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Unidirectional (chiral) emission of light from a circular dipole emitter into a waveguide is only possible at points of perfect circular polarisation (C points), with elliptical polarisations yielding a lower directional contrast. However,…

The functional space of biquaternions is considered on Minkovskiy space. The scalar-vector biquaternions representation is used which was offered by W. Hamilton for quaternions. With introduction of differential operator - a mutual complex…

Mathematical Physics · Physics 2013-02-05 L. A. Alexeyeva

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…

Classical Analysis and ODEs · Mathematics 2022-12-13 Xiaoxiao Hu , Dong Cheng , Kit Ian Kou

Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for…

Applications · Statistics 2019-03-05 Taewoon Kong , Brani Vidakovic

The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…

Functional Analysis · Mathematics 2020-06-15 Aajaz A. Teali

Starting from known results, due to Y. Tian in [Ti; 00], referring to the real matrix representations of the real quaternions, in this paper we will investigate the left and right real matrix representations for the complex quaternions and…

Rings and Algebras · Mathematics 2013-02-18 Cristina Flaut , Vitalii Shpakivskyi

Polaritons are quasiparticles resulting from strong quantum coupling of light and matter. Peculiar properties of polaritons are a mixture of physics usually restricted to one of these realms, making them interesting for study not only from…

Quantum Gases · Physics 2023-08-14 Andrzej Opala , Michał Matuszewski

Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…

Mathematical Physics · Physics 2015-03-09 K. Pushpa , J. C. A. Barata

Various methods of obtaining longitudinally polarized positrons for future linear colliders are reviewed. Special attention is paid to the schemes using circularly polarized high-energy photons for positron production. Most effectively such…

High Energy Physics - Phenomenology · Physics 2009-11-10 V. Strakhovenko , X. Artru , R. Chehab , M. Chevallier

By starting with the simpliest expression of the first order linear wave equation (Dirac's equation) and by confining the elements of the coefficients (matrices) to the quaternions, it is shown that the association of the imaginary bases of…

General Physics · Physics 2008-12-10 Lester C. Welch

We introduce {\em half-whole} dimensions for quaternionic matrices and propose a quaternionic version of the Frobenius-Schur theorem which allows us to obtain the proper quaternionic dimensionality for the representations of the Dirac and…

High Energy Physics - Theory · Physics 2009-10-30 Stefano De Leo

This study investigates the theoretical and computational aspects of quaternion generalized inverses, focusing on outer inverses and {1,2}-inverses with prescribed range and/or null space constraints. In view of the non-commutative nature…

Rings and Algebras · Mathematics 2026-04-30 Neha Bhadala , Ratikanta Behera

We use polarization operators known from quantum theory of angular momentum to expand the $N \times N$ dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties…

Quantum Physics · Physics 2007-05-23 Stanislaw Kryszewski , Mateusz Zachcial

Formal expressions are developed for the general five-fold differential cross section of incoherent $\pi$-photoproduction on the deuteron including beam and target polarization. The polarization observables of the cross section are…

Nuclear Theory · Physics 2009-11-11 H. Arenhoevel , A. Fix

Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the…

Classical Analysis and ODEs · Mathematics 2013-03-08 Roxana Bujack , Hendrik De Bie , Nele De Schepper , Gerik Scheuermann

Precision polarimetry is essential for future e+ e- colliders and requires Compton polarimeters designed for negligible statistical uncertainties. In this paper, we discuss the design and construction of a quartz Cherenkov detector for such…

Instrumentation and Detectors · Physics 2015-06-03 Jenny List , Annika Vauth , Benedikt Vormwald

Locating the zeros of quaternionic polynomials is a fundamental problem with significant implications across scientific and engineering disciplines, yet the noncommutative nature of quaternion multiplication makes it fundamentally more…

Complex Variables · Mathematics 2026-04-14 Ovaisa Jan , Idrees Qasim

We propose and experimentally demonstrate a novel type of polarization rotator which is capable of rotating the polarization plane of a linearly polarized light at any desired angle in either broad or narrow spectral bandwidth. The rotator…

Optics · Physics 2015-02-04 Emiliya Dimova , Andon Rangelov , Elica Kyoseva

Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the…

General Relativity and Quantum Cosmology · Physics 2013-11-11 Katie E. Leonard , T. Prokopec , R. P. Woodard

The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…

Quantum Physics · Physics 2021-01-07 Bertúlio de Lima Bernardo