Related papers: On the Realization and Analysis of Circular Harmon…
This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field…
Structured illumination enables the tailoring of an imaging device's optical transfer function to enhance resolution. We propose the incorporation of a temporal periodic modulation, specifically a rotating mask, to encode multiple transfer…
Inter pixel capacitance (IPC) is a deterministic electronic coupling resulting in a portion of signal incident on one pixel of a hybridized detector array being measured in adjacent pixels. Data collected by light sensitive HgCdTe arrays…
Conventional spectrometer and polarimeter systems rely on bulky optics, fundamentally limiting compact integration and hindering multi-dimensional optical sensing capabilities. Here, we propose a spectropolarimeter enabled by…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the…
Mechanical spectroscopy, i.e. cyclic deformations at varying frequencies, is used theoretically and numerically to measure dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency THz regime where…
Polarimetric imaging is one of the most effective techniques for high-contrast imaging and characterization of circumstellar environments. These environments can be characterized through direct-imaging polarimetry at near-infrared…
Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…
The two-point complex coherence function constitutes a complete representation for scalar quasi-monochromatic optical fields. Exploiting dynamically reconfigurable slits implemented with a digital micromirror device, we report on…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Circular dichroism spectroscopy is an essential technique for understanding molecular structure and magnetic materials, but spatial resolution is limited by the wavelength of light, and sensitivity sufficient for single-molecule…
We derive expressions for the scattering, extinction and conversion of the chirality of monochromatic light scattered by bodies which are characterized by a T-matrix. In analogy to the conditions obtained from the conservation of energy,…
A polarimetric synthetic aperture radar (PolSAR) system, which uses multiple images acquired with different polarizations in both transmission and reception, has the potential to improve the description and interpretation of the observed…
We have experimentally studied polarization properties of the two-dimensional coupled photonic crystal microcavity arrays, and observed a strong polarization dependence of the transmission and reflection of light from the structures - the…
The identification of a universal biosignature that could be sensed remotely is critical to the prospects for success in the search for life elsewhere in the universe. A candidate universal biosignature is homochirality, which is likely to…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having…
Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we…