650 research outputs found
Hyperbolic reflections as fundamental building blocks for multilayer optics
We reelaborate on the basic properties of lossless multilayers by using
bilinear transformations. We study some interesting properties of the
multilayer transfer function in the unit disk, showing that hyperbolic geometry
turns out to be an essential tool for understanding multilayer action. We use a
simple trace criterion to classify multilayers into three classes that
represent rotations, translations, or parallel displacements. Moreover, we show
that these three actions can be decomposed as a product of two reflections in
hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be
considered as the basic pieces for a deeper understanding of multilayer optics.Comment: 7 pages, 7 figures, accepted for publication in J. Opt. Soc. Am.
General unit-disk representation for periodic multilayers
We suggest a geometrical framework to discuss periodic layered structures in
the unit disk. The band gaps appear when the point representing the system
approaches the unit circle. We show that the trace of the matrix describing the
basic period allows for a classification in three families of orbits with quite
different properties. The laws of convergence of the iterates to the unit
circle can be then considered as universal features of the reflection.Comment: 3 pages, 2 eps-figures. To be published in Optics Letter
Quantum-limited time-frequency estimation through mode-selective photon measurement
By projecting onto complex optical mode profiles, it is possible to estimate
arbitrarily small separations between objects with quantum-limited precision,
free of uncertainty arising from overlapping intensity profiles. Here we extend
these techniques to the time-frequency domain using mode-selective
sum-frequency generation with shaped ultrafast pulses. We experimentally
resolve temporal and spectral separations between incoherent mixtures of
single-photon level signals ten times smaller than their optical bandwidths
with a ten-fold improvement in precision over the intensity-only Cram\'er-Rao
bound.Comment: Six pages, three figures. Comments welcome
Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons
Quantum key distribution is on the verge of real world applications, where
perfectly secure information can be distributed among multiple parties. Several
quantum cryptographic protocols have been theoretically proposed and
independently realized in different experimental conditions. Here, we develop
an experimental platform based on high-dimensional orbital angular momentum
states of single photons that enables implementation of multiple quantum key
distribution protocols with a single experimental apparatus. Our versatile
approach allows us to experimentally survey different classes of quantum key
distribution techniques, such as the 1984 Bennett \& Brassard (BB84),
tomographic protocols including the six-state and the Singapore protocol, and
to investigate, for the first time, a recently introduced differential phase
shift (Chau15) protocol using twisted photons. This enables us to
experimentally compare the performance of these techniques and discuss their
benefits and deficiencies in terms of noise tolerance in different dimensions.Comment: 13 pages, 4 figures, 1 tabl
Perfect antireflection via negative refraction
We suggest a geometrical framework to discuss the action of slabs of
negatively refracting materials. We show that these slabs generate the same
orbits as normal materials, but traced out in opposite directions. This
property allows us to confirm that the action of any lossless multilayer can be
optically cancelled by putting it together with the multilayer constructed as
the inverted mirror image, with and reversed in sign.Comment: Some typos corrected. New references addes. Accepted for publication
in Physics Letters
Unraveling beam self-healing
We show that, contrary to popular belief, non only diffraction-free beams may
reconstruct themselves after hitting an opaque obstacle but also, for example,
Gaussian beams. We unravel the mathematics and the physics underlying the
self-reconstruction mechanism and we provide for a novel definition for the
minimum reconstruction distance beyond geometric optics, which is in principle
applicable to any optical beam that admits an angular spectrum representation.
Moreover, we propose to quantify the self-reconstruction ability of a beam via
a newly established degree of self-healing. This is defined via a comparison
between the amplitudes, as opposite to intensities, of the original beam and
the obstructed one. Such comparison is experimentally accomplished by tailoring
an innovative experimental technique based upon Shack-Hartmann wave front
reconstruction. We believe that these results can open new avenues in this
field
Quantum phases of a qutrit
We consider various approaches to treat the phases of a qutrit. Although it
is possible to represent qutrits in a convenient geometrical manner by
resorting to a generalization of the Poincare sphere, we argue that the
appropriate way of dealing with this problem is through phase operators
associated with the algebra su(3). The rather unusual properties of these
phases are caused by the small dimension of the system and are explored in
detail. We also examine the positive operator-valued measures that can describe
the qutrit phase properties.Comment: 6 page
A geometrical setting for the classification of multilayers
We elaborate on the consequences of the factorization of the transfer matrix
of any lossless multilayer in terms of three basic matrices of simple
interpretation. By considering the bilinear transformation that this transfer
matrix induces in the complex plane, we introduce the concept of multilayer
transfer function and study its properties in the unit disk. In this
geometrical setting, our factorization translates into three actions that can
be viewed as the basic pieces for understanding the multilayer behavior.
Additionally, we introduce a simple trace criterion that allows us to classify
multilayers in three types with properties closely related to one (and only
one) of these three basic matrices. We apply this approach to analyze some
practical examples that are representative of these types of matrices.Comment: 8 pages, 5 figures. To be published in J. Opt. Soc. Am.
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