Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maxwell-consistent, symmetry- and energy-preserving solutions for
  ultrashort laser pulse propagation beyond the paraxial approximation   We analytically and numerically investigate the propagation of ultrashort
tightly focused laser pulses in vacuum, with particular emphasis on
Hermite-Gaussian and Laguerre-Gaussian modes. We revisit the Lax series
approach for forward-propagating linearly-polarized laser pulses, in order to
obtain Maxwell-consistent and symmetry-preserving analytical solutions for the
propagation of all field components beyond the paraxial approximation in
four-dimensional geometry (space and time). We demonstrate that our solution
conserves the energy, which is set by the paraxial-level term of the series.
The full solution of the wave equation towards which our series converges is
calculated in the Fourier space. Three-dimensional numerical simulations of
ultrashort tightly-focused pulses validate our analytical development.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys