# A review on propagation-invariant, quasi-propagation-invariant beams and coordinate axicons

About: This article is published in Journal of optics.The article was published on 2023-01-09. It has received None citations till now. The article focuses on the topics: Axicon & Coordinate system.

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TL;DR: The first experimental investigation of nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space, is reported.

Abstract: It was recently predicted that nondiffracting beams, with beam spots as small as a few wavelengths, can exist and propagate in free space. We report the first experimental investigation of these beams.

2,919 citations

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TL;DR: In this paper, exact nonsingular solutions of the scalar-wave equation for beams that are non-diffracting were presented, which means that the intensity pattern in a transverse plane is unaltered by propagating in free space.

Abstract: We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.

2,283 citations

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TL;DR: In this paper, the first observation of Airy optical beams has been reported in both one-and two-dimensional configurations, and they exhibit unusual features such as the ability to remain diffraction-free over long distances while they tend to freely accelerate during propagation.

Abstract: We report the first observation of Airy optical beams. This intriguing class of wave packets, initially predicted by Berry and Balazs in 1979, has been realized in both one- and two-dimensional configurations. As demonstrated in our experiments, these Airy beams can exhibit unusual features such as the ability to remain diffraction-free over long distances while they tend to freely accelerate during propagation.

1,841 citations

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TL;DR: The Hermiticity of the fractional Hamilton operator and the parity conservation law for fractional quantum mechanics are established and the energy spectra of a hydrogenlike atom and of a fractional oscillator in the semiclassical approximation are found.

Abstract: Some properties of the fractional Schrodinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrodinger equations.

1,391 citations

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TL;DR: In this article, it was shown that for a wave ψ in the form of an Airy function the probability density ψ 2 propagates in free space without distortion and with constant acceleration.

Abstract: We show that for a wave ψ in the form of an Airy function the probability density ‖ψ‖2 propagates in free space without distortion and with constant acceleration. This ’’Airy packet’’ corresponds classically to a family of orbits represented by a parabola in phase space; under the classical motion this parabola translates rigidly, and the fact that no other curve has this property shows that the Airy packet is unique in propagating without change of form. The acceleration of the packet (which does not violate Ehrenfest’s theorem) is related to the curvature of the caustic (envelope) of the family of world lines in spacetime. When a spatially uniform force F (t) acts the Airy packet continues to preserve its integrity. We exhibit the solution of Schrodinger’s equation for general F (t) and discuss the motion for some special forms of F (t).

1,298 citations