23,024 research outputs found
Elliptical beams
A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others
Normalization of the Mathieu-Gauss optical beams
A series scheme is discussed for the determination of the normalization constants of the even and odd Mathieu-Gauss (MG) optical beams. We apply a suitable expansion in terms of Bessel-Gauss (BG) beams and also answer the question of how many BG beams should be used to synthesize a MG beam within a tolerance. The structure of the normalization factors ensures that MG beams will always be normalized independently of the particular normalization adopted for the Mathieu functions. In this scheme, the normalization constants are expressed as rapidly convergent series that can be calculated to an arbitrary precision
Comment on 'Exact solution of resonant modes in a rectangular resonator'
We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation
Airy-Gauss beams and their transformation by paraxial optical systems
We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The model of the AiG beam describes in a more realistic way the propagation of the Airy wave packets because AiG beams carry finite power, retain the nondiffracting propagation properties within a finite propagation distance, and can be realized experimentally to a very good approximation
Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
We show that it is possible to have a topological phase in two-dimensional
quasicrystals without any magnetic field applied, but instead introducing an
artificial gauge field via dynamic modulation. This topological quasicrystal
exhibits scatter-free unidirectional edge states that are extended along the
system's perimeter, contrary to the states of an ordinary quasicrystal system,
which are characterized by power-law decay. We find that the spectrum of this
Floquet topological quasicrystal exhibits a rich fractal (self-similar)
structure of topological "minigaps," manifesting an entirely new phenomenon:
fractal topological systems. These topological minigaps form only when the
system size is sufficiently large because their gapless edge states penetrate
deep into the bulk. Hence, the topological structure emerges as a function of
the system size, contrary to periodic systems where the topological phase can
be completely characterized by the unit cell. We demonstrate the existence of
this topological phase both by using a topological index (Bott index) and by
studying the unidirectional transport of the gapless edge states and its
robustness in the presence of defects. Our specific model is a Penrose lattice
of helical optical waveguides - a photonic Floquet quasicrystal; however, we
expect this new topological quasicrystal phase to be universal.Comment: 12 pages, 8 figure
Galaxy Quenching from Cosmic Web Detachment
We propose the Cosmic Web Detachment (CWD) model, a framework to interpret
the star-formation history of galaxies in a cosmological context. The CWD model
unifies several starvation mechanisms known to disrupt or stop star formation
into one single physical framework. Galaxies begin accreting star-forming gas
at early times via a network of primordial filaments, simply related to the
pattern of density fluctuations in the initial conditions. But when
shell-crossing occurs on intergalactic scales, this pattern is disrupted, and
the galaxy detaches from its primordial filaments, ending the accretion of cold
gas. We argue that CWD encompasses known external processes halting star
formation, such as harassment, strangulation and starvation. On top of these
external processes, internal feedback processes such as AGN contribute to stop
in star formation as well.
By explicitly pointing out the non-linear nature of CWD events we introduce a
simple formalism to identify CWD events in N-body simulations. With it we
reproduce and explain, in the context of CWD, several observations including
downsizing, the cosmic star formation rate history, the galaxy mass-color
diagram and the dependence of the fraction of red galaxies with mass and local
density.Comment: 20 pages, accepted for publication in OJA. High-res version:
http://skysrv.pha.jhu.edu/~miguel/Papers/CWD/ms.pd
Higher-order moments and overlaps of Cartesian beams
We introduce a closed-form expression for the overlap between two different Cartesian beams. In the course of obtaining this expression, we establish a linear relation between the overlap of circular beams with azimuthal symmetry and the overlap of Cartesian beams such that the knowledge of the former allows the latter to be calculated very easily. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of Cartesian beams, and therefore of all their relevant special cases, including the standard, elegant, and generalized Hermite–Gaussian beams, cosh-Gaussian beams, Lorentz beams, and Airy beams, among others
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