Exceptional points for resonant states on parallel circular dielectric cylinders

Abstract

Exceptional points (EPs) are special parameter values of a non-Hermitian eigenvalue problem where eigenfunctions corresponding to a multiple eigenvalue coalesce. In optics, EPs are associated with a number of counter-intuitive wave phenomena, and have potential applications in lasing, sensing, mode conversion and spontaneous emission processes. For open photonic structures, resonant states are complex-frequency solutions of the Maxwell's equations with outgoing radiation conditions. For open dielectric structures without material gain or loss, the eigenvalue problem for resonant states can have EPs, since it is non-Hermitian due to radiation losses. For applications in nanophotonics, it is important to understand EPs for resonant states on small finite dielectric structures consisting of conventional dielectric materials. To achieve this objective, we study EPs of resonant states on finite sets of parallel infinitely-long circular dielectric cylinders with subwavelength radii. For systems with two, three and four cylinders, we develop an efficient numerical method for computing EPs, present examples for second and third order EPs, and highlight their topological features. Our work provides insight to understanding EPs on more complicated photonic structures, and can be used as a simple platform to explore applications of EPs.

Exceptional points of Bloch eigenmodes on a dielectric slab with a periodic array of cylinders

“…A theoretical justification for the second condition dλ 1 /dk = 0 is given in Ref. [24]. Since λ 1 is in general complex, the above two conditions are equivalent to four real conditions.…”

“…Since a balanced gain and loss is not always desirable, it is of significant interest to explore EPs in open photonic systems without material loss and artificial gain. Due to the possible radiation losses, EVPs for open systems are non-Hermitian and can have EPs [19][20][21][22][23][24]. For Maxwell's equations, the standard EVP formulation regards the frequency ω as the eigenvalue.…”

Exceptional points in dielectric spheroid

“…Since it is not always easy or desirable to keep a balanced gain and loss in an optical system there is of significant interest to explore EPs and their applications in non-PT-symmetric optical systems. Currently, there exist studies concerning EPs for resonant states in extended periodic dielectric structures sandwiched between two homogeneous half-spaces [25][26][27][28], dual-mode planar optical waveguides [29] and plasmonic waveguide [30], layered structures [31][32][33], two infinitely long dielectric cylinders [34][35][36][37][38] and even single rod with deformed cross-section [36,[39][40][41][42]. As for compact dielectric resonators we distinguish the only study of EPs in compact coated dielectric sphere [43].…”

Multimode parity-time and loss-compensation symmetries in coupled waveguides with loss and gain

“…In the PT -symmetric systems, the EPs mark the points of phase transitions between the PT -symmetric phase and the phase with spontaneously broken PT symmetry. It is important to emphasize, however, that the EPs are the general phenomenon observed also in purely passive systems (such as whispering-gallery-mode microresonators [16], ring cavities [17], and anisotropic waveguides [18]) and even in the systems with radiative loss only [19].…”