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Electricity and Magnetism
Papers by Raul Hernandez Aranda
Orbital angular momentum of optical vortices from power measurements and the cross-correlation function
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.
Measurement of orbital angular momentum with an off-axis superposition of vector modes
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.
Quasi One-dimensional Nondiffracting Beams for Soliton Manipulation
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.
Optics Letters, 2014
Based on angular spectrum engineering, we report the generation of optical lattices whose two-dim... more Based on angular spectrum engineering, we report the generation of optical lattices whose two-dimensional transverse nondiffracting pattern can be reduced to a quasi-one-dimensional intensity structure formed by either a single or multiple parallel channels. Remarkably, many features for each channel such as its maximum intensity, modulation, width, or separation among channels, can be controlled and modified in order to meet the requirements of particular applications. In particular, we demonstrate that these lattices can provide useful schemes for soliton routing and steering. We demonstrate the existence domain of ground-state solitons for the single quasi-onedimensional lattice, and we show that these nondiffracting beams allow "push and pull" dynamics among the neighbor solitons propagated along the nondiffracting channels generated.
Optical Rankine Vortex and Anomalous Circulation of Light
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.
JOSA A, Jan 1, 2005
A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The... more A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens-Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the curvature of the output coupler, the cavity length, and the angle of the axicon. Our analysis revealed that while the stable Bessel resonator retains a Gaussian radial modulation on the Bessel rings, the unstable configuration exhibits a more uniform amplitude modulation that produces output profiles more similar to ideal Bessel beams. The unstable cavity also possesses higher-mode discrimination in favor of the fundamental mode than does the stable configuration.
Journal of Optics, 2013
We study the dynamics of polarization singularities in the superposition of two off-axis optical ... more We study the dynamics of polarization singularities in the superposition of two off-axis optical vortices with orthogonal polarization states. The motion of C points, states of circular polarization, is described by varying parameters such as separation distance, constant phase difference and topological charge. We analyze the zeros of the Stokes parameters and find analytical solutions for particular cases. The results could be used to realize an alternative method to measure the vortex topological charge.
Electricity and Magnetism
Orbital angular momentum of optical vortices from power measurements and the cross-correlation function
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.
Measurement of orbital angular momentum with an off-axis superposition of vector modes
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.
Quasi One-dimensional Nondiffracting Beams for Soliton Manipulation
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.
Optics Letters, 2014
Based on angular spectrum engineering, we report the generation of optical lattices whose two-dim... more Based on angular spectrum engineering, we report the generation of optical lattices whose two-dimensional transverse nondiffracting pattern can be reduced to a quasi-one-dimensional intensity structure formed by either a single or multiple parallel channels. Remarkably, many features for each channel such as its maximum intensity, modulation, width, or separation among channels, can be controlled and modified in order to meet the requirements of particular applications. In particular, we demonstrate that these lattices can provide useful schemes for soliton routing and steering. We demonstrate the existence domain of ground-state solitons for the single quasi-onedimensional lattice, and we show that these nondiffracting beams allow "push and pull" dynamics among the neighbor solitons propagated along the nondiffracting channels generated.
Optical Rankine Vortex and Anomalous Circulation of Light
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.
JOSA A, Jan 1, 2005
A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The... more A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens-Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the curvature of the output coupler, the cavity length, and the angle of the axicon. Our analysis revealed that while the stable Bessel resonator retains a Gaussian radial modulation on the Bessel rings, the unstable configuration exhibits a more uniform amplitude modulation that produces output profiles more similar to ideal Bessel beams. The unstable cavity also possesses higher-mode discrimination in favor of the fundamental mode than does the stable configuration.
Journal of Optics, 2013
We study the dynamics of polarization singularities in the superposition of two off-axis optical ... more We study the dynamics of polarization singularities in the superposition of two off-axis optical vortices with orthogonal polarization states. The motion of C points, states of circular polarization, is described by varying parameters such as separation distance, constant phase difference and topological charge. We analyze the zeros of the Stokes parameters and find analytical solutions for particular cases. The results could be used to realize an alternative method to measure the vortex topological charge.