Perturbative representation of ultrashort nonparaxial elegant Laguerre-Gaussian fields

Abstract

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.

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

“…Perturbative models have long provided a straightforward means of calculating the electromagnetic (EM) fields of optical beams with various spatiotemporal structures [1][2][3][4][5]. To be generally applicable, such models must allow for the accurate description of beams which are focused to arbitrarily small spot sizes, have arbitrarily short temporal durations [5], and carry arbitrarily many quanta of orbital angular momentum (OAM) [4][5][6], among other properties. The OAM carried by the beam manifests itself as an optical vortex [7][8][9][10], whereby the beam's phase exhibits a helical structure about the optical axis.…”

“…Perturbative models generally entail a power series expansion in a parameter that is small in the paraxial limit of loose focusing, such as (kw 0 ) −1 [1][2][3][4][5][11][12][13] or (k ⊥ /k) [4], where k is the wave number and w 0 is the beam waist. The zeroth order term of such a series represents the optical beam in the paraxial limit, and higher order terms introduce nonparaxial corrections.…”

“…A perturbative model describing tightly focused elegant Laguerre-Gauss (eLG) beams was presented by Bandres and Gutiérrez-Vega (BGV) [4], but this result was limited to a frequency-domain description for the case of monochromatic fields. Reference [5] extended this description in two ways: (i) It modified the BGV model by introducing a frequency spectrum, thus allowing for the description of pulses with arbitrary temporal duration; and (ii) it Fourier transformed this modified frequency-domain phasor into the time domain, from which one can obtain the EM fields by straightforward differentiation. The first two orders of perturbative correction to the time-domain phasor were also presented in Ref.…”

“…The first two orders of perturbative correction to the time-domain phasor were also presented in Ref. [5], and a method for generating higher order corrections was described in detail.…”

“…For the model of Ref. [5], it was shown that the number of terms that must be retained in the perturbation series in order to achieve convergence depends not only on the spot size of the beam but also on the LG mode. For beams carrying large values of OAM (which can be created, e.g., in highharmonic generation processes [10,15,16]), the perturbative order required to achieve convergence can become large.…”