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- Manuel Guizar-Sicairos, Julio C Gutiérrez-Vega
- Journal of the Optical Society of America. A…
- 2004

The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially… (More)

- Miguel A Bandres, Julio C Gutiérrez-Vega
- Optics express
- 2007

We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The model… (More)

We show that the complex-amplitude cross-correlation function between two beams can be obtained by the global Stokes parameters. We apply this approach to determine the topological charge of a Laguerre-Gaussian (LG) beam by performing power measurements only. Additionally, we study the connection of the cross-correlation function with the degree of… (More)

- Joel B Bentley, Jeffrey A Davis, Miguel A Bandres, Julio C Gutiérrez-Vega
- Optics letters
- 2006

We generate helical Ince-Gaussian (HIG) beams by using complex amplitude and phase masks encoded onto a liquid-crystal display (LCD). These beams display an intensity pattern consisting of elliptic rings, whose number and ellipticity can be controlled, and a phase exhibiting a number of in-line vortices, each with a unitary topological charge. We show… (More)

- J C Gutiérrez-Vega, M D Iturbe-Castillo, S Chávez-Cerda
- Optics letters
- 2000

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… (More)

- Julio C Gutiérrez-Vega, Miguel A Bandres
- Journal of the Optical Society of America. A…
- 2005

A detailed study of the propagation of an arbitrary nondiffracting beam whose disturbance in the plane z = 0 is modulated by a Gaussian envelope is presented. We call such a field a Helmholtz-Gauss (HzG) beam. A simple closed-form expression for the paraxial propagation of the HzG beams is written as the product of three factors: a complex amplitude… (More)

- Miguel A Bandres, Julio C Gutiérrez-Vega
- Optics letters
- 2008

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general… (More)

- Miguel A Bandres, Julio C Gutiérrez-Vega, Sabino Chávez-Cerda
- Optics letters
- 2004

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… (More)

- Manuel Guizar-Sicairos, Julio C Gutiérrez-Vega
- Optics letters
- 2006

We introduce the generalized Helmholtz-Gauss (gHzG) beam and analyze its propagation through optical systems described by ABCD matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive… (More)

- Carlos López-Mariscal, Julio C Gutiérrez-Vega, Graham Milne, Kishan Dholakia
- Optics express
- 2006

We observe the transfer of orbital angular momentum to trapped particles in the azimuthally asymmetric transverse intensity distribution of a helical Mathieu beam. The average rotation rate, instantaneous angular displacement and terminal velocity of the trapped particles are measured experimentally. The angular dependence of these parameters is found to be… (More)