No abstract

A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross-sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is based on the expansion of the Green's function into the resonant states of the system. These can be calculated by any means, including the popular finite element and finite-difference time-domain methods. However, using the resonant-state expansion with a spherically-symmetric analytical basis, such as that of a homogeneous sphere, allows to determine a complete set of the resonant states of the system within a given frequency range. Furthermore, it enables to take full advantage of the expansion of the field outside the system into vector spherical harmonics, resulting in simple analytic expressions. We verify and illustrate the developed approach on an example of a dielectric sphere in vacuum, which has an exact analytic solution known as Mie scattering.

A new rigorous approach for precise and efficient calculation of light propagation along nonuniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoingwave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

The age at onset of motor symptoms in Huntington’s disease (HD) is driven by HTT CAG repeat length but modified by other genes. In this study, we used exome sequencing of 683 patients with HD with extremes of onset or phenotype relative to CAG length to identify rare variants associated with clinical effect. We discovered damaging coding variants in candidate modifier genes identified in previous genome-wide association studies associated with altered HD onset or severity. Variants in FAN1 clustered in its DNA-binding and nuclease domains and were associated predominantly with earlier-onset HD. Nuclease activities of purified variants in vitro correlated with residual age at motor onset of HD. Mutating endogenous FAN1 to a nuclease-inactive form in an induced pluripotent stem cell model of HD led to rates of CAG expansion similar to those observed with complete FAN1 knockout. Together, these data implicate FAN1 nuclease activity in slowing somatic repeat expansion and hence onset of HD.