ABCD-matrix elements for a chirped diffraction grating

The ABCD-matrix elements for a chirped diffraction grating, used at an arbitrary angle of incidence and in an arbitrary diffraction order, are derived both for the tangential and sagittal planes. The derivation is based on the notion of optical path difference and assumes a spherical chirped grating used in reflection in air or vacuum, but the results apply to transmission grating as well. The matrix elements are then employed to establish the effective focal length of the chirped grating and the position of its cardinal points. In this paper, by chirped gratings (also called varied line-space gratings or varied pitch gratings), it is meant gratings whose grooves are straight and parallel but not equally spaced.