Characterising elegant and standard Hermite-Gaussian beam modes

S. Saghafi; C. J R Sheppard; J. A. Piper

doi:10.1016/S0030-4018(01)01110-5

Characterising elegant and standard Hermite-Gaussian beam modes

S. Saghafi^*, C. J R Sheppard, J. A. Piper

^*Corresponding author for this work

Faculty of Science and Engineering

Research output: Contribution to journal › Article › peer-review

73 Citations (Scopus)

Abstract

Two tool parameters, the beam propagation factor M² and kurtosis factor k, are used to analyse solutions of the paraxial scalar wave equation (for rectangular coordinates) i.e. the so-called the standard and elegant Hermite-Gaussian modes (SHG and EHG). Analytical expressions for M² and k are derived and the correspondence between them for each form of solution is discussed in detail. These two parameters reveal information about the solutions, which leads us to derive the asymptotic representation of EHG modes (i.e. in the near-field, for a large number of modes).

Original language	English
Pages (from-to)	173-179
Number of pages	7
Journal	Optics Communications
Volume	191
Issue number	3-6
DOIs	https://doi.org/10.1016/S0030-4018(01)01110-5
Publication status	Published - 8 May 2001

Keywords

Beam propagation
Higher-order Gaussian
Kurtosis
M

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10.1016/S0030-4018(01)01110-5

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abstract = "Two tool parameters, the beam propagation factor M2 and kurtosis factor k, are used to analyse solutions of the paraxial scalar wave equation (for rectangular coordinates) i.e. the so-called the standard and elegant Hermite-Gaussian modes (SHG and EHG). Analytical expressions for M2 and k are derived and the correspondence between them for each form of solution is discussed in detail. These two parameters reveal information about the solutions, which leads us to derive the asymptotic representation of EHG modes (i.e. in the near-field, for a large number of modes).",

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AU - Sheppard, C. J R

AU - Piper, J. A.

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N2 - Two tool parameters, the beam propagation factor M2 and kurtosis factor k, are used to analyse solutions of the paraxial scalar wave equation (for rectangular coordinates) i.e. the so-called the standard and elegant Hermite-Gaussian modes (SHG and EHG). Analytical expressions for M2 and k are derived and the correspondence between them for each form of solution is discussed in detail. These two parameters reveal information about the solutions, which leads us to derive the asymptotic representation of EHG modes (i.e. in the near-field, for a large number of modes).

AB - Two tool parameters, the beam propagation factor M2 and kurtosis factor k, are used to analyse solutions of the paraxial scalar wave equation (for rectangular coordinates) i.e. the so-called the standard and elegant Hermite-Gaussian modes (SHG and EHG). Analytical expressions for M2 and k are derived and the correspondence between them for each form of solution is discussed in detail. These two parameters reveal information about the solutions, which leads us to derive the asymptotic representation of EHG modes (i.e. in the near-field, for a large number of modes).

KW - Beam propagation

KW - Higher-order Gaussian

KW - Kurtosis

KW - M

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ER -

Characterising elegant and standard Hermite-Gaussian beam modes

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Keywords

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