Ternary one-dimensional photonic band-gap structures: Dispersion relation,extended phase-matching abilities, and attosecond outlook

The capabilities of one-dimensional photonic band-gap (PBG) structures to s imultaneously 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 thre e different materials is derived. Analysis of this dispersion relation show s that structures of this type provide additional degrees of freedom in dis persion control relative to conventional, binary one-dimensional PBG struct ures. In particular, the increase in the number of layers with different re fractive indices in a unit cell of a PBG structure allows a larger number o f optical fields with different frequencies to be simultaneously phase-matc hed. The possibilities of using this property of ternary PBG structures for synthesizing trains of subfemtosecond pulses are discussed.