Large near resonance third order nonlinearity in GaN

We have studied third order nonlinearities, including two-photon absorption coefficient and nonlinear refractive index n ₂, of GaN in below bandgap ultraviolet (UV) wavelength regime by using UV femtosecond pulses. Two-photon absorption was investigated by demonstrating femtosecond UV pulsewidth autocorrelation in a GaN thin film while femtosecond Z-scan measurements revealed information for both n ₂ and . The distribution of n ₂ versus wavelength was found to be consistent with a model described by the quadratic Stark effect, which is the dominant factor contributed to the nonlinear refractive index near the bandgap. Large on the order of 10 cm/GW and large negative n ₂ with a magnitude on the order of several 10^–12 cm²/W were obtained. The at near mid-gap infrared (IR) wavelength was also found to be on the order of several cm/GW by using two-photon-type autocorrelations in a GaN thin film. Taking advantage of the large two-photon absorption at mid-gap wavelengths, we have demonstrated excellent image quality on two-photon confocal microscopy, including two-photon-scanning-photoluminescence imaging and two-photon optical-beam-induced current microscopy, on a GaN Hall measurement sample and an InGaN green light emitting diode.     

Note on Characterization of Projective Spaces

We prove a numerical characterization of ?ⁿ for varieties with at worst isolated local complete intersection quotient singularities. In dimension 3, we prove such a numerical characterization of ?³ for normal ?-Gorenstein projective varieties.     

Cone theorem via Deligne–Mumford stacks

We prove the cone theorem for varieties with LCIQ singularities using deformation theory of stable maps into Deligne–Mumford stacks. We also obtain a sharper bound on −(K _X + D)-degree of (K _X + D)-negative extremal rays for projective -factorial log terminal threefold pairs (X, D).