  We study the light modes in nonlinear electrodynamics of Plebanski class,
such as Post-Maxwellian Lagrangian, Born-Infeld Lagrangian, ModMax Lagrangian,
and Heisenberg-Euler-Schwinger QED Lagrangian. Nonlinear electrodynamics
provides light, a probe photon, with not only the permittivity and permeability
but also the magneto-electric effect, which result in vacuum birefringence in
the studied models but multirefringence in the most general Plebanski-class
Lagrangians. In the Minkowski spacetime, we advance a 3+1 formulation for
polarization vectors and propagation of light, and find a factorization of the
Fresnel equation into two quadratures, practically allowing to find refractive
indices. The polarization vectors form a basis of reciprocal vectors in the
non-degenerate case. We apply the formulation to find the refractive indices
and polarization vectors for the Post-Maxwellian Lagrangian, Born-Infeld
Lagrangian, ModMax Lagrangian, and HES Lagrangian in an arbitrarily strong
magnetic field.
