abstract
One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Drawing on the concepts of band-structure topology, I describe the formation of exponentially localized, topologically protected midgap states [1]. When gain and loss are suitably arranged these states maintain their topological protection and then acquire a selectively tunable amplification rate. This finds applications in the beam dynamics along a photonic lattice and in the lasing of quasi-one-dimensional photonic crystals. I also describe the formation of highly degenerate Landau-like levels in strained photonic honeycomb lattices [2]. These states display a related selective amplification mechanism and could form the basis of a degenerate laser.
[1] Topologically protected midgap states in complex photonic lattices
H. Schomerus, arXiv:1301.0777 [physics.optics].
[2] Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
H. Schomerus and N. Yunger Halpern, Phys. Rev. Lett. 110, 013903 (2013), arXiv:1208.2901 [cond-mat.mes-hall].