[PDF]
http://dx.doi.org/10.3952/lithjphys.50103
Open access article / Atviros prieigos straipsnis
Lith. J. Phys. 50, 89–94 (2010)
IMAGE FORMATION OF RADIALLY AND
TEMPORALLY TRUNCATED BESSEL BEAMS
O. Rebane, M. Lõhmus, and P. Saari
University of Tartu, Institute of Physics, 142 Riia St, Tartu,
51014 Estonia
E-mail: ott.rebane@gmail.com
Received 16 October 2009; accepted
19 March 2010
The Fourier-lens-formatted image
of a radially truncated Bessel beam is theoretically calculated
and compared with the experimentally measured results. A
peculiarity – the weak central spot in the focused image of an
apertured Bessel beam – has been recorded for the first time.
Femtosecond-domain temporal evolution of the image of two types of
superluminal localized wave packets – the so-called Bessel-X pulse
and the focused X wave – is studied theoretically. For the
Bessel-X pulse the aperture truncation leads to appearance of twin
pulses in the image plane. In the case of the focused X wave, the
ring changes its colour revealing the full bandwidth of the
ultrashort wave packet.
Keywords: Bessel beam, Bessel-X pulse,
Fourier optics
PACS: 42.25.Fx, 42.25.Gy, 42.30.Kq
LAIKE IR ERDVĖJE APRIBOTŲ
BESELIO PLUOŠTŲ VAIZDO FORMAVIMAS
O. Rebane, M. Lõhmus, P. Saari
Tartu universiteto Fizikos institutas, Tartu, Estija
Lęšio suformuotas radialiai apriboto Beselio
pluošto Furjė vaizdas yra apskaičiuotas teoriškai ir palygintas su
eksperimentiniais matavimo rezultatais. Jo ypatybė – silpna
centrinė dėmė apertūrą perėjusio Beselio pluošto fokusuotame
vaizde – užfiksuota pirmą kartą. Teoriškai tiriama dviejų tipų
šviesos lokalizuotų bangų paketų – vadinamojo Beselio X impulso ir
fokusuotosios X bangos – atvaizdo evoliucija femtosekundiniame
diapazone. Beselio X impulso apertūrinis apribojimas sukelia
dvigubų impulsų atsiradimą atvaizdo plokštumoje. Fokusuotosios X
bangos atveju žiedas keičia spalvą, parodydamas visą ultratrumpųjų
bangų paketo spektrinį plotį.
References / Nuorodos
[1] Localized Waves, eds. H.E. Hernández-Figueroa, M.
Zamboni-Rached, and E. Recami, Wiley Series in Microwave and Optical
Engineering, ser. ed. K. Chang (Wiley, New Jersey, 2008),
http://www.amazon.com/Localized-Waves-Microwave-Optical-Engineering/dp/0470108851/
[2] J.N. Brittingham, Focus wave modes in homogeneous Maxwell
equations: Transverse electric mode, J. Appl. Phys. 54, 1179
(1983),
http://dx.doi.org/10.1063/1.332196
[3] P. Saari and K. Reivelt, Evidence of X-shaped
propagation-invariant localized light waves, Phys. Rev. Lett. 79,
4135 (1997),
http://dx.doi.org/10.1103/PhysRevLett.79.4135
[4] P. Saari and K. Reivelt, Generation and classification of
localized waves by Lorentz transformations in Fourier space, Phys.
Rev. E 69, 036612 (2004),
http://dx.doi.org/10.1103/PhysRevE.69.036612
[5] B. Lü, W. Huang, and B. Zhang, Fraunhofer diffraction of a
Bessel beam focused by an aperture lens, Opt. Commun. 119, 6
(1995),
http://dx.doi.org/10.1016/0030-4018%2895%2900242-Z
[6] B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, Focusing
properties of Bessel beams, Opt. Commun. 131, 223 (1996),
http://dx.doi.org/10.1016/0030-4018%2896%2900274-X
[7] B. Lü and W. Huang, Three-dimensional intensity distribution of
focused Bessel–Gauss beams, J. Mod. Opt. 43, 509 (1996),
http://dx.doi.org/10.1080/09500349608232760
[8] Z.L. Horvath and Zs. Bor, Diffraction of short pulses with
boundary diffraction wave theory, Phys. Rev. E 63, 026601
(2001),
http://dx.doi.org/10.1103/PhysRevE.63.026601
[9] H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino,
and P. Saari, Direct spatiotemporal measurements of accelerating
ultrashort Bessel-type light bullets, Opt. Express 17, 14948
(2009),
http://dx.doi.org/10.1364/OE.17.014948
[10] P. Bowlan, U. Fuchs, R. Trebino, and U.D. Zeitner, Measuring
the spatiotemporal electric field of tightly focused ultrashort
pulses with sub-micron spatial resolution, Opt. Express 16,
13663 (2008),
http://dx.doi.org/10.1364/OE.16.013663
[11] H. Valtna, K. Reivelt, and P. Saari, Methods for generating
wideband localized waves of superluminal group velocity, Opt.
Commun. 278, 1 (2007),
http://dx.doi.org/10.1016/j.optcom.2007.05.059
[12] I. Besieris, M. Abdel-Rahman, and A. Shaarawi, Two fundamental
representations of localized pulse solutions to the scalar wave
equation, Prog. Electromagn. Res. 19, 1 (1998),
http://dx.doi.org/10.2528/PIER97072900