Reflection of wave beams, pulses, and packets from apodized and chirped Bragg layered structures

The time delay, space shift and widening of wave packet transmitted and reflected by structures with Bragg mirrors have been investigated. The specific structures such as Bragg mirrors, resonators, and structures with chirp variation of thickness of the “period” have been considered. The calculation has been carried out under the conditions that carrier frequency and incidence angle is in the vicinity of the Bragg resonance. Integral (mass center) and differential (group) estimates of the delay time and space shift have been compared. The conditions for the appearance of anomalous (negative) mass center delay or mass center shift (Goos-Hänchen shift) of the reflected wave packet have been determined. The shape transformations of the wave packet illuminating periodic and quasiperiodic apodized Bragg reflectors have been under consideration. Spatial apodization of permittivity contrast yields much smaller shape deformation of the transmitted wave packet upon incidence at angles and carrier frequency near the edges of reflection band, as well in Bragg reflection band, in comparison with phenomena in similar periodic structures. The values of group delay for layered structures with a small chirp variation of optical (electrical) thickness of the period along longitudinal coordinates have been experimentally obtained in microwave range.