Flat bands and quasi-bound states in the continuum in a photonic Moiré lattice
Ibrahim Nasidi, Ran Hao, Shangzhong Jin, Er‐Ping Li
Abstract
This paper proposes flat bands and quasi-bound states in the continuum (Q-BIC) in a moiré lattice. In addition to the inter-layer coupling and small rotation angle, we show that the inter-node coupling in a single-layer moiré lattice can be controlled to obtain moiré flat bands. Unlike any flat bands reported in lattices such as kagome, rhombus, Lieb, and stub, we show that the moiré lattice exhibits both singular and non-singular flat bands simultaneously. We investigate the flat band’s eigenmodes to confirm their flatness and assess their singularity. The robustness of the flat bands to variation of background permittivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:mrow> </mml:math> is studied. Moreover, by further engineering the inter-node distance, the moiré flat band states change to a quasi-bound state at a non-zero wave vector. The Q-BIC exhibit an ultra-high quality factor (Q-factor) of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>2.7142</mml:mn> <mml:mo>×</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> , ultra-low mode volume of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>0.214318</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mtext>µ</mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> </mml:math> , and very narrow linewidth centred at 350.54 THz. We demonstrate the capability of the Q-BIC for lasing and nanocavity applications. Our results show that a single-layer photonic moiré lattice provides a suitable platform to explore fundamental phenomena related to flat band systems.