Exceptional points of resonant states on a periodic slab

Abdrabou, Amgad; Lu, Ya Yan

doi:10.1103/physreva.97.063822

Cited by 20 publications

(25 citation statements)

References 34 publications

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“…Using a highly accurate numerical method [12], we calculate guided, resonant, improper and leaky modes for a periodic slab. In Fig.…”

Section: Periodic Slabmentioning

confidence: 99%

“…The BICs are isolated guided modes above the lightline, and they can also be regarded as special resonant modes with infinite quality factors [5]. EPs of resonant modes have been found on various open dielectric structures [9][10][11][12][13]. This is not unexpected, since the eigenvalue problems for res- * Corresponding author: mabdrabou2-c@my.cityu.edu.hk onant modes on open structures are non-Hermitian due to radiation losses.…”

Section: Introductionmentioning

confidence: 96%

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Indirect link between resonant and guided modes on uniform and periodic slabs

Abdrabou¹,

Lu²

2019

Phys. Rev. A

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A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline, but isolated guided modes may exist above the lightline and they are the so-called bound states in the continuum. Resonant modes are usually studied above the lightline (defined using the real part of the complex frequency), but they are not connected to the guided modes on the lightline. In this work, through analytic and numerical calculations for uniform and periodic slabs, we establish an indirect link between the resonant and guided modes. It is shown that as the (Bloch) wavenumber is increased, a resonant mode continues its existence below the lightline, until it reaches its end at an Exceptional Point (EP) where a pair of improper modes emerge, and one branch of improper modes eventually approaches the lightline at the starting point of a guided mode. Leaky modes with a real frequency and a complex (Bloch) wavenumber (propagation constant) are also related to the improper modes. They emerge at EPs in eigenvalue formulations where the frequency is regarded as a parameter. Our study is based on a non-Hermitian eigenvalue formulation that includes resonant, improper and leaky modes, and provides a complete picture for different kinds of eigenmodes on uniform and periodic slabs.

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“…Using a highly accurate numerical method [12], we calculate guided, resonant, improper and leaky modes for a periodic slab. In Fig.…”

Section: Periodic Slabmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Indirect link between resonant and guided modes on uniform and periodic slabs

Abdrabou¹,

Lu²

2019

Phys. Rev. A

Self Cite

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“…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].…”

Section: Introductionmentioning

confidence: 99%

Exceptional points in dielectric spheroid

Bulgakov,

Pichugin,

Sadreev

2021

Preprint

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Evolution of resonant frequencies and resonant modes as dependent on the aspect ratio is considered in a dielectric high index spheroid. Because of rotational symmetry of the spheroid the solutions are separated by the azimuthal index m. By the two-fold variation of a refractive index and the aspect ratio we achieve exceptional points (EPs) at which the resonant frequencies and resonant modes are coalesced in the sectors m = 0 for both TE and TM polarizations and m = 1.

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“…Similar structures, also with low‐order exceptional points, have been considered in Refs. 16–18. By asymptotic exceptional points, we mean parameter values such that the eigenvalues and eigenvectors coincide at leading order in the asymptotic parameters.…”

Section: Introductionmentioning

confidence: 99%

High‐order exceptional points and enhanced sensing in subwavelength resonator arrays

et al. 2020

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Systems exhibiting degeneracies known as exceptional points have remarkable properties with powerful applications, particularly in sensor design. These degeneracies are formed when eigenstates coincide, and the remarkable effects are exaggerated by increasing the order of the exceptional point (i.e., the number of coincident eigenstates). In this work, we use asymptotic techniques to study scriptPT‐symmetric arrays of many subwavelength resonators and search for high‐order asymptotic exceptional points. This analysis reveals the range of different configurations that can give rise to such exceptional points and provides efficient techniques to compute them. We also show how systems exhibiting high‐order exceptional points can be used for sensitivity enhancement.

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Exceptional points of resonant states on a periodic slab

Cited by 20 publications

References 34 publications

Indirect link between resonant and guided modes on uniform and periodic slabs

Indirect link between resonant and guided modes on uniform and periodic slabs

Exceptional points in dielectric spheroid

High‐order exceptional points and enhanced sensing in subwavelength resonator arrays

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