Lens-System Diffraction Integral Written in Terms of Matrix Optics*

Collins, Stuart A.

doi:10.1364/josa.60.001168

Cited by 1,211 publications

(398 citation statements)

References 13 publications

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“…Assume that the transverse electrical field distribution of the incident beam is E 0 (x 0 , y 0 ). So, the electrical field E 1 (x 1 , y 1 ) of the beam received at an arbitrary point of the transverse SLM plane (just before the SLM) is given from E 0 (x 0 , y 0 ) using the generalized Huygens-Fresnel integral [33] as…”

Section: Generation Of Finite Airy Array Beam By An Optical Airy Tranmentioning

confidence: 99%

See 1 more Smart Citation

Novel Finite Airy Array Beams Generated From Gaussian Array Beams Illuminating an Optical Airy Transform System

Ez-zariy¹,

Hricha²,

Belafhal³

2016

PIER M

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Abstract-In this work, a novel family of Finite Airy array beams have been produced by an optical Airy transform system illuminated by Gaussian Array beams. Based on the generalized HuygensFresnel integral, an analytical expression is developed to describe the pattern properties of the beam generated at the output plan of the optical system. The well-known Finite Airy beam generated from the fundamental Gaussian beam using an optical Airy transform system is deduced, here, as a particular case of the main result of the actual study. Numerical calculations are performed to show the possibility to create a multitude of Finite Airy array beams with controllable parameters depending on the number of beamlets, the distance between the adjacent modules and the positions and orientations of the beamlets.

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Section: Generation Of Finite Airy Array Beam By An Optical Airy Tranmentioning

confidence: 99%

“…Finally, always based on the generalized Huygens-Fresnel diffraction principle [33], the outgoing electrical field of the beam exiting the output plane of the Airy transform system is written as…”

Section: Generation Of Finite Airy Array Beam By An Optical Airy Tranmentioning

confidence: 99%

Novel Finite Airy Array Beams Generated From Gaussian Array Beams Illuminating an Optical Airy Transform System

Ez-zariy¹,

Hricha²,

Belafhal³

2016

PIER M

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“…The propagation of the light beam passing through a paraxial optical system, described by an ABCD matrix, obeys to the generalized Huygens-Fresnel integral, which connects the output electric field 2 U with the input one 1 U [40] ( ) ( ) ( )…”

Section: Fogbs Passing Through a Paraxial Abcd Optical Systemmentioning

confidence: 99%

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Hennani¹,

Ez-zariy²,

Belafhal³

2015

OPJ

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In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation properties of the FOGBs through general optical systems characterized by given ABCD matrix are studied on the basis of the generalized Huygens-Fresnel diffraction integral, which permits to show the behavior of this laser beams family and its properties depending of the laser parameters. This research is of interest to prove some investigations done in the past by other researchers.

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“…For an axial-symmetric lenslike system, the complex electric field on the output plane is related to the one on the input plane by an ABCD ray matrix [207,208]. Let the laser electric field on the input plane (the exit plane of a hollow-core fiber) be given by E(ρ)=E 0 J 0 (2.405ρ/a) with ρ ≤ a, where ρ is the radial coordinate, E 0 the on-axis peak electric field, a the capillary radius, and J 0 the zero-order Bessel function of the first kind.…”

Section: D2 Truncated Bessel Beammentioning

confidence: 99%

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

Jin

2013

Springer Theses

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In this thesis, we establish the theoretical tools to investigate high-order harmonic generation (HHG) by intense infrared lasers in a gaseous medium. The macroscopic propagation of both the fundamental and the harmonic fields is taken into account by solving Maxwell's wave equations, while the single-atom (or single-molecule) response is obtained by quantitative rescattering theory. The initial spatial mode of the fundamental laser is assumed either a Gaussian or a truncated Bessel beam. On the examples of Ar, N 2 and CO 2 , we demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N 2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO 2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continuous harmonic spectrum of Xe due to the reshaping of the fundamental laser field can be used to produce an isolated attosecond pulse by spectral and spatial filtering in the far field. For on-going application of using HHG to ionize aligned molecules, we present the photoelectron angular distribution from aligned N 2 and CO 2 in the laboratory frame, which can be compared directly with future experiments. demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N 2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO 2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continu...

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Lens-System Diffraction Integral Written in Terms of Matrix Optics*

Cited by 1,211 publications

References 13 publications

Novel Finite Airy Array Beams Generated From Gaussian Array Beams Illuminating an Optical Airy Transform System

Novel Finite Airy Array Beams Generated From Gaussian Array Beams Illuminating an Optical Airy Transform System

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

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