Hamilton–Jacobi theory for gauge field theories

Recently, M. de León et al. (Campos et al., 2015) have developed a geometrical description of Hamilton–Jacobi theory for multisymplectic field theory. In our paper we analyze in the same spirit a special kind of field theories which are gauge field theories. The Hamilton–Jacobi theory for this kind of fields is shown.This work has been partially supported by MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa projects SEV-2011-0087 and SEV-2015-0554

Transparency of Semi-Insulating, n-Type, and p-Type Ammonothermal GaN Substrates in the Near-Infrared, Mid-Infrared, and THz Spectral Range

GaN substrates grown by the ammonothermal method are analyzed by Fast Fourier Transformation Spectroscopy in order to study the impact of doping (both n- and p-type) on their transparency in the near-infrared, mid-infrared, and terahertz spectral range. It is shown that the introduction of dopants causes a decrease in transparency of GaN substrates in a broad spectral range which is attributed to absorption on free carriers (n-type samples) or dopant ionization (p-type samples). In the mid-infrared the transparency cut-off, which for a semi-insulating GaN is at ~7 µm due to an absorption on a second harmonic of optical phonons, shifts towards shorter wavelengths due to an absorption on free carriers up to ~1 µm at n ~ 1020 cm−3 doping level. Moreover, a semi-insulating GaN crystal shows good transparency in the 1–10 THz range, while for n-and p-type crystal, the transparency in this spectral region is significantly quenched below 1%. In addition, it is shown that in the visible spectral region n-type GaN substrates with a carrier concentration below 1018 cm−3 are highly transparent with the absorption coefficient below 3 cm−1 at 450 nm, a satisfactory condition for light emitting diodes and laser diodes operating in this spectral range