Resonant-state expansion for planar photonic-crystal structures

Abstract

We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in photonic-crystal structures in terms of the analytic resonant states of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the resonant states of a photonic-crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of the present approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound states in the continuum.

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• Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings
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• Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the resonant-state expansion
• Optical resonances in graded index spheres: A resonant-state expansion study and analytic approximations
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• Exceptional points in perturbed dielectric spheres: A resonant-state expansion study
• Rigorous theory of coupled resonators
• Excitonic bound states in the continuum in van der Waals heterostructure metasurfaces
• Resonant states of structured photonic time crystals