Perturbative generalization of nonparaxial ultrashort tightly-focused elegant Laguerre-Gaussian beams

An analytical method for calculating the electromagnetic fields of a nonparaxial elegant Laguerre-Gaussian (eLG) vortex beam is presented for arbitrary pulse duration, spot size, and LG mode. This perturbative approach provides a numerically tractable model for the calculation of arbitrarily high radial and azimuthal LG modes in the nonparaxial regime, without requiring integral representations of the fields. A key feature of this perturbative model is its use of a Poisson-like frequency spectrum, which allows for the proper description of pulses of arbitrarily short duration. The time-domain representation of this model is presented as a non-recursive closed-form expression to any order of perturbative correction. This presentation enables calculation of the complex EM fields for such general beams without requiring evaluation of any Fourier integrals, and is therefore straightforward to implement for both analytical and numerical applications. Other recent models are discussed and compared. In addition, numerical simulations are carried out in which high energy electron bunches are generated via vacuum acceleration by a tightly focused eLG beam. By examination of accelerated electron properties far from the beam waist, it is shown that eLG beams of higher radial index can increase the electronic energy gain. The utility of such an acceleration model applied to ensemble acceleration is explored, and compared to standard modern techniques. Adviser: Professor Anthony F. Starac

Discontinuities in the Electromagnetic Fields of Vortex Beams in the Complex Source/Sink Model

An analytical discontinuity is reported in what was thought to be the discontinuity-free exact nonparaxial vortex beam phasor obtained within the complex source/sink model. This discontinuity appears for all odd values of the orbital angular momentum mode. Such discontinuities in the phasor lead to nonphysical discontinuities in the real electromagnetic field components. We identify the source of the discontinuities, and provide graphical evidence of the discontinuous real electric fields for the first and third orbital angular momentum modes. A simple means of avoiding these discontinuities is presented.Comment: 10 pages, 4 figure

Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain

An analytic expression for a polychromatic phasor representing an arbitrarily short elegant Laguerre-Gauss (eLG) laser pulse of any spot size and LG mode is presented in the time domain as a nonrecursive, closed-form perturbative expansion valid to any order of perturbative correction. This phasor enables the calculation of the complex electromagnetic fields for such beams without requiring the evaluation of any Fourier integrals. It is thus straightforward to implement in analytical or numerical applications involving eLG pulses

Perturbative representation of ultrashort nonparaxial elegant Laguerre-Gaussian fields

An analytical method for calculating the electromagnetic fields of a nonparaxial elegant Laguerre-Gaussian (LG) vortex beam is presented for arbitrary pulse duration, spot size, and LG mode. This perturbative approach provides a numerically tractable model for the calculation of arbitrarily high radial and azimuthal LG modes in the nonparaxial regime, without requiring integral representations of the fields. A key feature of this perturbative model is its use of a Poisson-like frequency spectrum, which allows for the proper description of pulses of arbitrarily short duration. This model is thus appropriate for simulating laser-matter interactions, including those involving short laser pulses

Perturbative generalization of nonparaxial ultrashort tightly-focused elegant Laguerre-Gaussian beams

An analytical method for calculating the electromagnetic fields of a nonparaxial elegant Laguerre-Gaussian (eLG) vortex beam is presented for arbitrary pulse duration, spot size, and LG mode. This perturbative approach provides a numerically tractable model for the calculation of arbitrarily high radial and azimuthal LG modes in the nonparaxial regime, without requiring integral representations of the fields. A key feature of this perturbative model is its use of a Poisson-like frequency spectrum, which allows for the proper description of pulses of arbitrarily short duration. The time-domain representation of this model is presented as a non-recursive closed-form expression to any order of perturbative correction. This presentation enables calculation of the complex EM fields for such general beams without requiring evaluation of any Fourier integrals, and is therefore straightforward to implement for both analytical and numerical applications. Other recent models are discussed and compared. In addition, numerical simulations are carried out in which high energy electron bunches are generated via vacuum acceleration by a tightly focused eLG beam. By examination of accelerated electron properties far from the beam waist, it is shown that eLG beams of higher radial index can increase the electronic energy gain. The utility of such an acceleration model applied to ensemble acceleration is explored, and compared to standard modern techniques. Adviser: Professor Anthony F. Starac

Perturbative Generalization of Nonparaxial Ultrashort Tightly-focused Elegant Laguerre-Gaussian Beams

An analytical method for calculating the electromagnetic fields of a nonparaxial elegant Laguerre-Gaussian (eLG) vortex beam is presented for arbitrary pulse duration, spot size, and LG mode. This perturbative approach provides a numerically tractable model for the calculation of arbitrarily high radial and azimuthal LG modes in the nonparaxial regime, without requiring integral representations of the fields. A key feature of this perturbative model is its use of a Poisson-like frequency spectrum, which allows for the proper description of pulses of arbitrarily short duration. The time-domain representation of this model is presented as a non-recursive closed-form expression to any order of perturbative correction. This presentation enables calculation of the complex EM fields for such general beams without requiring evaluation of any Fourier integrals, and is therefore straightforward to implement for both analytical and numerical applications. Other recent models are discussed and compared. In addition, numerical simulations are carried out in which high energy electron bunches are generated via vacuum acceleration by a tightly focused eLG beam. By examination of accelerated electron properties far from the beam waist, it is shown that eLG beams of higher radial index can increase the electronic energy gain. The utility of such an acceleration model applied to ensemble acceleration is explored, and compared to standard modern techniques

Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain

An analytic expression for a polychromatic phasor representing an arbitrarily short elegant Laguerre-Gauss (eLG) laser pulse of any spot size and LG mode is presented in the time domain as a nonrecursive, closed-form perturbative expansion valid to any order of perturbative correction. This phasor enables the calculation of the complex electromagnetic fields for such beams without requiring the evaluation of any Fourier integrals. It is thus straightforward to implement in analytical or numerical applications involving eLG pulses

Perturbative representation of ultrashort nonparaxial elegant Laguerre-Gaussian fields

An analytical method for calculating the electromagnetic fields of a nonparaxial elegant Laguerre-Gaussian (LG) vortex beam is presented for arbitrary pulse duration, spot size, and LG mode. This perturbative approach provides a numerically tractable model for the calculation of arbitrarily high radial and azimuthal LG modes in the nonparaxial regime, without requiring integral representations of the fields. A key feature of this perturbative model is its use of a Poisson-like frequency spectrum, which allows for the proper description of pulses of arbitrarily short duration. This model is thus appropriate for simulating laser-matter interactions, including those involving short laser pulses