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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.

In recent years, researchers have found that changes in the body's microbial ecosystems are linked to a whole range of different medical conditions, from cancer [1,2] to gastrointestinal problems [3] and even neurological diseases like Parkinson's. [4]

The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by P T symmetry of such loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibit unusual features such as zig-zag trajectories or closed-loops. To quantify the dispersion, we establish a non-Hermitian Hamiltonian model that can account for the zig-zag and closed-loop behaviour for arbitrary Bloch momentums. The properties of the interface states near the Brillouin zone center can also be explained within the framework of effective medium theory. It is shown that turning points of the dispersion are exceptional points (EPs), which are characteristic features of non-Hermitian systems. When the permittivity of photonic crystal changes, these EPs can coalesce into higher order EPs or anisotropic EPs. These interface modes hence exhibit and exemplify many complex phenomena related to exceptional point physics.