An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g _n, in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.

The translational addition theorem for the spherical vector wave functions (SVWFs) of the first kind is derived in an integral form by the use of the relations between the SVWFs and cylindrical vector wave functions. The integral representation provides a theoretical procedure for the calculation of the beam shape coefficients in the generalized Lorenz–Mie theory. The beam shape coefficients in the cylindrical or spheroidal coordinates, which correspond to an arbitrarily oriented infinite cylinder or spheroid, can be obtained conveniently by using the addition theorem for the SVWF under coordinate rotations and the expansions of the SVWF in terms of the cylindrical or spheroidal vector wave functions.

Structural health monitoring is currently a crucial measure for the analysis of structural safety. As a structural asset management approach, it can provide a cost-effective measure and has been used successfully in a variety of structures. In recent years, the development of fiber optic sensing technology and vision sensing technology has led to further advances in structural health monitoring. This paper focuses on the basic principles, recent advances, and current status of applications of these two sensing technologies. It provides the reader with a broad review of the literature. It introduces the advantages, limitations, and future directions of these two sensing technologies. In addition, the main contribution of this paper is that the integration of fiber optic sensing technology and vision sensing technology is discussed. This paper demonstrates the feasibility and application potential of this integration by citing numerous examples. The conclusions show that this new integrated sensing technology can effectively utilize the advantages of both fields.

For practical wireless communication links, one of the critical challenges is the random fluctuation of turbulence that will impair link performance. Here a transmission model of partially coherent elegant Laguerre–Gaussian (ELG) beams in oceanic turbulence is established. An analytical formula for channel capacity of a partially coherent ELG beam propagating through a turbulent ocean is derived. The effects of oceanic turbulence on the evolution of channel capacity performance are studied quantitatively in a series of numerical simulations. Research results show that decreasing the rate of dissipation of mean-square temperature and ratio of temperature to salinity, as well as increasing the dissipation rate of turbulent kinetic energy per unit mass of fluid of a turbulent ocean can significantly improve communication channel capacity. Furthermore, choosing optimum beam source parameters is favorable to mitigate the influence of oceanic turbulence. Results also show that in the underwater turbulence, the partially coherent ELG beams are more affected by turbulence as compared to the fully coherent ELG beams. These study results may provide potential help in designing the free-space optical vortex communication systems.

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