Boundary Conditions and Edge States at Photonic Crystal Interface

Modern nano-electronics faces a problem if reducing power losses and increasing signal transfer speed in interchip and intrachip interconnects. These demands can be satisfied with electrical/optical conversion and implementation of different types of optical interconnects. In the paper, a quantum mechanical theory of interfacial localized electronic states in envelope function approximation is generalized to the description of photonic modes in quasi-periodic media with an abrupt change of optical characteristics, which are localized near the interface. It is shown that there exist both donor-like and acceptor-like photonic modes corresponding the levels in the photonic gap split off either the upper or lower edge of the photonic gap. The description of localized modes regarding envelope functions is presented, and the conditions of mode stability are studied. The possibility of fabricating photonic crystal interfaces with topologically nontrivial edge modes is discussed.