Omnidirectional reflection by multilayer dielectric mirrors

Periodic structures reflect strongly at frequencies and angles of incidence corresponding to photonic bandgaps. It has recently been shown that for a suitable choice of high and low refractive indices n(h) and n(e), a high-low dielectric multilayer can reflect strongly at all angles of incidence. An accurate and simple analytic approximation for the location of the band edges for the s and p polarizations is given. The region in the (n(e), n(h)) plane where omnidirectional reflection occurs is determined. This region lies above a curve which has its minimum value of n(h) (approximate to 2.247n(1)) at n(e) approximate to 1.492n(1), where n(1) is the refractive index of the medium of incidence. The minimum occurs when the optical paths in the high and low refractive index layers are in the ratio 1.362 to 1.