We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Ring et al (2012) Opt. Express 20 18955, since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectra of plane waves, which are non-zero at a half parabola. For functions of HP-beam complex amplitudes, the orthogonality properties have been revealed. Using a spatial phase modulator, we generated superposition of HP-beams. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.
We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional structurally stable half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Opt. Express, 20, 18955 (2012), since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectrum of plane waves, which is non-zero at a half of parabola. For functions of HP-beams complex amplitudes, the orthogonality properties have been revealed. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.
We derive a diffraction integral to describe the paraxial propagation of an optical beam in a graded index medium with the permittivity linearly varying with the transverse coordinate. This integral transformation is irreducible to the familiar ABCD transformation. The form of the integral transformation suggests that, unlike a straight path in a homogeneous space, any paraxial optical beam will travel on a parabola bent toward the denser medium. By way of illustration, an explicit expression for the complex amplitude of a Hermite-Gaussian beam in the linear index medium is derived.
We studied a generalization of the family of Laguerre-Gaussian (LG) laser modes with asymmetrical intensity distribution. As the asymmetrical LG beam is propagating in a homogeneous medium, the asymmetry of its main (central) bright ring reduces, while the contrast of the rest rings increases. The number of bright rings coincides with that of a standard (symmetrical) LG mode. Using the expansion of the complex amplitude into the angular spectrum of plane waves, we calculated analytically the power of the asymmetrical LG beams and projection of their orbital angular momentum (OAM) on the optical axis. It is found that the normalized OAM (OAM per photon) is completely determined by the topological charge and the ratios between the shifts and the waist radius. We also found the conditions under which the normalized OAM coincides with the topological charge (as is the case for the optical vortices).
The trajectory of all nonparaxial accelerating two-dimensional (2-D) light beams known to date cannot bend higher than a semicircle. A recent paper by Alonso and Bandres suggested the use of an additional mirror to generate an accelerating beam's path that would be curved greater than a semicircle but less than an entire circle. We, for the first time, show how to generate a 2-D light field with its power flux circulating about a ring. Also, we consider accelerating nonparaxial asymmetric 2-D Bessel beams, which are obtained from a conventional 2-D Bessel beam by shifting its center to the complex plane. We show numerically that with increasing asymmetry parameter of the Bessel beam, its curved path becomes shorter, whereas the side-lobes are suppressed with respect to the central peak. Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/16/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Optical Engineering 111303-3 November 2015 • Vol. 54(11) Kotlyar, Kovalev, and Zaskanov: Light field with its power flux circulating along a ring Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/16/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Optical Engineering 111303-6 November 2015 • Vol. 54(11) Kotlyar, Kovalev, and Zaskanov: Light field with its power flux circulating along a ring Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/16/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
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