  Dynamical symmetries of laser-dressed matter determine selection rules that
determine its absorption spectrum. We explore selection rules for
polarization-sensitive absorption in Floquet matter, using Floquet group theory
in synthetic dimensions. We present comprehensive tables of selection rules
that polarization-structured light impose on Floquet dark states and Floquet
dark bands. Notably, our tables encompass nonlinear absorption, to all
nonlinear orders, revealing that different nonlinear orders follow distinct
polarization selection rules, potentially leading to polarization-tunable
optical filters.
