Dynamical constants of structured photons with parabolic-cylindrical symmetry

Rodríguez-Lara, B. M.; Jáuregui, R.

doi:10.1103/physreva.79.055806

Cited by 22 publications

(25 citation statements)

References 22 publications

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“…Propagation invariant beams are nonlocalized waves (the electric fields do not become zero fast enough as |x| → ∞) so that the orthonormalization requirement (A1) gives rise to delta functions on the modulus of k ⊥ . Explicit results for TE and TM modes have been reported for Bessel [9], Mathieu [12], and Weber [15] modes.…”

Section: Appendix A: Normalization Of the Em Modesmentioning

confidence: 89%

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Control of atomic transition rates via laser-light shaping

Jáuregui

2015

Phys. Rev. A

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A modular systematic analysis of the feasibility of modifying atomic transition rates by tailoring the electromagnetic field of an external coherent light source is presented. The formalism considers both the center of mass and internal degrees of freedom of the atom, and all properties of the field: frequency, angular spectrum, and polarization. General features of recoil effects for internal forbidden transitions are discussed. A comparative analysis of different structured light sources is explicitly worked out. It includes spherical waves, Gaussian beams, Laguerre-Gaussian beams, and propagation invariant beams with closed analytical expressions. It is shown that increments in the order of magnitude of the transition rates for Gaussian and Laguerre-Gaussian beams, with respect to those obtained in the paraxial limit, require waists of the order of the wavelength, while propagation invariant modes may considerably enhance transition rates under more favorable conditions. For transitions that can be naturally described as modifications of the atomic angular momentum, this enhancement is maximal (within propagation invariant beams) for Bessel modes, Mathieu modes can be used to entangle the internal and center-of-mass involved states, and Weber beams suppress this kind of transition unless they have a significant component of odd modes. However, if a recoil effect of the transition with an adequate symmetry is allowed, the global transition rate (center of mass and internal motion) can also be enhanced using Weber modes. The global analysis presented reinforces the idea that a better control of the transitions between internal atomic states requires both a proper control of the available states of the atomic center of mass, and shaping of the background electromagnetic field.

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Section: Appendix A: Normalization Of the Em Modesmentioning

confidence: 89%

“…(c) In parabolic coordinates, they are known as Weber beams [14,15]. For even parity and aperture α:…”

Section: Light Field: Structured Beams and Their Angular Spectramentioning

confidence: 99%

Control of atomic transition rates via laser-light shaping

Jáuregui

2015

Phys. Rev. A

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“…As is shown in [11] this simple physical reinterpretation of the solution has profound implications. Therefore, we define the Weber waves as [14,15] W (η, ξ ; a) = 1 2π…”

Section: Weber Wavesmentioning

confidence: 99%

Nondiffracting accelerating waves: Weber waves and parabolic momentum

2013

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Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a specific class of nondiffracting spatially accelerating solutions of the Maxwell equations: the Weber waves. These nonparaxial waves propagate along parabolic trajectories while approximately preserving their shape. They are expressed in an analytic closed form and naturally separate in forward and backward propagation. We show that the Weber waves are self-healing, can form periodic breather waves and have a well-defined conserved quantity: the parabolic momentum. We find that our Weber waves for moderate to large values of the parabolic momenta can be described by a modulated Airy function. Because the Weber waves are exact time-harmonic solutions of the wave equation, they have implications for many linear wave systems in nature, ranging from acoustic, electromagnetic and elastic waves to surface waves in fluids and membranes. Gesellschaft and applications, e.g. particle and cell micromanipulation [4,5], plasma physics [6], nonlinear optics [7], plasmonics [8,9] and micromachining [10], among others.Recently, new nondiffractive accelerating waves called 'half a Bessel' waves were theoretically introduced [11] and experimentally verified [12]. These waves propagate along a circular trajectory; during a quarter of the circle they are quasi shape-preserving and after this, diffraction broadening takes over and the waves spread out. The importance of these waves consists in having the same characteristics as the paraxial accelerating beams [1-3] but in the nonparaxial regime, i.e. these waves can bend to broader angles. Therefore, the 'half a Bessel' waves allow one to extrapolate all the intriguing applications of accelerating beams to the nonparaxial regime, and because these waves are solutions to the wave equation, they have implications for many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes. Therefore, a natural question is: are there other accelerating nondiffractive solutions to the wave equation?In this paper, we present new nonparaxial spatially accelerating shape-preserving waves: the Weber waves. These nonparaxial waves propagate along parabolic trajectories while approximately preserving their shape within a range of propagation distances. Our Weber waves, like the 'half a Bessel' waves, are self-healing, they can form breather waves, and they are a complete and orthogonal family of waves. The Weber waves naturally separate in forward and backward propagation, and they have an analytic closed-form solution.The 'half a Bessel' waves by construction break the circular symmetry and do not have a well-defined angular momentum. In contrast, we show that the Weber waves have a well-defined conserved quantity: the parabolic momentum. We found that our Weber waves for moderate to large values of the parabolic mom...

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“…Parabolic beams constitute the fourth family of nondiffracting beam solutions to the wave equation and exhibit an unusual nonrotational phase structure across their transverse profile [11]. The experimental generation of the parabolic beam was reported some years ago [12,13], and its dynamical properties and applications in the scattering of free-falling dilute thermal atom clouds have been studied in detail as well [14][15][16]. The set of unitary vortices of the parabolic beam are located along the semi-axis…”

Section: Introductionmentioning

confidence: 99%