]'; % Index
60St99@O t = n.*dt;
*,=WaODO % ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
%l8nTcL_? w=2*pi*n./T;
:i_kA'dl& g1=-i*ww./2;
!%_H1jk g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
hr] :bR g3=-i*ww./2;
(6Sf#M P1=0;
J((.zLvz P2=0;
,"!P{c P3=1;
HJ,sZ4*]] P=0;
m+/-SG for m1=1:M1
1*Ui=M4 p=0.032*m1; %input amplitude
WxFrqUz s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
DG
$._ s1=s10;
a>{b'X^LV s20=0.*s10; %input in waveguide 2
MJ:>ZRXCE s30=0.*s10; %input in waveguide 3
-O=a"G= s2=s20;
^"d!(npw s3=s30;
4x
JOPu p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
d.3O1TXK %energy in waveguide 1
[ZP8[Zl'? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
&JpFt^IHi %energy in waveguide 2
%Pb 5PIk4 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
{!C ';^ %energy in waveguide 3
(gl/NH! for m3 = 1:1:M3 % Start space evolution
6:Nz=sw8 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
$N#f)8v s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
SEc3`y;j% s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
=Xc[EUi<;g sca1 = fftshift(fft(s1)); % Take Fourier transform
c=T^)~$$ sca2 = fftshift(fft(s2));
Sr`gQ#b@r} sca3 = fftshift(fft(s3));
3=r8kh7, sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
aQEMCWxZ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Svmyg] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
i cf[.
s3 = ifft(fftshift(sc3));
ReCmv/AE s2 = ifft(fftshift(sc2)); % Return to physical space
Hop$w s1 = ifft(fftshift(sc1));
EMe6Z!k end
$z+iB;x p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
!$>d75zli p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
nJ|8#U7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
2b]'KiX P1=[P1 p1/p10];
$e|G#mMd- P2=[P2 p2/p10];
7FVu[Qu P3=[P3 p3/p10];
qYW{$K P=[P p*p];
xi=qap=S^9 end
eYurg6Ob~ figure(1)
X"W%(x`w plot(P,P1, P,P2, P,P3);
kQ$Q}3f .d5|Fs~B 转自:
http://blog.163.com/opto_wang/