Electrical tunability due to coalescence of exceptional points in parity-time symmetric waveguides

Abstract

We demonstrate theoretically the electric tunability due to coalescence of exceptional points in PT-symmetric waveguides bounded by imperfect conductive layers. Owing to the competition effect of multimode interaction, multiple exceptional points and PT phase transitions could be attained in such a simple system and their occurrences are strongly dependent on the boundary conductive layers. When the conductive layers become very thin, it is found that the oblique transmittance and reflectance of the same system can be tuned between zero and one by a small change in carrier density. The results may provide an effective method for fast tuning and modulation of optical signals through electrical gating. PACS numbers:A wide class of non-Hermitian Hamiltonians with parity-time (PT) symmetric complex potentials have been extensively studied since Bender et al. [1,2] showed such systems can exhibit purely real spectra. By tuning the degree of non-Hermiticity, PT-symmetric systems may experience an abrupt phase transition between PTsymmetric phase with a real spectrum and PT-broken phase with a complex spectrum. The transition point is called the exceptional point (EP), at which two or more eigenvalues coincide. The existence of EPs have been investigated in various types of PT-symmetric physical systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], giving rise to a wide range of counterintuitive wave phenomena, such as loss-induced transparency [3], nonreciprocal Bloch oscillation [4], unidirectional invisibility [5][6][7], coexisting coherent perfect absorption and lasing [8,9], enhanced spontaneous emission [10], and enhanced nano-particle sensing [11].Recently, there has been strong interest in more complex phenomena closely related to the occurrence of EPs in multistate systems and high-order EPs [10,[20][21][22][23][24][25][26][27]. Multiple optical waveguide systems [20,21] and photonic crystals [10,22] have been proposed for the realization of high-order EPs. For example, Ding et al. [22] demonstrated theoretically two different kinds of EP evolution process in one-dimensional PT-symmetric photonic crystals. One type is the occurrence of a ring of EPs, leading to the restoration behavior of PT symmetry phase. Another type is the coalescence of EPs to form high-order singularity. Zhen et al. [23] observed experimentally that a ring of EPs could be supported near a Dirac-like cone in a two-dimensional photonic crystal slab. Also, the emergence and interaction of multiple EPs have been studied in a four-state acoustic system [24], exhibiting richer physical behaviors than those seen in two-state systems.Taking the advantage of the abrupt change near an EP, one may tune the properties of a system drastically by a small change in certain parameters. However, previous studies on evolution process of EPs and various types of phase transitions, are mostly on tuning by geometrical parameters. In this Letter, we demonstrate that the PTsymmetric plasmonic waveguide bounded by imperfect conducting materials...

Coalescence of nonreciprocal exceptional points in magnetized PT -symmetric systems

“…It is worthy of noting that the occurrence of coalescence and rebifurcation of EPs shown above is attributed to the competition interacting effect among multiple states, which has also been discussed and analyzed in other multistate systems [19,21,22]. Remarkably, the external magnetic field applied on our proposed PT -symmetric waveguide could effectively tune the interaction among multiple states, but in a nonreciprocal manner, giving rise to the different evolution process between positive and negative guided modes.…”

“…Recently, more complex phenomena involved in the occurrence and evolution of EPs have been theoretically proposed and experimentally observed in PT -symmetric multistate systems [18][19][20][21][22][23][24][25][26][27][28]. For example, Alaeian and Dionne [18] demonstrated that in a five-layer plasmonic waveguide having PT symmetry, coalescence and evolution of EPs could be tuned to support positive or negative refractive indices by changing the coupling between the waveguide layers.…”

“…Richer physical behaviors such as phase space with distinct topological properties could be present in a four-state acoustic system [21]. Given the abrupt change of system phase near an EP, one may tune the properties of a system flexibly by a small variation of certain external parameters [22][23][24][25].…”

Extraordinary transmission and reflection in PT -symmetric two-segment-connected triangular optical waveguide networks with perfect and broken integer waveguide length ratios*

“…Similar to the 𝒫𝒯 -symmetric mechanical system, 𝒫𝒯 -symmetric optical systems can produce extraordinary optical features and phenomena near the spontaneous 𝒫𝒯 -symmetric breaking point. Subsequently, 𝒫𝒯 -symmetric optical systems, such as 𝒫𝒯symmetric optical lattices, [6][7][8][9][10] optical waveguides, [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] inhomogeneous nonlinear optical media, [30] and graphene, [31,32] have been widely investigated and some extraordinary optical characteristics, for instance, birefringence, [6] unidirec-tional invisibility, [8,9] ultrastrong absorption, [31] and singlemode lasing, [33,34] have been found.…”