Eigenmode in a misaligned triangular optical cavity

We derive relationships between various types of small misalignments on a triangular Fabry-Perot cavity and associated geometrical eigenmode changes. We focus on the changes of beam spot positions on cavity mirrors, the beam waist position, and its angle. A comparison of analytical and numerical results shows excellent agreement. The results are applicable to any triangular cavity close to an isosceles triangle, with the lengths of two sides much bigger than the other, consisting of a curved mirror and two flat mirrors yielding a waist equally separated from the two flat mirrors. This cavity shape is most commonly used in laser interferometry. The analysis presented here can easily be extended to more generic cavity shapes. The geometrical analysis not only serves as a method of checking a simulation result, but also gives an intuitive and handy tool to visualize the eigenmode of a misaligned triangular cavity.Comment: 17 pages, 21 figure

Local Energy Gap in Deformed Carbon Nanotubes

The effects of graphite surface geometrical deformation on the dynamics of conducting electrons are investigated theoretically. The analysis is performed within the framework of a deformation-induced gauge field and corresponding deformation-induced magnetic field. It is shown that the latter gives a local energy gap along the axis of a deformed nanotube. We compare our energy gap results with experimental data on energy gaps in nanotubes and peapods. We also discuss the mixing of two Fermi points and construct a general model of low energy dynamics, including a short-range deformation of the graphite sheet. This model is equivalent to the Weyl equation in {\it U}(1) Abelian and {\it SU}(2) non-Abelian deformation-induced gauge fields.Comment: 18 pages, 4 figures, corrected typos, added references, improved presentation (v4, published version