Evaluation of Integral Transforms in Terms of Humbert and Lauricella Functions and Their Applications

Belafhal, A.; Benzehoua, H.; Usman, Talha

doi:10.1007/978-3-031-19082-7_13

Cited by 4 publications

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To solve this last integral, we will use our main result mentioned in Ref. (Belafhal et al 2022) (a formula which gives l m K in terms of the Humbert confluent 2  ) ( ) ( ) Then, the expression of Eq. ( 7) may be rewritten in a more compact form as ( )…”

Section: Theoretical Framework Of Generation and Propagation Of Hbiimentioning

confidence: 99%

Generation of donut Humbert beam of type-II

Chib,

Khannous,

Belafhal

2023

Opt Quant Electron

View full text Add to dashboard Cite

A new family of donut beams known as Humbert beam of type-II (HBII) was developed by converting circular beams (CiBs) that were travelling through an ABCD paraxial optical system with a spiral phase plate (SPP). Either the superposition of the Whittaker, Besselmodulated, Laguerre, and Hermite beams, can be used to represent the amplitude field of CiBs.The transformation and propagation of CiBs using a SPP after propagating the examined optical system, is shown and deduced in detail. To investigate the comportment of Humbert beams of the type-II in free space and through telescope, numerical simulations are performed.

show abstract

Section: Theoretical Framework Of Generation and Propagation Of Hbiimentioning

confidence: 99%

Generation of donut Humbert beam of type-II

Chib,

Khannous,

Belafhal

2023

Opt Quant Electron

View full text Add to dashboard Cite

show abstract

“…(A.1) into Eq. (A.2) and helped by the identity(Gradshteyn and Ryzhik We will use our main finding from Ref (Belafhal et al 2022…”

mentioning

confidence: 99%

Fresnel diffraction of Humbert beam of type-II by a helical axicon

Chib¹,

Khannous²,

Belafhal³

2023

Opt Quant Electron

View full text Add to dashboard Cite

The current study examines the diffraction of Humbert beam of type-II by a helical axicon based on the diffraction integral formula. The considered beam is a new donut beam family which generated by converting the Bessel-Gaussian beams passing through a paraxial ABCD optical system with a SPP. For the diffracted beam produced by the stationary phase approach, we have formulated the intensity distribution. By adjusting the input beam features and the topological charge of the helical axicon, numerical simulations are carried out to examine the behavior of the diffracted beam.

show abstract

Propagation of Bessel-Gaussian beams through a Spiral Phase Plate: Generation of Donut Humbert beam of type-II

Chib

Khannous

Belafhal

2023

Preprint

View full text Add to dashboard Cite

A new family of donut beams known as Humbert beam of type-II (HBII) was developed by converting circular beams (CiBs) that were travelling through an ABCD paraxial optical system with a spiral phase plate (SPP). Either the superposition of the Whittaker, Bessel-modulated, Laguerre, and Hermite beams, can be used to represent the amplitude field of CiBs. The transformation and propagation of CiBs using a SPP after propagating the examined optical system, is shown and deduced in detail. To investigate the comportment of Humbert beams of the type-II in free space and through telescope, numerical simulations are performed.

show abstract

Evaluation of Integral Transforms in Terms of Humbert and Lauricella Functions and Their Applications

Cited by 4 publications

References 15 publications

Generation of donut Humbert beam of type-II

Generation of donut Humbert beam of type-II

Fresnel diffraction of Humbert beam of type-II by a helical axicon

Propagation of Bessel-Gaussian beams through a Spiral Phase Plate: Generation of Donut Humbert beam of type-II

Contact Info

Product

Resources

About