Related papers: Quaternionic representation and design of depolari…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
This work provides a quaternioinc reprsentation for real symplectic matrices in dimension four, analogous to the pair of unit quaternions representation for special orthogonal matrices. In the process of finding formulae for this…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
Recently, novel quaternion-valued wavelets on the plane were constructed using an optimisation approach. These wavelets are compactly supported, smooth, orthonormal, non-separable and truly quaternionic. However, they have not been tested…
We demonstrate an isotropic depolarizing channel with a controllable degree of depolarization. The depolarizer is composed of four birefringent crystals and half-wave plates. Quantum process tomography results of the depolarization effect…
We show that calculation of a final fermion polarization (for a pure initial state) is equivalent to the problem of looking for complete polarization axis of bispinor. This gives the method for calculation of polarization applicable both…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
The control of polarization, an essential property of light, is of wide scientific and technological interest. Polarizer is an indispensable optical element for direct polarization generations. Except common linear and circular…
It is well known that state transformation from one polarization state to another can be achieved with a minimal gadget consisting of two quarter waveplates. A constructive, geometric approach is presented, which provides a direct…
While any two-dimensional mixed state of polarization of light can be represented by a combination of a pure state and a fully random state, any Mueller matrix can be represented by a convex combination of a pure component and three…
We present an operator approach to the description of photon polarization, based on Wigner's concept of elementary relativistic systems. The theory of unitary representations of the Poincare group, and of parity, are exploited to construct…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
We theoretically introduce several types of arbitrary polarization retarders constructed from sequences of half-wave and quarter-wave plates, each rotated at specific angles. By integrating these arbitrary polarization retarders with…
Based on a recent proposal [Phys. Rev. A 71, 062337 (2005)], we have experimentally realized two photon polarization qutrits by using non-maximally entangled states and linear optical transformations. By this technique high fidelity…
We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two…
In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.
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…
We theoretically propose and experimentally demonstrate a novel composite polarization controller. With our design, which comprises two half-wave plates and two quarter-wave plates the retardance and rotation can be changed continuously by…