Abstract
Abstract Although parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, PT-symmetry is actually not a necessary condition for the real spectra. Here, we show that non-PT-symmetric photonic crystals (PCs) carrying Dirac-like cone dispersions can always exhibit real spectra as long as the average non-Hermiticity strength within the unit cell for the eigenstates is zero. By building a non-Hermitian Hamiltonian model, we find that the real spectra of the non-PT-symmetric system can be explained using the concept of pseudo-Hermiticity. We demonstrate using effective medium theories that, in the long-wavelength limit, such non-PT-symmetric PCs behave like the so-called complex conjugate medium (CCM) whose refractive index is real but whose permittivity and permeability are complex numbers. The real refractive index for this effective CCM is guaranteed by the real spectrum of the PCs, and the complex permittivity and permeability come from non-PT-symmetric loss-gain distributions. We show some interesting phenomena associated with CCM, such as the lasing effect.
Highlights
Abstract: parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, PT-symmetry is not a necessary condition for the real spectra
We demonstrate using effective medium theories that, in the long-wavelength limit, such non-PT-symmetric photonic crystals (PCs) behave like the so-called complex conjugate medium (CCM) whose refractive index is real but whose permittivity and permeability are complex numbers
The real refractive index for this effective CCM is guaranteed by the real spectrum of the PCs, and the complex permittivity and permeability come from non-PT-symmetric lossgain distributions
Summary
Abstract: parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, PT-symmetry is not a necessary condition for the real spectra. PT-symmetry is not a necessary condition for achieving a real spectrum [13] and some studies about realizing real spectra in non-PT-symmetric systems have been presented recently [14–18]. From the EMT point of view, achieving a CCM using a PC requires the non-Hermitian PC to exhibit real frequency bands near the Brillouin zone center (Γ point) as the effective refractive index is real. To understand the underlying physics, we build a two-band non-Hermitian Hamiltonian model for non-PTsymmetric PCs. We show that the model Hamiltonian is pseudo-Hermitian as long as the average non-Hermiticity strength (to be defined below) within the unit cell for the relevant states is zero and this condition can always be achieved in PCs that have Dirac-like cone dispersions. In the long-wavelength limit, the scattering properties of such an inhomogeneous PC behave like a homogeneous CCM
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