Multicomponent one-dimensional photonic band-gap structures: dispersion relations and extended phase-matching abilities

Abstract

The capabilities of one-dimensional photonic band-gap (PBG) structures to simultaneously phase-match several optical fields with different frequencies propagating in a dispersive medium are examined. A dispersion relation for an infinite one-dimensional PBG structure whose unit cell consists of three different materials is derived. Analysis of this dispersion relation shows that structures of this type provide additional degrees of freedom in dispersion control relative to conventional, binary one-dimensional PBG structures. In particular, the increase in the number of layers with different refractive indices in a unit cell of a PBG structure allows a larger number of optical fields with different frequencies to be simultaneously phase-matched. The possibilities of using this property of ternary PBG structures for synthesizing trains of subfemtosecond pulses are discussed.