Lorentz beams and symmetry properties in paraxial optics

The Relativistic Hermite Polynomials and the Wave Equation

“…It has also been recalled that they have been recently re-considered within the context of the paraxial wave propagation in [26], where an "optical interpretation" of the Hermite-Lorentzian functions Φ (N ) n has been suggested, enlightening their relation with the Lorentz beams, i.e., beams described by fields displaying a spatial dependence at the plane z = 0 of the type 1 1+x 2 . The latter have been introduced in [46] on the basis of the experimental observations reported in [47,48].…”

Evolution and Collapse of a Lorentz Beam in Kerr Medium

“…Recent investigations confirmed the importance of beam propagation properties in linear region [1][2][3][4][5]. The radiation force of highly focused Lorentz-Gauss beams on a dielectric sphere has been studied in the Rayleigh scattering regime [6].…”

“…Recently, there has been growing interest in the Lorentz beam since it was introduced by Gawhary and Severini [1]. The beam is appropriate for describing certain laser sources, e.g., in double-heterojunction Ga 1−x Al x As lasers [2,3].…”

Coherent transient phenomena in quantum systems by spatially shaping femtosecond optical pulses

“…Monochromatic Bessel beams are the best known examples of nondiffracting beams and can nowadays be generated in the laboratory using different methods [12][13][14][15]. Strictly speaking, they are not physically realizable, because their total energy in plane z constant is infinite, but in practice the introduction of an envelope removes this problem, as in the known case of Bessel-Gauss beams [16,17]. The nondiffracting nature of these fields stems from noticing that all plane waves, constituting the angular spectrum, possess the same phase velocity along the z direction and thus interfere always in the same way during propagation.…”