Some focusing properties of chirped gratings

In the past the focusing properties of chirped grating structures have been investigated in various disciplines including optics, acousto-optics and acoustics. In this paper we present the results of a detailed theoretical and experimental study of one such amplitude grating structure, namely the chirped optical diffraction grating, although many of the conclusions are of more general validity. We derive some useful fundamental properties of such focusing gratings, and show that to first order their behaviour is similar to that of various other classical components such as focusing lenses, grating spectrometers and matched filters for chirped waveforms. However, we also describe a range of second-order differences in behaviour, for example concerning the physical location of the multiple foci, and the sidelobe structures within and perpendicular to the focal plane. For devices of large numerical aperture we demonstrate the advantages of using a non-linear grating structure — for example, for sidelobe suppression in the focal plane - and point out that surface acoustic wave (SAW) techniques can be used to generate the non-linear chirp waveforms necessary to implement such gratings in acousto-optic devices.