PROPOSAL OF NEW OPTICAL ELEMENTS

A overview of our patented proposals of new optical elements is presented. The elements are suitable for laser pulse analysis, telescopy, X-ray microscopy and X-ray telescopy. They are based on the interference properties of light: a special grating for a double slit pattern, parabolic strip imaging for a telescope, and Bragg’s condition for X-ray scattering on a slice of a single crystal for X-raymicroscopy and X-ray telescopy

THE SHMUSHKEVICH METHOD FOR HIGHER SYMMETRY GROUPS OF INTERACTING PARTICLES

About 60 years ago, I. Shmushkevich presented a simple ingenious method for computing the relative probabilities of channels involving the same interacting multiplets of particles, without the need to compute the Clebsch-Gordan coefficients. The basic idea of Shmushkevich is “isotopic non-polarization” of the states before the interaction and after it. Hence his underlying Lie group was SU(2). We extend this idea to any simple Lie group. This paper determines the relative probabilities of various channels of scattering and decay processes following from the invariance of the interactions with respect to a compact simple a Lie group. Aiming at the probabilities rather than at the Clebsch-Gordan coefficients makes the task easier, and simultaneous consideration of all possible channels for given multiplets involved in the process, makes the task possible. The probability of states with multiplicities greater than 1 is averaged over. Examples with symmetry groups O(5), F(4), and E(8) are shown

Transformation design and nonlinear Hamiltonians

We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.Comment: Accepted for publication in Journal of Modern Optic

Polytopes vibrations within Coxeter group symmetries

We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean space R3. By changing one simple element of the polytope (position of one vertex or length of an edge), one can retain the exact symmetry of the polytope by simultaneously changing other corresponding elements of the polytope. A simple method of using the symmetry of polytopes in order to determine several resonant frequencies is presented. Knowledge of these frequencies, or at least their ratios can be used for control of some principal changes of the polytopes

A Common Assessment Space for Different Sensor Structures

The study of the evolution process of our visual system indicates the existence of variational spatial arrangement; from densely hexagonal in the fovea to a sparse circular structure in the peripheral retina. Today’s sensor spatial arrangement is inspired by our visual system. However, we have not come further than rigid rectangular and, on a minor scale, hexagonal sensor arrangements. Even in this situation, there is a need for directly assessing differences between the rectangular and hexagonal sensor arrangements, i.e., without the conversion of one arrangement to another. In this paper, we propose a method to create a common space for addressing any spatial arrangements and assessing the differences among them, e.g., between the rectangular and hexagonal. Such a space is created by implementing a continuous extension of discrete Weyl Group orbit function transform which extends a discrete arrangement to a continuous one. The implementation of the space is demonstrated by comparing two types of generated hexagonal images from each rectangular image with two different methods of the half-pixel shifting method and virtual hexagonal method. In the experiment, a group of ten texture images were generated with variational curviness content using ten different Perlin noise patterns, adding to an initial 2D Gaussian distribution pattern image. Then, the common space was obtained from each of the discrete images to assess the differences between the original rectangular image and its corresponding hexagonal image. The results show that the space facilitates a usage friendly tool to address an arrangement and assess the changes between different spatial arrangements by which, in the experiment, the hexagonal images show richer intensity variation, nonlinear behavior, and larger dynamic range in comparison to the rectangular images.open access</p