Analysis of 2-Isogeny Properties of Generalized Form Edwards Curves

The analysis of the 2-isogeny existence conditions of generalized Edwards form curves over a prime field, including complete, quadratic, and twisted Edwards curves, is presented. An overview of the properties of these three classes of curves is given. Generalization of the results known for the classes of complete and quadratic curves to the class of twisted Edwards curves is obtained. A modified law of point’s addition is used to correctly determine the isogeny degree

Nearly perfect routing of chiral light by plasmonic grating on slab waveguide

Grating couplers are widely used to couple waveguide modes with the far field. Their usefulness is determined not only by energy efficiency but also by additional supported functionality. In this paper, we demonstrate a plasmonic grating on a silicon nitride slab waveguide that couples both TE and TM waveguide modes with circularly polarized light in the far field. Specifically, we experimentally confirmed that circularly polarized light excites TE and TM modes propagating in opposite directions, and the direction is controlled by the handedness. The routing efficiency for normally incident light reaches up to 95%. The same structure operates in the outcoupling regime as well, demonstrating up to 97% degree of circular polarization, where the handedness is determined by the polarization and propagation direction of outcoupled modes. Our results pave the way for the realization of polarization-division multiplexers and demultiplexers, integrated circular polarization emitters, as well as detectors of the polarization state of the incident optical field

Nearly perfect routing of chiral light by plasmonic grating on slab waveguide

Grating couplers are widely used to couple waveguide modes with the far field. Their usefulness is determined not only by energy efficiency but also by additional supported functionality. In this paper, we demonstrate a plasmonic grating on a silicon nitride slab waveguide that couples both TE and TM waveguide modes with circularly polarized light in the far field. Specifically, we experimentally confirmed that circularly polarized light excites TE and TM modes propagating in opposite directions, and the direction is controlled by the handedness. The routing efficiency for normally incident light reaches up to 95%. The same structure operates in the outcoupling regime as well, demonstrating up to 97% degree of circular polarization, where the handedness is determined by the polarization and propagation direction of outcoupled modes. Our results pave the way for the realization of polarization-division multiplexers and demultiplexers, integrated circular polarization emitters, as well as detectors of the polarization state of the incident optical field

Precision measurement of the structure of the CMS inner tracking system using nuclear interactions

The structure of the CMS inner tracking system has been studied using nuclear interactions of hadrons striking its material. Data from proton-proton collisions at a center-of-mass energy of 13 TeV recorded in 2015 at the LHC are used to reconstruct millions of secondary vertices from these nuclear interactions. Precise positions of the beam pipe and the inner tracking system elements, such as the pixel detector support tube, and barrel pixel detector inner shield and support rails, are determined using these vertices. These measurements are important for detector simulations, detector upgrades, and to identify any changes in the positions of inactive elements

Precision measurement of the structure of the CMS inner tracking system using nuclear interactions

The structure of the CMS inner tracking system has been studied using nuclear interactions of hadrons striking its material. Data from proton-proton collisions at a center-of-mass energy of 13 TeV recorded in 2015 at the LHC are used to reconstruct millions of secondary vertices from these nuclear interactions. Precise positions of the beam pipe and the inner tracking system elements, such as the pixel detector support tube, and barrel pixel detector inner shield and support rails, are determined using these vertices. These measurements are important for detector simulations, detector upgrades, and to identify any changes in the positions of inactive elements