Fig. 4. Pseudo-Hermitian dynamics.

a The spectrum is shown for the metamaterial with arg(P) = π/2. We note that the reality of the frequencies is maintained, while the modulus P breaks the k → −k symmetry. L is the unit cell length. b Transverse displacement wave fields for the waves traveling in different directions. The left and right traveling modes are excited at equal frequencies, but have differing wavenumbers due to the odd micropolarity. The red arrows indicate the direction of travel of the wave, and H is the transfer function such that P = ΠH.