Debye representation of dispersive focused waves

Abstract

We report on a matrix-based diffraction integral that evaluates the focal field of any diffractionlimited 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.

Ultrathin high-index metasurfaces for shaping focused beams

“…According to Debye diffraction theory, the wave field in the focal region can be estimated by means of the following diffraction integral [13,14]:…”

Recent Progress in Far-Field Optical Metalenses

“…The Fresnel zone plates are composed of concentric circles with their radii proportional to the square root of integers times the wavelength. The diffracted wave fields in the focal region can be accurately estimated by using for instance the Debye diffraction integral [9], provided that the focusing geometry is characterized by a high Fresnel number. From the practical point of view, by using nanoimprint lithography one can use molds to pattern PMMA on silicon substrates and PMMA patterns later being transferred to metals by lift-off, reaching a 20 nm minimum feature size [10].…”

Light capsules shaped by curvilinear meta-surfaces

“…In addition, this will be of help in order to excite surface plasmon resonances in the elementary nano-slits taking part of the designed meta-surface. According to the Debye diffraction theory, the wave field in the focal region of the shaped converging beam can be obtained by means of the following diffraction integral 23,24 …”