  The family of solutions to the Dirac equation for an electron moving in an
electromagnetic lattice with the chiral structure created by counterpropagating
circularly polarized plane electromagnetic waves is obtained. At any nonzero
quasimomentum, the dispersion equation has two solutions which specify bispinor
wave functions describing electron states with different energies and mean
values of momentum and spin operators. The inversion of the quasimomentum
results in two other linearly independent solutions. These four basic wave
functions are uniquely defined by eight complex scalar functions (structural
functions), which serve as convenient building blocks of the relations
describing the electron properties. These properties are illustrated in
graphical form over a wide range of quasimomentums. The superpositions of two
basic wave functions describing different spin states and corresponding to (i)
the same quasimomentum (unidirectional electron states with the spin
precession) and (ii) the two equal-in-magnitude but oppositely directed
quasimomentums (bidirectional electron states) are also treated.
