Hermite–gaussian functions of complex argument as optical-beam eigenfunctions

Siegman, A. E.

doi:10.1364/josa.63.001093

Cited by 253 publications

(104 citation statements)

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“…Two sets of such beams will be considered in this Section within the paraxial approximation -elegant Hermite-Gaussian (EHG) beams and elegant Laguerre-Gaussian (ELG) beams [12,13,19,20], as the grounds on which the vector modes of the interface can be build. They specify solutions to the problem in the two coordinate systems: Cartesian OXY Z of rectangular symmetry and cylindrical Or ⊥ ψZ of cylindrical symmetry.…”

Section: Basic Definitions For Elegant Beamsmentioning

confidence: 99%

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Cross-polarized normal mode patterns at a dielectric interface

Nasalski¹

2010

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. Basic features of narrow optical beam interactions with a dielectric interface are analysed. As it was recently shown, two types of paraxial beams -elegant Hermite-Gaussians of linear polarization and elegant Laguerre-Gaussians of circular polarization -can be treated as vector normal modes of the interface [1]. In this contribution the problem of normal modes is discussed with special attention paid for the case of beam oblique incidence. Excitation of higher-order modes by cross-polarization coupling is described and it is shown that this process critically depends on a propagation direction of the incident beam. Besides the expected changes of mode indices induced by generalised transmission and reflection matrices, the new phenomenon of optical vortex spectral splitting at the interface is revealed and off-axis spectral placements of the splitted vortices are determined. Results of numerical simulations given here for beam reflection entirely confirm theoretical predictions even for beams beyond the range of paraxial approximation.

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Section: Basic Definitions For Elegant Beamsmentioning

confidence: 99%

“…The HG and LG beams in their elegant version, devised some time ago by Siegman [12,13], served as a starting point in this analysis. Such beams, with their definitions appropriately modified and their possible non-paraxial extensions, appeared to be good candidates for normal modes at any planar dielectric structure.…”

Section: Introductionmentioning

confidence: 99%

Cross-polarized normal mode patterns at a dielectric interface

Nasalski¹

2010

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…The exact Laguerre-Gauss beams given by the formula (31) are similar to the so called elegant LG beams [23,24]. However, in contrast to the elegant LG beams, the exact LG beams are not monochromatic but they solve the Maxwell equations exactly and not only in the paraxial approximation.…”

Section: Spectral Decomposition Of Exact Laguerre-gauss Beamsmentioning

confidence: 99%

Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence

Bialynicki‐Birula

Bialynicka‐Birula

2006

Optics Communications

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All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector -a complex combination of the electric and magnetic field vectors -that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.

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“…(46) differentiated m times with respect to x and n times with respect to y. As a result, one obtains the azimuthally asymmetric Hermite-Gauss FWM localized wave [23,24] …”

Section: T) (47)mentioning

confidence: 99%

Bateman Conformal Transformations Within the Framework of the Bidirectional Spectral Representation

Besieris¹,

Shaarawi²,

Attiya³

2004

PIER

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Abstract-Four-dimensional conformal transformations due originally to Bateman have been used in the past by Hillion as alternative approaches to focus wave mode solutions to the 3D scalar wave equation. More recently, more extended families of focus wave mode solutions to the 3D scalar wave equation have been derived by Borisov and Utkin, as well as Kiselev, based on Bateman transformations together with a dimension-reduction approach, whereby the wave function is separated incompletely into a product of two functions. One particular goal in this exposition is to comment on and extend the work of Borisov and Utkin and simplify and extend the method used by Kiselev. More generally, however, the aim is to show that an already existing method, known as the bidirectional spectral representation, when examined in conjunction with Bateman conformal transformations, encompasses the Borisov-Utkin-Kiselev theories as special cases and allows a systematic derivation of extended families of FWM-type localized waves beyond the ranges of their applicability. † Dedicated to the memory of Frederick D. Tappert

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Hermite–gaussian functions of complex argument as optical-beam eigenfunctions

Cited by 253 publications

References 1 publication

Cross-polarized normal mode patterns at a dielectric interface

Cross-polarized normal mode patterns at a dielectric interface

Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence

Bateman Conformal Transformations Within the Framework of the Bidirectional Spectral Representation

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