We show that Parity-time symmetry in matching electric permittivity to magnetic permeability can be established by considering an effective Parity operator involving both mirror symmetry and coupling between electric and magnetic fields. This approach extends the discussion of Parity-time symmetry to the situation with more than one material potential. We show that the band structure of a one-dimensional photonic crystal with alternating purely dielectric and purely magnetic slabs can undergo a phase transition between propagation modes and evanescent modes when the balanced gain/loss parameter is varied. The cross-matching between different material potentials also allows exceptional points of the constitutive matrix to appear in the long wavelength limit where they can be used to construct ultrathin metamaterials with unidirectional reflection.

We propose a novel design principle for ultrathin metasurfaces to realize optically amplified sensing with a performance that exceeds those of passive coherent perfect absorbers by several orders of magnitude. Our strategy is based on a generalized condition of lasing, coherent perfect absorption and their coexistence in metamaterials that feature an effective PT-symmetry. The devices we introduce here can be operated in configurations that involve both a one-sided or a two-sided wave incidence, where the latter case allows us to tune the degree of amplified absorption through the coherent phase between the two input beams. We also discuss how the conditions on the material parameters can be relaxed, away from the ideal case, such that a substantial amplification of the sensing performance can easily be reached in practical applications.

We introduce here the concept of establishing parity-time (PT)-symmetry through a gauge transformation involving a shift of the mirror plane for the parity operation. The corresponding unitary transformation on the system's constitutive matrix allows us to generate and explore a family of equivalent PT-symmetric systems. We further derive that unidirectional zero reflection for a reciprocal two-port system can always be associated with a passively gauged PT-symmetry. We demonstrate this experimentally using a microstrip transmission-line with magnetoelectric coupling. This study allows us to use bianisotropy as a practical route to realise and explore exceptional point behaviour of PT-symmetric or generally non-Hermitian systems.

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