Demonstrating Arago–Fresnel laws with Bessel beams from vectorial axicons

Abstract

Two-dimensional Bessel beams, both vectorial and scalar, have been extensively studied to date, finding many applications. Here we mimic a vectorial axicon to create one-dimensional scalar Bessel beams embedded in a two-dimensional vectorial field. We use a digital micro-mirror device to interfere orthogonal conical waves from a holographic axicon, and study the boundary of scalar and vectorial states in the context of structured light using the Arago–Fresnel laws. We show that the entire field resembles a vectorial combination of parabolic beams, exhibiting dependence on solutions to the inhomogeneous Bessel equation and asymmetry due to the orbital angular momentum associated rotational diffraction. Our work reveals the rich optical processes involved at the interplay between scalar and vectorial interference, opening intriguing questions on the duality, complementarity, and non-separability of vectorial light fields.

Fresnel–Arago laws: an easily feasible demonstration and laboratory exercise for students

“…In Crew [10] the original formulations of the laws are given (see page 155). More contemporary formulations of the Fresnel-Arago laws are given in several university textbooks [11][12][13] and research papers [14][15][16][17][18][19][20][21][22][23]. The four Fresnel-Arago laws are:…”

“…Since the Fresnel-Arago laws connect two phenomena characteristic of the wave nature of light (polarization and interference), they were the subject of scientific research. In [14][15][16][17][18][19][20] theoretical interpretations are given, while in [19][20][21][22][23][25][26][27], experimental setups are proposed for their demonstration. The use of a laser as a source of monochromatic light made it possible to obtain a clearer and sharper interference pattern [28].…”