Complex band structure and bound states in the continuum: a unified theoretical framework

Area of Science:

• Optics and Photonics
• Condensed Matter Physics
• Materials Science

Background:

• Band structure analysis is crucial for understanding wave propagation in periodic media.
• Open systems like photonic crystal (PhC) slabs present challenges due to energy leakage.
• Existing methods using non-Hermitian Hamiltonians rely on manual mode selection and can suffer from basis incompleteness.

Purpose of the Study:

• To develop a systematic first-principles approach for deriving the complex band structure in open periodic systems.
• To elucidate the physical mechanisms behind phenomena like bound states in the continuum (BICs) and exceptional points (EPs).
• To provide a unified framework for studying complex band structure and light confinement.

Main Methods:

• Determining minimal channels in the scattering matrix based on propagating bulk Bloch waves.
• Analyzing interactions between these Bloch waves to reveal the complex band structure.
• Incorporating orthogonally polarized waves to characterize far-field polarization and EPs.

Main Results:

• Two Bloch waves predict the leading-order imaginary frequency and identify accidental BICs.
• Three Bloch waves reveal robust Friedrich-Wintgen and symmetry-protected BICs, along with linewidth behaviors.
• The framework accurately predicts imaginary frequencies, encompasses all known BICs, and tracks their parameter evolution in 2D periodic structures.

Conclusions:

• The presented first-principles approach offers a unified foundation for studying complex band structure in periodic media.
• This method systematically reveals phenomena such as BICs and EPs without relying on manual mode selection.
• Facilitates a deeper exploration of light confinement and wave propagation in open periodic systems.