Nonparaxial shape-preserving Airy beams with Bessel signature

Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. Taking these truncated Bessel wave fields to the paraxial limit, some authors sustained that it is recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off-axis focused beams instead of finite-energy AiBs. The latter will arise under the umbrella of a nonparaxial approach following elliptical trajectories in place of parabolas. Deviations from full-wave simulations appear more severely in beam positioning rather than its local profile

Symmetry characterization of the collective modes of the phase diagram of the ν=0\nu=0 quantum Hall state in graphene: Mean-field and spontaneously broken symmetries

We devote this work to the study of the mean-field phase diagram of the $\nu=0$ quantum Hall state in bilayer graphene and the computation of the corresponding neutral collective modes, extending the results of recent works in the literature. Specifically, we provide a detailed classification of the complete orbital-valley-spin structure of the collective modes and show that phase transitions are characterized by singlet modes in orbital pseudospin, which are independent of the Coulomb strength and suffer strong many-body corrections from short-range interactions at low momentum. We describe the symmetry breaking mechanism for phase transitions in terms of the valley-spin structure of the Goldstone modes. For the remaining phase boundaries, we prove that the associated exact $SO(5)$ symmetry existing at zero Zeeman energy and interlayer voltage survives as a weaker mean-field symmetry of the Hartree-Fock equations. We extend the previous results for bilayer graphene to the monolayer scenario. Finally, we show that taking into account Landau level mixing through screening does not modify the physical picture explained above.Comment: 44 pages, 10 figure

Light capsules shaped by curvilinear meta-surfaces

We propose a simple yet efficient method for generating in-plane hollow beams with a nearly-full circular light shell without the contribution of backward propagating waves. The method relies on modulating the phase in the near field of a centro-symmetric optical wavefront, such as that from a high-numericalaperture focused wave field. We illustrate how beam acceleration may be carried out by using an ultranarrow non-flat meta-surface formed by engineered plasmonic nanoslits. A mirrorsymmetric, with respect to the optical axis, circular caustic surface is numerically demonstrated that can be used as an optical bottle

Debye representation of dispersive focused waves

We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matrix-based Debye integral to several examples. Concretely, we present an optical system for beam focusing with strong angular dispersion and free of longitudinal chromatic aberration. This simple formalism leaves an open door for analysis and design of focused beams with arbitrary angular dispersion. Our results are valid for ultrashort pulsed and polychromatic incoherent sources