Non-Hermitian sensing in photonics and electronics
Francesco De Leonardis
Polytechnic University of Bari, Italy
: Res J Opt Photonics
Abstract
In this review an overview of the theory of non-Hermitian (PT-symmetric and anti-PT-symmetric) Hamiltonians in optics and electronics will be provided, with a focus on the most interesting recent applications related to sensing. During the 20th century, non-Hermitian Hamiltonians (Ĥ ≠ Ĥ†) were introduced to describe open systems [1]. Non-Hermitian Hamiltonians generally exhibit complex eigenvalues, and their eigenstates can be non-orthogonal. Non-Hermitian degeneracies happen at an exceptional point (EP) where two or more eigenvalues and the corresponding eigenstates coalesce simultaneously. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, exploiting the physics of exceptional points. About PT and antiPT symmetries, a lot of research both theoretical and experimental has been carried out, especially in optics, dealing with power oscillations, PT-symmetric lasers, non-reciprocal optical propagation, unidirectional lasing, unidirectional invisibility, coherent-perfect absorption, electromagnetically induced transparency, orbital angular momentum lasers, nonlinear switching, nonlinear quantum spectroscopy, optomechanical actuation, optomechanical amplification, and magneto-optic isolation [2-6]. Among all the studied applications of non-Hermitian Hamiltonians, sensing is one of the most investigated. The reason for this interest relies upon the fact that at the EP the eigenvalues of the system are extremely sensitive to applied perturbations. In particular, given a perturbation ε applied to the system, the eigenvalues (that coalesce at the EP) exhibit a square-root dependence on the perturbation (ε 1/2) [6]. This justifies the theoretically infinite sensitivity for very small perturbations, and the consequent interest for sensing applications [7-10].
Biography
Francesco De Leonardis is IEEE Senior Member, Associate Editor of Sensors (MDPI). He is Associate professor in Electronics at the Department of Electrical and Information Engineering, Politecnico di Bari, Italy. His research interests are in the field of the integrated Optoelectronics, Nanophotonics, Nonlinear and Quantum Photonics. In particular he developed, giving significant and original improvements, the physical-mathematical modelling, the design and the simulations of both passive and active photonic devices for a large number of applications, such as communications, sensing, optical filtering, quantum and space applications. He has published more than 200 papers in international journals and conferences.
