Double-resonant processes in χ^(2) nonlinear periodic media

0 Double resonant processes in χ ( 2 ) nonlinear periodic media

In a one-dimensional periodic nonlinear χ (2) medium, by choosing a proper material and geometrical parameters of the structure, it is possible to obtain two matching conditions for simultaneous generation of second and third harmonics. This leads to new diversity of the processes of the resonant three-wave interactions, which are discussed within the framework of slowly varying envelope approa...

Optical Solitons in Periodic Media with Resonant and Off - Resonant Nonlinearities

On Double Periodic Non–Homogeneous Poisson Processes

Non-homogenous Poisson processes with periodic claim intensity rate are proposed as the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long term trends, illustrated by a double-beta intensity function. Here periodicity does not repeat the exact same short term pattern every year, but lets its peak intensity vary over a longer period. This mode...

Equilibrium Quasi-periodic Configurations with Resonant Frequencies in Quasi-periodic Media Ii: Kam Theory

We develop an a-posteriori KAM theory for the equilibrium equations for quasi-periodic solutions in a quasi-periodic Frenkel-Kontorova model when the frequency of the solutions resonates with the frequencies of the substratum. The KAM theory we develop is very different both in the methods and in the conclusions from the more customary KAM theory for Hamiltonian systems or from the KAM theory i...

Equilibrium Quasi-periodic Configurations with Resonant Frequencies in Quasi-periodic Media I: Perturbative Expansions

We consider 1-D quasi-periodic Frenkel-Kontorova models (describing, for example, deposition of materials in a quasi-periodic substratum). We study the existence of equilibria whose frequency (i.e. the inverse of the density of deposited material) is resonant with the frequencies of the substratum. We study perturbation theory for small potential. We show that there are perturbative expansions ...