Durnin, Miceli, and Eberly reply

Durnin, J.; Miceli, Joseph J.; Eberly, J. H.

doi:10.1103/physrevlett.66.838

Cited by 29 publications

(16 citation statements)

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“…Laser resonators with BB modes have been studied previously, but the designs have lacked inherent simplicity and the concepts have consequently not been fully exploited [5][6][7][8][9][10]. With the exception of the model in Ref.…”

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confidence: 99%

“…With the exception of the model in Ref. [10] where the diffractive features of Bessel-Gauss beams were applied, all previous designs for laser resonators with BB modes were based on Durnin's scheme in which a BB was created with an annular slit followed by a lens [5][6][7][8][9]. Since the overlap between the mode and the gain medium is limited in these designs, their efficiency is generally low.…”

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confidence: 99%

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Bessel–Gauss beam optical resonator

Rogel-Salazar

New

Chávez-Cerda

2001

Optics Communications

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confidence: 99%

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confidence: 99%

Bessel–Gauss beam optical resonator

Rogel-Salazar

New

Chávez-Cerda

2001

Optics Communications

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“…Regarding the beams, Bessel [1][2][3], Bessel-Gauss [4] and Mathieu [3,5] are the most popular. Only a few papers have been addressed to the use of superpositions of Bessel beams with the same frequency, but with different longitudinal wave numbers to get confinement in both transverse or longitudinal direction.…”

Section: Introductionmentioning

confidence: 99%

“…Since they were first discovered both theoretically and experimentally by Durnin [1], many investigations have been carried out to realize diffraction-free beams. These waves have been verified in many fields like optics, microwaves and acoustics, and their different applications [2,3].…”

Section: Introductionmentioning

confidence: 99%

Study of Frozen Waves’ theory through a continuous superposition of Bessel beams

Dartora

Nóbrega

Dartora

et al. 2007

Optics & Laser Technology

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“…Specifically, we analyze the field due to a ring-shaped aperture over a metallic screen on which a linearly polarized plane wave impinges. On this basis, and in the far field approximation, we can obtain information about the propagation of energy flux and the velocity of the energy.The motion of a Bessel beam is of great interest in physics both for its characteristic as a non-diffracting beam [1,2,3,4,5,6,7], and for its implications with regard to the topic of superluminality [8,9,10,11,12,13]. Extended studies have been devoted to these subjects from both an experimental and a theoretical point of view.…”

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confidence: 99%

SuperluminalX-wave propagation: Energy localization and velocity

Mugnai

Mochi

2006

Phys. Rev. E

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The propagation of a Bessel beam (or Bessel-X wave) is analyzed on the basis of a vectorial treatment. The electric and magnetic fields are obtained by considering a realistic situation able to generate that kind of scalar field. Specifically, we analyze the field due to a ring-shaped aperture over a metallic screen on which a linearly polarized plane wave impinges. On this basis, and in the far field approximation, we can obtain information about the propagation of energy flux and the velocity of the energy.The motion of a Bessel beam is of great interest in physics both for its characteristic as a non-diffracting beam [1,2,3,4,5,6,7], and for its implications with regard to the topic of superluminality [8,9,10,11,12,13]. Extended studies have been devoted to these subjects from both an experimental and a theoretical point of view. However, in spite of the many efforts devoted to this topic, no definite answer has been found about the amount of the energy transfer and its velocity.As far as Bessel beam propagation is concerned, the problem is mainly related to the difficulty in finding the vectorial field that describes this system, while, on the contrary, the field in the scalar approximation is well-known.The purpose of the present work is to investigate the propagation of a Bessel beam on the basis of a vectorial treatment. This kind of approach allows us to obtain information regarding the propagation of the energy flux and the energy mean velocity.A Bessel beam consists of a set of plane waves with directions of propagation s = α 1 i+ β 1 j + γ 1 k which makes the same angle θ 0 (0 ≤ θ 0 < π/2) with the z-axis (hence γ 1 = cos θ 0 for all the plane waves). In spherical coordinates (ρ, θ, ϕ), the direction of propagation is specified by α 1 = sin θ 0 cos ϕ , β 1 = sin θ 0 sin ϕ γ 1 = cos θ 0 .(1)Thus, for propagation in vacuum or air, each one of these waves, at the point x, y, z, can be written aswhere u 0 dϕ is the amplitude of the elementary wave, ω is the angular frequency, k 0 = ω/c is the wavenumber, and x, y and z denotes the Cartesian coordinates of P . In cylindrical coordinates ρ, ψ, z around the z-axis x = ρ cos ψ, y = ρ sin ψ, z ≡ z, and the total field U , given by the superposition of all the waves (2), can be obtained by integrating over dϕ, that is,where J 0 denotes the zero-order Bessel function of first kind [14]. The scalar field of Eq. (3) is known as a Bessel beam (or Bessel-X wave), the unusual features of which are -that it does not change its shape during propagation, since its amplitude is independent of z[15];

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Durnin, Miceli, and Eberly reply

Cited by 29 publications

References 4 publications

Bessel–Gauss beam optical resonator

Bessel–Gauss beam optical resonator

Study of Frozen Waves’ theory through a continuous superposition of Bessel beams

SuperluminalX-wave propagation: Energy localization and velocity

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