Laser fields and proxy fields

TL;DR

This paper critically examines the limitations of proxy fields in AMO physics, emphasizing the superiority of true laser fields and the inaccuracies introduced by the dipole approximation, especially at low frequencies and high intensities.

Contribution

It highlights the fundamental differences between laser and proxy fields, critiques the use of proxy fields in calculations, and advocates for the continued use of transverse laser field methods.

Findings

Proxy fields are longitudinal and cannot be gauge equivalent to laser fields.

Numerical solutions of the TDSE are exact for laser fields but not for proxy fields.

Transverse-field methods outperform proxy-field approaches across various frequency domains.

Abstract

The convention in Atomic, Molecular, and Optical (AMO) physics of employing the dipole approximation to describe laser-induced processes replaces four source-free Maxwell equations governing laser fields with a single Maxwell equation for a "proxy" field that requires a virtual source current for its existence. Laser fields are transverse, but proxy fields are longitudinal; there can be no gauge equivalence. The proxy field is sometimes serviceable, but its limitations are severe. One example is the "above-threshold ionization" (ATI) phenomenon; surprising by proxy-field understanding, but natural and predicted in advance of observation with a laser-field method. An often-overlooked limitation is that numerical solution of the time-dependent Schr\"odinger equation (TDSE) is exact for proxy fields, but not for laser fields. Acceptance of proxy-field concepts has been costly in terms of inefficiently deployed research resources. Calculations with a nearly-40-year old transverse-field method remain unmatched with proxy fields. The transverse-field method is applicable in the "tunneling" domain, the "multiphoton" domain, and, as shown here, in the low-frequency "magnetic" domain. Attempts to introduce low-frequency magnetic field corrections into TDSE cannot be expected to produce meaningful results. They would be based on inappropriate Maxwell equations, a non-existent virtual source, and would approach constant electric field properties as the field frequency declines. Laser fields propagate at the speed of light for all frequencies; they cannot approach a constant-field limit. Extremely strong laser fields are unambiguously relativistic; a nonrelativistic limit that connects continuously to the relativistic domain is simpler conceptually and mathematically than is a theory constructed with a proxy field that is certain to fail as intensities increase.