Phase Delay in Grating-Pair Pulse Compressors

Compressors based on a pair of identical parallel gratings are widely used for stretching, compressing and shaping ultrashort light pulses. The basic parameters of a light pulse compressor are the group delay τg, and the group-delay dispersion, Dg, which are calculated from the phase delay ϕ(ω) in accordance with: τg=∂(ω)/∂ω, and Dg=∂2ϕ(ω)/∂ω2, respectively. The expression for the phase delay was first derived more than two decades ago by Treacy /1/. However, it has been always confusing due to an additional phase term whose physical interpretation is not clear /2-4/. According to Treacy, the phase delay between two identical parallel gratings (for the simplified geometry of normal incidence transmission gratings as presented in Fig.1) is given by: Here G denotes the perpendicular distance between the two gratings, d is the grating constant, α is the angle of diffraction, and c is the speed of light.