Degree of chirality of electromagnetic fields and maximally chiral light

Recently, synthetic chiral light was introduced and theoretically shown to be highly effective for chiral light-matter interactions [D. Ayuso, O. Neufeld, A. F. Ordonez, P. Decleva, G. Lerner, O. Cohen, M. Ivanov, and O. Smirnova, Nat. Photonics 13, 866 (2019)]. This electromagnetic (EM) field possesses a new intrinsic property denoted local chirality. Contrary to standard circularly polarized light, it is chiral within the electric dipole approximation, even if the field is spatially uniform. The degree of chirality (DOC) of such light was defined, but has not yet been explored. Here we provide a comprehensive study of the DOC of locally chiral EM fields. We present numerical schemes that are capable of calculating this quantity for arbitrary fields at a low computational cost (we provide open access codes). We utilize these approaches to explore the functional dependence of the degree of chirality of bichromatic laser beams on their various degrees of freedom such as beam intensities, polarization states, and so on. We perform an extensive numerical search for the bichromatic EM field that possesses the maximal possible value of local chirality, and find a field that exhibits a 69.6% degree of chirality (out of the theoretical limit of 200%). This geometry sets the current record for a maximally chiral EM field. The numerical approach and results presented here will be useful for future investigations of chiral light-matter interactions.