Anomalous Index of Refraction in Photonic Bandgap Materials

Near the gap in a photonic bandgap material the effective index of refraction can become less than unity and in fact can approach zero at the band edge itself—leading to ultra-refractive optical effects. We illustrate this effect quantitatively in a simple one-dimensional Kronig-Penney model of a three-dimensional bandgap structure. As a complement to index-enhancing schemes involving lasing without inversion, ultra-refractive optics with photonic band materials has many applications, including laser accelerators and lenses of ultra-short focal lengths.