• Corpus ID: 236469460

On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions

@inproceedings{Steinberg2021OnTP,
  title={On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions},
  author={Shlomi Steinberg and Omer Eugeciouglu and Ling-Qi Yan},
  year={2021}
}
The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions, the anisotropic HermiteGauss functions, arise by endowing the standard univariate Hermite-Gauss functions with a positive definite quadratic form. These multivariate functions admit useful applications in optics, signal analysis and probability theory, however they have received little attention in… 

References

SHOWING 1-10 OF 18 REFERENCES

Multivariate holomorphic Hermite polynomials

We introduce holomorphic Hermite polynomials in n complex variables that generalize the Hermite polynomials in n real variables introduced by Hermite in the late 19th century. We discuss cases in

Differential geometry of edgeworth expansions in curved exponential family

SummaryIn order to construct a higher-order asymptotic theory of statistical inference, it is useful to know the Edgeworth expansions of the distributions of related statistics. Based on the

Generalized Hermite–Gauss decomposition of the two-photon state produced by spontaneous parametric down conversion

We provide a general decomposition of the two-photon state produced by spontaneous parametric down conversion in Hermite–Gaussian modes, in the case that the pump beam is described by a

Physical light-matter interaction in hermite-gauss space

Our purpose in this paper is two-fold: introduce a computationally-tractable decomposition of the coherence properties of light; and, present a general-purpose light-matter interaction framework for

Elegant Gaussian beams: nondiffracting nature and self-healing property.

TLDR
It is shown that the eGBs in cartesian and cylindrical coordinates are asymptotically equivalent to pseudo-nondiffracting beams (pNDBs) in the same coordinates (cosine-Gauss and Bessel- Gauss, respectively), which means that theeGBs class can be used as an alternative to pNDBs.

Laguerre–Gauss and Hermite–Gauss soft X-ray states generated using diffractive optics

Light’s capacity to carry angular momentum is integral to our knowledge of physics and ability to probe matter. In addition to spin, photons can occupy free-space orbital angular momentum

Higher-order Hermite-Gauss modes as a robust flat beam in interferometric gravitational wave detectors

Higher-order Laguerre-Gauss (LG) modes have previously been investigated as a candidate for reducing test-mass thermal noise in ground-based gravitational-wave detectors like Advanced LIGO. It has

Novel fiber-optic geometries for fast quantum communication

Recent experiments have generated great interest in combined wavlength (WDM) and spatial (SDM) divison multiplexing using optical angular momentum (OAM) at data rates orders of magnitude better than

Goos–Hänchen shift for elegant Hermite–Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene

The Goos–Hänchen (GH) shift for the reflection of the elegant Hermite–Gauss beams (EHGBs) impinging on single-layer graphene-coated surfaces is theoretically studied. The factors influencing the GH