2,569 research outputs found
Diffraction-Attenuation Resistant Beams: their Higher Order Versions and Finite-Aperture Generations
Recently, a method for obtaining diffraction-attenuation resistant beams in
absorbing media was developed through suitable superposition of ideal
zero-order Bessel beams. In this work, we will show that such beams maintain
their resistance to diffraction and absorption even when generated by finite
apertures. Also, we shall extend the original method to allow a higher control
over the transverse intensity profile of the beams. Although the method has
been developed for scalar fields, it can be applied to paraxial vector wave
fields as well. These new beams can possess potential applications, such as
free space optics, medical apparatuses, remote sensing, optical tweezers, etc..Comment: 24 pages, 6 figure
Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures
In this paper, starting from some general and plausible assumptions based on
geometrical optics and on a common feature of the truncated Bessel beams, a
heuristic derivation is presented of very simple analytical expressions,
capable of describing the longitudinal (on-axis) evolution of axially-symmetric
nondiffracting pulses when truncated by finite apertures. We apply our
analytical formulation to several situations involving subluminal, luminal or
superluminal localized pulses and compare the results with those obtained by
numerical simulations of the Rayleigh-Sommerfeld diffraction integrals. The
results are in excellent agreement. The present approach can be very useful,
because it can yield, in general, closed analytical expressions, avoiding the
need of time-consuming numerical simulations, and also because such expressions
provide a powerful tool for exploring several important properties of the
truncated localized pulses, as their depth of fields, the longitudinal pulse
behavior, the decaying rates, and so on.Comment: 27 pages, 7 figure
Chirped optical X-shaped pulses in material media
In this paper we analyze the properties of chirped optical X-shaped pulses
propagating in material media without boundaries. We show that such
("superluminal") pulses may recover their transverse and longitudinal shape
after some propagation distance, while the ordinary chirped gaussian-pulses can
recover their longitudinal shape only (since gaussian pulses suffer a
progressive spreading during their propagation). We therefore propose the use
of chirped optical X-type pulses to overcome the problems of both dispersion
and diffraction during the pulse propagation.Comment: Replaced with a much larger and deepened version (the number of pages
going on from 4 to 24; plus 4 Figures added
Frozen Waves: Stationary optical wavefields with arbitrary longitudinal shape, by superposing equal-frequency Bessel beams
In this paper it is shown how one can use Bessel beams to obtain a stationary
localized wavefield with high transverse localization, and whose longitudinal
intensity pattern can assume any desired shape within a chosen interval 0 < z <
L of the propagation axis. This intensity envelope remains static, i.e., with
velocity v=0; and because of this we call "Frozen Waves" such news solutions to
the wave equations (and, in particular, to the Maxwell equations). These
solutions can be used in many different and interesting applications, as
optical tweezers, atom guides, optical or acoustic bistouries, various
important medical purposes, etc.Comment: LaTeX file (10 pages, including 2 sets of two Figures
Diffraction-Attenuation Resistant Beams in Absorbing Media
In this work, in terms of suitable superpositions of equal-frequency Bessel
beams, we develop a theoretical method to obtain nondiffractive beams in
absorbing media (weakly conductive) capable to resist the loss effects for long
distances.Comment: 12 pages, 3 figure
Further results for the Dunkl Transform and the generalized Ces\`aro operator
In this paper, we consider Dunkl theory on R^d associated to a finite
reflection group. This theory generalizes classical Fourier anal- ysis. First,
we give for 1 < p <= 2, sufficient conditions for weighted Lp-estimates of the
Dunkl transform of a function f using respectively the modulus of continuity of
f in the radial case and the convolution for f in the general case. In
particular, we obtain as application, the integrability of this transform on
Besov-Lipschitz spaces. Second, we provide necessary and sufficient conditions
on nonnegative functions phi defined on [0; 1] to ensure the boundedness of the
generalized Ces\`aro operator C_phi on Herz spaces and we obtain the
corresponding operator norm inequalities.Comment: 19 page
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