Author

# Sabino Chávez-Cerda

Other affiliations: Imperial College London, Monterrey Institute of Technology and Higher Education, Federal University of Alagoas ...read more

Bio: Sabino Chávez-Cerda is an academic researcher from National Institute of Astrophysics, Optics and Electronics. The author has contributed to research in topics: Bessel function & Angular momentum. The author has an hindex of 28, co-authored 120 publications receiving 3584 citations. Previous affiliations of Sabino Chávez-Cerda include Imperial College London & Monterrey Institute of Technology and Higher Education.

##### Papers published on a yearly basis

##### Papers

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TL;DR: A class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other and are described by the radial and angular Mathieu functions is presented.

Abstract: Based on the separability of the Helmholtz equation into elliptical cylindrical coordinates, we present another class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. These fields are described by the radial and angular Mathieu functions. We identify the corresponding function in the McCutchen sphere that produces this kind of beam and propose an experimental setup for the realization of an invariant optical field.

489 citations

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TL;DR: It is shown that the orbital angular momentum can be used to unveil lattice properties hidden in diffraction patterns of a simple triangular aperture, and this effect can beused to measure the topological charge of light beams.

Abstract: We show that the orbital angular momentum can be used to unveil lattice properties hidden in diffraction patterns of a simple triangular aperture. Depending on the orbital angular momentum of the incident beam, the far field diffraction pattern reveals a truncated optical lattice associated with the illuminated aperture. This effect can be used to measure the topological charge of light beams.

398 citations

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TL;DR: In this paper, the orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment, which allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams.

Abstract: The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page.

364 citations

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TL;DR: The existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and their associated angular spectrum is demonstrated and their eigenvalue spectrum is continuous.

Abstract: We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.

307 citations

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TL;DR: In this article, the behavior of the Mathieu functions is illustrated by using a variety of plots with representative examples taken from mechanics, and they show how they can be applied to describe standing, traveling, and rotating waves in physical systems.

Abstract: The behavior of the Mathieu functions is illustrated by using a variety of plots with representative examples taken from mechanics. We show how Mathieu functions can be applied to describe standing, traveling, and rotating waves in physical systems. Some background is provided on notation and analogies with other mathematical functions. Our goal is to increase the familiarity with Mathieu functions in the scientific and academic community using visualization. For this purpose we adopt a strategy based on visual recognition rather than only looking at equations and formulas.

201 citations

##### Cited by

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

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TL;DR: In this paper, it was shown that if every polarization vector rotates, the light has spin; if the phase structure rotates and if a light has orbital angular momentum (OAM), the light can be many times greater than the spin.

Abstract: As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.

2,508 citations

01 Jan 2016

TL;DR: In this paper, the authors present the principles of optics electromagnetic theory of propagation interference and diffraction of light, which can be used to find a good book with a cup of coffee in the afternoon, instead of facing with some infectious bugs inside their computer.

Abstract: Thank you for reading principles of optics electromagnetic theory of propagation interference and diffraction of light. As you may know, people have search hundreds times for their favorite novels like this principles of optics electromagnetic theory of propagation interference and diffraction of light, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their computer.

2,213 citations

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TL;DR: This work investigates the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations and shows that this class of finite energy waves can retain their intensity features over several diffraction lengths.

Abstract: We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.

1,522 citations

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TL;DR: The authors survey the steady refinement of techniques used to create optical vortices, and explore their applications, which include sophisticated optical computing processes, novel microscopy and imaging techniques, the creation of ‘optical tweezers’ to trap particles of matter, and optical machining using light to pattern structures on the nanoscale.

Abstract: Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

1,016 citations