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We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of…
The Classification of Polarization elements, the polarization affecting optical devices which have a Jones matrix representation, according to the types of eigenvectors they possess, is given a new visit through the Group-theoretical…
Parallel transport of a vector around a closed curve on the surface of a sphere leads to a direction holonomy which can be related with a geometric phase that is equal to the solid angle subtended by the closed curve. Since Pancharatnam…
We demonstrate, in the full vector formulation of electromagnetic fields, that the well-known optical theorem pertinent for the characterization of a scatterer's extinction power and associated cross section can be expressed in a multitude…
In polarization optics, various topological constructs, namely Poincar\'e spheres of different orders, are used to represent uniform and structured polarization distributions. Similarly, there are also structured polarization optical…
The Mueller Matrix Polar Decomposition method decomposes a Mueller matrix into a diattenuator, a retarder, and a depolarizer. Among these elements, the retarder, which plays a key role in medical and material characterization, is modelled…
Characterizing and controlling matter driven far from equilibrium represents a major challenge for science and technology. Here we develop a theory for the optical absorption of electronic materials driven far from equilibrium by resonant…
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show…
In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to retrieve a nonlinear anomaly embedded in…
Polarization-resolved control and measurement of the optical field are essential for a wide range of photonic systems, including coherent communication, polarimetric sensing, and quantum information processing. We present a photonic…
The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…
Polarization independent Mie scattering of building blocks is foundational for constructions of optical systems with robust functionalities. Conventional studies for such polarization independence are generally restricted to special states…
Based on the broken spatial symmetry, we propose a novel scheme for engineering a unidirectional photonic reflector using a one-dimensional atomic lattice with defective cells that have been specifically designed to be vacant. By trapping…
The Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are…
Photons are elementary particles of lights, which have both spin and orbital angular momentum as internal degrees of freedom. Nature of spin is known as polarisation, which is widely used for sunglasses, liquid-crystal displays,…
The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total…
Using the Jones matrix formalism, crystal optical properties of inhomogeneous material consisting of a pile of weakly birefringent plates are analysed in relation to the cell model adopted in polarization tomography of 3D dielectric tensor…
In time-reversal invariant electronic systems the scattering matrix is anti-symmetric. This property enables an effect, designated here as "scattering anomaly", such that the electron transport does not suffer from back reflections,…
We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…
In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…