Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions

Abstract

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

14 pages, 5 figures

References in corpus (4)

• On two-dimensional Bessel functions
• Particle physics with a laser-driven positronium atom
• Muon pair creation from positronium in a linearly polarized laser field
• Quantum transport and localization in biased periodic structures under bi- and polychromatic driving

Cited by in corpus (14)

• Advances in QED with intense background fields
• Narrowband inverse Compton scattering x-ray sources at high laser intensities
• Quantum electron self-interaction in a strong laser field
• Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions
• Observation of Stueckelberg oscillations in dipole-dipole interactions
• Simulations of laser-driven strong-field QED with Ptarmigan: Resolving wavelength-scale interference and $\gamma$-ray polarization
• Fully polarized nonlinear Breit-Wheeler pair production in pulsed plane waves
• Numerical calculation of Bessel, Hankel and Airy functions
• High-resolution modeling of nonlinear Compton scattering in focused laser pulses
• Locally monochromatic two-step nonlinear trident process in a plane wave
• Identities and Properties of Multi-Dimensional Generalized Bessel Functions
• From First Principles of QED to an Application: Hyperfine Structure of P States of Muonic Hydrogen
• Nonlinear effects in the laser-assisted scattering of a positron by a muon
• Relativistic elastic scattering of a muon neutrino by an electron in an elliptically polarized laser field