TAMM STATES AND GAP TOPOLOGICAL NUMBERS IN PHOTONIC CRYSTALS (INVITED PAPER)

Abstract

|We introduce the concept of gap Zak or Chern topological invariants for photonic crystals of various dimensionalities. Speci(cid:12)cally, we consider a case where Tamm states are formed at an interface of two semi-in(cid:12)nite Bragg mirrors and derive the formulism for gap Zak phases of two constituent Bragg mirrors. We demonstrate that gap topological numbers are instrumental in studies of interface states both in conventional and photonic crystals.