Laser beams with phase singularities

Heckenberg, N. R.; McDuff, R.; Smith, C.P.; Rubinsztein‐Dunlop, Halina; Wegener, Margaret

doi:10.1007/bf01588597

Cited by 338 publications

(109 citation statements)

References 10 publications

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“…Among the DOEs that generate optical vortices are phase spiral plates [2,3], helical axicons [4,5,6] and spiral zone plates [7]. The ability of the fork-shaped holograms and diffraction gratings to produce vortex beams from an incident Gaussian laser beam was experimentally verified [8,9] and after, widely used for guiding cold atoms [10,11], optical manipulation of micron-sized objects [12,13], and in quantum information applications [14,15], since these vortex beams carry definite photon orbital angular momentum [16].…”

Section: Introductionmentioning

confidence: 99%

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

Topuzoski

Janicijevic

2011

Journal of Modern Optics

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Abstract:In this article we present a theoretical study for Fraunhofer diffraction of a LaguerreGaussian laser beam with zeroth radial mode number and azimuthal mode number l by diffractive grating with embedded fork-shaped dislocations of integer order p. Analytical expressions describing the diffracted wavefield amplitude and intensity distributions in the Fourier plane are deduced and analyzed. They are also followed by the vortex radii expressions.

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Section: Introductionmentioning

confidence: 99%

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

Topuzoski

Janicijevic

2011

Journal of Modern Optics

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“…Generation of helically phased beams with OAM is most usually accomplished using a diffractive optical element, i.e., hologram, the design of which is a diffraction grating containing an '-fold fork dislocation on the beam axis [10,11]. If the hologram is illuminated by the output from a laser, or single-mode fiber, the first-order diffracted beam has the required helical phase structure.…”

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confidence: 99%

Efficient Sorting of Orbital Angular Momentum States of Light

et al. 2010

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We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical elements perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient. A subsequent lens then focuses each input OAM state to a different lateral position. We demonstrate the concept experimentally by using two spatial light modulators to create the desired optical elements, applying it to the separation of eleven OAM states.

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“…Paraxial wave solutions of the source free Maxwell equations with helical wavefronts were shown to possess OAM in the units of ž (Planck constant/2π) in [1], and a nice early exposition of the phase singularities and their generation using computer-generated holograms can be found in [2]. For a recent review we refer to [3].…”

Section: Introductionmentioning

confidence: 99%

Geometric phase in optics and angular momentum of light

Tiwari¹

2004

Journal of Modern Optics

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Physical mechanism for the geometric phase in terms of angular momentum exchange is elucidated. It is argued that geometric phase arising out of the cyclic changes in the transverse mode space of Gaussian light beams is a manifestation of the cycles in the momentum space of the light. Apparent non-conservation of orbital angular momentum in the spontaneous parametric down conversion for the classical light beams is proposed to be related with the geometric phase.2 Phase singularities in light beams had been an active area of research, however prior to 1992 [1] their relationship with a well defined orbital angular momentum (OAM) of electromagnetic (EM) waves was not clear. Paraxial wave solutions of the source free Maxwell equations with helical wavefronts were shown to possess OAM in the units of ž (Planck constant/2π) in [1], and a nice early exposition of the phase singularities and their generation using computer-generated holograms can be found in [2]. For a recent review we refer to [3]. On the other hand, stimulated by the Berry phase in quantum mechanics [4], its optical analogues i.e. Pancharatnam phase in the polarization state space (geometrically represented by the Poincare sphere) and Rytov-Vladimirskii phase in the wave-vector space (geometrically represented by the sphere of directions in the momentum space) were rediscovered. There exists a considerable debate on the question whether GP in optics is a classical or a quantum phenomenon, see [5] and also the review [6], however the issue of the physical origin of GP was addressed in [5]. It was suggested that spin and orbital parts of the angular momentum were responsible for the Pancharatnam and Rytov-Vladimirskii-ChiaoWu (RVCW) phases respectively. [Note that Chiao and Wu proposed the spin redirection phase [7] similar to the earlier work of Rytov-Vladimirskii, hence the name RVCW phase].Earlier Jiao et al [8] considered both phases simultaneously, and used the geometry of a generalized Poincare sphere to suggest that the angular momentum exchange of light with optical elements was common origin of both the phases. Later the analyses by van Enk [9] and Banerjee [10] supported the hypothesis [5] that angular momentum exchange was a physical mechanism for the GP. In [9] van Enk proposed that geometric phase arising out of the cycles in the mode space of Gaussian light beams was a new phase. A Poincare-sphere equivalent for OAM states was proposed by Padgett and Courtial [11], and rotational frequency shift in a rotating mode converter for OAM bearing beams was interpreted in terms of this GP. In a recent paper, Galvez et al [12] claim to have made first direct measurement of GP in the mode space. The meaning of angular momentum exchange remains obscure in the cited works though we clearly related it with the angular momentum holonomy in [5], and gave a plausibility argument for the gauge theoretic approach for the Pancharatnam phase in [13].In this paper we address three issues. Since the light beams with OAM are now well Mathematically, GP...

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Laser beams with phase singularities

Cited by 338 publications

References 10 publications

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

Efficient Sorting of Orbital Angular Momentum States of Light

Geometric phase in optics and angular momentum of light

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