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- 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
- Optics express
- 2008

A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation.… (More)

- 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)

- 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)

- 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)

- Miguel A Bandres, Julio C Gutiérrez-Vega
- Journal of the Optical Society of America. A…
- 2004

We present the Ince-Gaussian modes that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators. The transverse shape of these modes is described by the Ince polynomials and is structurally stable under propagation. Ince-Gaussian… (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)

- 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)

- Ulrich T Schwarz, Miguel A Bandres, Julio C Gutiérrez-Vega
- Optics letters
- 2004

We report what is to our knowledge the first observation of Ince-Gaussian modes directly generated in a stable resonator. By slightly breaking the symmetry of the cavity of a diode-pumped Nd:YVO4 laser and its pump beam configuration we were able to generate single high-order Ince-Gaussian modes of high quality. The observed transverse modes have an… (More)