Exceptional Bound States in the Continuum (2309.01501v2)

Abstract: Bound states in the continuum (BICs) and exceptional points (EPs) are unique singularities of non-Hermitian systems. BICs demonstrate enhancement of the electromagnetic field at the nanoscale, while EPs exhibit high sensitivity to small perturbations. Here, we demonstrate that several BICs can be merged into one EP, forming an EP-BIC. The resulting state inherits properties from both BICs and EP, namely, it does not radiate and shows extremely high sensitivity to perturbations. We validate the developed theory with numerical simulations and demonstrate the formation of second and third-order EP-BICs in stacked dielectric metasurfaces. We also show that the losses of the resulting leaky resonances exhibit an anomalous behavior when the unit cell is broken, which differs from the asymptotics commonly attributed to BICs.

• The paper introduces EP-BICs by merging bound states in the continuum with exceptional points through intrinsic loss in dielectric metasurfaces.
• Numerical simulations validate the framework by demonstrating second and third-order EP-BICs in bilayer and trilayer systems.
• Practical implications include enhancing lossless optical devices and developing highly sensitive photonic sensors.

Exceptional Bound States in the Continuum

The paper addresses a novel configuration in the field of non-Hermitian physics, exploring the intersection between Bound States in the Continuum (BICs) and Exceptional Points (EPs). BICs are known for their unique characteristic of residing in the continuum of radiation modes while not radiating, translating into a theoretically infinite Q-factor. Conversely, EPs, which emerge in non-Hermitian systems, offer high sensitivity to perturbations, owing to their non-Hermitian degeneracy where eigenvalues and their vectors coalesce.

The research presented demonstrates the potential to synthesize both phenomena into a singular state, termed an EP-BIC. This state amalgamates the properties of BICs and EPs, retaining the non-radiating attribute of BICs while simultaneously being highly sensitive to external perturbations characteristic of EPs. The authors develop a theoretical framework and validate it through numerical simulations, showing the feasibility of creating second and third-order EP-BICs in dielectric metasurfaces.

Key Findings and Methodology

• Theoretical Framework: The paper utilizes an effective Hamiltonian formalism to describe the emergence of EP-BICs. The key differentiation allowing such a singularity is the introduction of intrinsic (dissipative) loss into conventional BIC systems, which overcomes the inherent limitation of lossless systems that prevent BICs from coalescing into EPs.
• Numerical Validation: The merging of several BICs into an EP was demonstrated through numerical simulations involving stacked dielectric metasurfaces. A bilayer metasurface in particular showcased the formation of second-order EP-BICs, while a trilayer metasurface exhibited the characteristics of a third-order EP-BIC. These metasurfaces were modeled to support symmetry-protected BICs, and by introducing small asymmetry through intrinsic losses, the EP conditions were satisfied.
• Implications of Symmetry Breaking: Upon minor symmetry breaking in these EP-BIC systems, the induced quasi-BICs showed an anomalous response in their radiative losses. Unlike traditional BICs which exhibit linear loss responses to perturbation, the EP-BICs demonstrate a square-root-like dependency due to their exceptional point characteristics.

Practical and Theoretical Implications

The theoretical and empirical findings in this paper present notable implications for the design and utilization of optical systems. The EP-BICs identified maintain infinite radiative Q factors due to the BIC component, which could significantly enhance devices where lossless propagation is crucial, such as in lasers or photonic crystal designs. Furthermore, the high sensitivity derived from the EP nature of these states makes them ideal for sensing applications where minute changes need to be detected accurately.

The synthesis of EPs and BICs into a single higher-order state could also influence future developments in meta-material design, enabling new capabilities in controlling light-matter interactions, enhancing light capture, or designing advanced cloaking mechanisms.

Future Directions

The paper opens numerous avenues for future research. Notably, it invites exploration into the existence and application of EP-BICs in other physical domains, such as acoustics or quantum systems. Additionally, the possibility of higher-order EP-BICs beyond third order could be an area to explore to further leverage the sensitivity improvements and non-radiating properties demonstrated.

The interplay between dissipation and radiative features in these exceptional bound states offers a new perspective for designing materials that exploit their unique spectral properties. As this work interfaces two complex phenomena in non-Hermitian physics, it paves the path for a deeper understanding of wave dynamics in complex media.