Abstract
A numerical method combining complex-k band calculations and absorbing boundary conditions for Bloch waves is presented. We use this method to study photonic crystals with Dirac cones. We demonstrate that the photonic crystal behaves as a zero-index medium when excited at normal incidence, but that the zero-index behavior is lost at oblique incidence due to excitation of modes on the flat band. We also investigate the formation of monomodal and multimodal cavity resonances inside the photonic crystals, and the physical origins of their different line-shape features.
Highlights
Photonic crystals (PhCs), known as the semiconductors of electromagnetic waves, have been shown to exhibit a variety of novel properties and promising applications [1,2,3,4,5]
Due to the symmetry of the lattice, a flat band crossing the Dirac point corresponding to magnetic longitudinal modes inevitably appears, and it is known that off-normal incident waves can excite modes from this flat band
We reported on a numerical study of the flat band Bloch modes in a photonic crystal with Dirac cones
Summary
Photonic crystals (PhCs), known as the semiconductors of electromagnetic waves, have been shown to exhibit a variety of novel properties and promising applications [1,2,3,4,5]. To reach the critical requirement on the geometrical parameters to obtain the accidental degeneracy, we set a = 4.66153r This structure has a Dirac cone at the Γ point of its reciprocal lattice, i.e., at the center of the Brillouin zone. The PhC no longer has an effective zero-index when modes from this band are excited This can be shown by calculating the transmission spectrum. The angular transmission spectrum of the PhC has Fabry-Perot-like features [see Fig. 2(a)] This indicates that modes with a non-zero ky have been excited. We present the results from our numerical investigation on these modes and we explore how these resonances are formed
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