Raul Hernandez Aranda | Tecnológico de Monterrey (original) (raw)

Teaching Documents by Raul Hernandez Aranda

Papers by Raul Hernandez Aranda

We show that the complex-amplitude cross-correlation function between two beams can be obtained b... 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 polarization for nonuniformly polarized beams, and we obtain closed-form expressions of the cross correlation for LG vector modes and the generalized full Poincaré beams.

We propose an off-axis superposition of vector modes with orthogonal polarizations, constructed f... more We propose an off-axis superposition of vector modes with orthogonal polarizations, constructed from a general scalar helical vortex mode with unknown topological charge m, as a method to measure its orbital angular momentum. We derived analytic expressions for sets of solutions to find lines of linear polarization (L lines) within the composite polarization field. We found that the solutions corresponding to the angular component of the composite field depend only on the displacement of the beams and the topological charge m, and they are invariant under propagation and changes in the relative amplitude and phase between the beams.

Image Processing: Algorithms and Systems IV, 2005

An image processing algorithm, mainly based on morphological enhancement and segmentation, is dev... more An image processing algorithm, mainly based on morphological enhancement and segmentation, is developed and applied to optical microscope images of transverse cuts of fabric filaments, to retrieve useful shape characteristics. Adaptive filtering and non-linear fitting algorithms are also applied. Computer generated noisy images are used to estimate the algorithm accuracy with excellent results. This algorithm is a significant improvement over

Laser Resonators and Beam Control VIII, 2005

We present a detailed study of the unstable Bessel resonator. The cavity of this laser consists o... more We present a detailed study of the unstable Bessel resonator. The cavity of this laser consists of a reflective axicon and a convex spherical output coupler. A matrix method analysis for the bare resonator is employed to extract the eigenmodes and eigenvalues of the cavity, which allows us to obtain the fundamental and higher-order modes. Diffractive losses and relative phase shift behavior, in terms of both the varying radius of curvature of the output coupler and the cavity length, are studied with the matrix method and the Fox-Li algorithm. Direct comparison of the transverse mode profiles with a similar resonator employing a concave output coupler is performed, showing excellent agreement for large values of the radius of curvature. We also considered the effects of varying the aperture of the output coupler and the wedge angle of the axicon on the transverse mode profiles and diffractive losses.

Latin America Optics and Photonics Conference, 2014

ABSTRACT We report the generation of nondiffracting beams whose two-dimensional transverse patter... more ABSTRACT We report the generation of nondiffracting beams whose two-dimensional transverse pattern can be reduced to a quasi-one dimensional structure formed by either a single or multiple parallel channels. We demonstrate that these beams can provide useful schemes for soliton routing and steering.

Physical Review Letters, 2007

Rankine vortex characteristics of a partially coherent optical vortex are explored using classica... more Rankine vortex characteristics of a partially coherent optical vortex are explored using classical and physical optics. Unlike a perfectly coherent vortex mode, the circulation is not quantized. Excess circulation is predicted owing to the wave nature of composite vortex fields. Based on these findings, we propose a vortex stellar interferometer.

We show that the complex-amplitude cross-correlation function between two beams can be obtained b... 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 polarization for nonuniformly polarized beams, and we obtain closed-form expressions of the cross correlation for LG vector modes and the generalized full Poincaré beams.

We propose an off-axis superposition of vector modes with orthogonal polarizations, constructed f... more We propose an off-axis superposition of vector modes with orthogonal polarizations, constructed from a general scalar helical vortex mode with unknown topological charge m, as a method to measure its orbital angular momentum. We derived analytic expressions for sets of solutions to find lines of linear polarization (L lines) within the composite polarization field. We found that the solutions corresponding to the angular component of the composite field depend only on the displacement of the beams and the topological charge m, and they are invariant under propagation and changes in the relative amplitude and phase between the beams.

Image Processing: Algorithms and Systems IV, 2005

An image processing algorithm, mainly based on morphological enhancement and segmentation, is dev... more An image processing algorithm, mainly based on morphological enhancement and segmentation, is developed and applied to optical microscope images of transverse cuts of fabric filaments, to retrieve useful shape characteristics. Adaptive filtering and non-linear fitting algorithms are also applied. Computer generated noisy images are used to estimate the algorithm accuracy with excellent results. This algorithm is a significant improvement over

Laser Resonators and Beam Control VIII, 2005

We present a detailed study of the unstable Bessel resonator. The cavity of this laser consists o... more We present a detailed study of the unstable Bessel resonator. The cavity of this laser consists of a reflective axicon and a convex spherical output coupler. A matrix method analysis for the bare resonator is employed to extract the eigenmodes and eigenvalues of the cavity, which allows us to obtain the fundamental and higher-order modes. Diffractive losses and relative phase shift behavior, in terms of both the varying radius of curvature of the output coupler and the cavity length, are studied with the matrix method and the Fox-Li algorithm. Direct comparison of the transverse mode profiles with a similar resonator employing a concave output coupler is performed, showing excellent agreement for large values of the radius of curvature. We also considered the effects of varying the aperture of the output coupler and the wedge angle of the axicon on the transverse mode profiles and diffractive losses.

Latin America Optics and Photonics Conference, 2014

ABSTRACT We report the generation of nondiffracting beams whose two-dimensional transverse patter... more ABSTRACT We report the generation of nondiffracting beams whose two-dimensional transverse pattern can be reduced to a quasi-one dimensional structure formed by either a single or multiple parallel channels. We demonstrate that these beams can provide useful schemes for soliton routing and steering.

Physical Review Letters, 2007

Rankine vortex characteristics of a partially coherent optical vortex are explored using classica... more Rankine vortex characteristics of a partially coherent optical vortex are explored using classical and physical optics. Unlike a perfectly coherent vortex mode, the circulation is not quantized. Excess circulation is predicted owing to the wave nature of composite vortex fields. Based on these findings, we propose a vortex stellar interferometer.