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Previously, the infrared permittivity tensor of monoclinic β-Ga 2 O 3 crystals has been determined using ellipsometry reflection measurements from two differently oriented monoclinic β-Ga 2 O 3 crystals with surfaces parallel to (010) and (−201). The (010) surface places the crystallographic a-c plane in the table of the instrument. The permittivity tensor consists of four complex values, and in order to compute it, four or more combinations of measurements are required at selected table rotations and incidence angles. However, the (010) orientation also places the transverse optical (TO) modes with Au symmetry parallel to the z-axis of the instrument, and we find that these modes are not fully excited and, hence, not measurable due to underlying selection rules. This makes additional measurements on surfaces other than (010) necessary. The second orientation has been the (−201) crystal, which places the crystallographic b axis in the plane of the table to access the transverse Au phonons. In prior work, the overall tensor has been determined by combining measurements of the two crystal orientations [Schubert et al., Phys. Rev. B 93, 125209 (2016)]. The goal of the work here is to find single crystal orientations for which all TO modes can be determined from measurements. The use of a set of measurements employed for such a single crystal is inextricably linked to the choice of incidence angles and table rotations. Consequently, determining suitable angles for these is linked to the selection of a crystal orientation, which is, therefore, an integral part of the overall goal. The TO contribution to the permittivity strongly dominates at or near the TO mode wavenumber resonances and, therefore, are used in this work to identify suitable orientations for a single crystal. Any such crystal orientation will also provide measurements useful to compute permittivity across the entire measured wavenumber range. In principle, any crystal orientation that does not place the direction of any TO mode at or near the z-axis may be suitable due to the underlying physics and mathematics of the problem. We discuss which of these measurement parameters contain the most sensitivity for the (111) orientation. For accuracy, we seek the best or very good orientations. Our investigation follows a previously demonstrated approach where at a single wavelength, the full tensor of an orthorhombic absorbing crystal was obtained from a low-symmetry surface of stibnite [Schubert and Dollase, Opt. Lett. 27, 2073 (2002)]. We discuss which of these measurement parameters contain the most sensitivity for the (111) orientation. The methods presented here will also be useful for other monoclinic materials as well as other materials of different crystal structures, including orthorhombic and triclinic materials. 

Abstract In this paper, we present the first high‐speed video observation of a cloud‐to‐ground lightning flash and its associated downward‐directed Terrestrial Gamma‐ray Flash (TGF). The optical emission of the event was observed by a high‐speed video camera running at 40,000 frames per second in conjunction with the Telescope Array Surface Detector, Lightning Mapping Array, interferometer, electric‐field fast antenna, and the National Lightning Detection Network. The cloud‐to‐ground flash associated with the observed TGF was formed by a fast downward leader followed by a very intense return stroke peak current of −154 kA. The TGF occurred while the downward leader was below cloud base, and even when it was halfway in its propagation to ground. The suite of gamma‐ray and lightning instruments, timing resolution, and source proximity offer us detailed information and therefore a unique look at the TGF phenomena.