Analytical Lah-Laguerre optical formalism for perturbative chromatic dispersion.

We present a generalized perturbative analytical formalism for evaluation and optimization of the chromatic dispersion of complex ultrafast optical systems. Notably, we identify polynomial and recursive relations associated with the chromatic dispersion orders that are identical to the Lah and Laguerre transforms. We explicitly outline the first ten dispersion terms and dispersion slope parameters and visualize the significance of the chromatic dispersion orders for several advanced ultrafast optical and photonic systems consisting of various optical materials and nanostructures, grating and prism-pair compressors, and hollow-core photonic anti-resonant fibers. The derived simple hypergeometric transforms are applicable for evaluation of infinitely high orders for any type of frequency-dependent phase and can facilitate the optimization of complex optical systems with controlled dispersion balance at the single-cycle waveform extreme.