Chirped quasi-phase-matching with Gauss sums for production of biphotons

We study the theory of linearly chirped biphoton wave packets produced in two basic quasi-phase-matching configurations: chirped photonic-like crystals and chirped aperiodically poled crystals. The novelty is that these structures are considered as definite assembles of nonlinear layers that leads to a detailed description of spontaneous parametric down-conversion processes through the discrete Gauss sums. In this approach, the spectra of biphoton wave packets for each of the two presented quasi-phase-matching configurations display new important properties that were not obtained and explained in the standard phenomenological approach.