Proceedings Article | 9 September 2019
KEYWORDS: Mirrors, Photonics, Quantum mechanics, Molecules, Acoustics, Crystals, Photonic crystals, Interfaces, Photonic devices, Germanium
Mirror symmetry or parity is a fundamental symmetry in nature found on scales ranging from celestial bodies to atomic structures. It occurs when there is a mirror plane separating a shape or an object into two halves that are mirror images of each other. In the microscopic world described by quantum mechanics and in other wave phenomena, mirror symmetry warrants that the mathematical function ψ(x) describing the underlying object, such as the probability amplitude of finding an electron in a water molecule or an acoustic mode of a violin, is either symmetric or anti-symmetric about the mirror plane. In other words, the relative phase angle θ between the two halves of ψ(x) is either 0 or π. An intellectual curiosity one may have is whether there exists a “complex mirror symmetry” that would remove this restriction on θ, extending it to the entire 2π range while maintaining the identical probability density or intensity distribution of the two halves given by |ψ(x)|^2. Here we show theoretically that this complex mirror symmetry can be realized and observed in an artificial crystal such as a photonic lattice, through the inclusion of a non-Hermitian interface formed by a double-layer of optical gain and loss materials [1,2]. By utilizing complex mirror symmetry and its recursive applications, we find a straightforward paradigm to construct high-order non-Hermitian degeneracies, which can potentially increase the spontaneous emission rate and sensing sensitivity of photonic devices [3,4] by orders of magnitude.
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