150 research outputs found
Classical optics representation of the quantum mechanical translation operator via ABCD matrices
The ABCD matrix formalism describing paraxial propagation of optical beams
across linear systems is generalized to arbitrary beam trajectories. As a
by-product of this study, a one-to-one correspondence between the extended ABCD
matrix formalism presented here and the quantum mechanical translation operator
is established
Generalized Bessel beams with two indices
We report on a new class of exact solutions of the scalar Helmholtz equation
obtained by carefully engineering the form of the angular spectrum of a Bessel
beam. We consider in particular the case in which the angular spectrum of such
generalized beams has, in the paraxial zone, the same radial structure as
Laguerre-Gaussian beams. We investigate the form of these new beams as well as
their peculiar propagation properties
Goos-Haenchen and Imbert-Fedorov shifts for bounded wave packets of light
We present precise expressions of the spatial and angular Goos-Haenchen and
Imbert-Fedorov shifts experienced by a longitudinally and transversally limited
beam of light (wave packet) upon reflection from a dielectric interface, as
opposed to the well-known case of a monochromatic beam which is bounded in
transverse directions but infinitely extended along the direction of
propagation. This is done under the assumption that the detector time is longer
than the temporal length of the wave packet (wave packet regime). Our results
will be applied to the case of a Gaussian wave packet and show that, at the
leading order in the Taylor expansion of reflected-field amplitudes, the
results are the same of the monochromatic case
Goos-H\"anchen and Imbert-Fedorov shifts for astigmatic Gaussian beams
In this work we investigate the role of the beam astigmatism in the
Goos-H\"anchen and Imbert-Fedorov shift. As a case study, we consider a
Gaussian beam focused by an astigmatic lens and we calculate explicitly the
corrections to the standard formulas for beam shifts due to the astigmatism
induced by the lens. Our results show that astigmatism may enhance the angular
part of the shift
Radially Self-Accelerating Optical Pulses
We generalise the concept of radially self-accelerating beams, to the domain
of optical pulses. In particular, we show, how radially self-accelerating
optical pulses (RSAPs) can be constructed by suitable superpositions of
X-waves, which are a natural extension of Bessel beams in the pulsed domain.
Moreover, we show, that while field rotating RSAPs preserve their
self-acceleration character, intensity rotating RSAPs only possess pseudo
self-acceleration, as their transverse intensity distribution is deformed
during propagation, due to their propagation-dependent angular velocity
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