A study on the optical non-linearity near the band gap energy region of CuCl by the non-degenerate reflected four-wave mixing

We have demonstrated three beam non-degenerate reflected four-wave mixing (reflected FWM) in which two driving fields have the same photon energy (?ω₁) and the monitor and the resulting mixed light fields have another equal photon energy (?ω₂). Mixed light has been observed with the driving field's energy from Z₃ exciton up to band gap energy when ?ω₂ is fixed in the Z₃ and Z_1,2 exciton resonance region. The mechanism by which such non-degenerate optical non-linearity occurs is discussed according to a calculation by a simple model.     

Evolution inclusions governed by subdifferentials in reflexive Banach spaces

The existence, uniqueness and regularity of strong solutions for Cauchy problem and periodic problem are studied for the evolution equation: where is the so-called subdifferential operator from a real Banach space V into its dual V*. The study in the Hilbert space setting (V = V* = H: Hilbert space) is already developed in detail so far. However, the study here is done in the V–V* setting which is not yet fully pursued. Our method of proof relies on approximation arguments in a Hilbert space H. To assure this procedure, it is assumed that the embeddings are both dense and continuous.