We report on the observation of multiple third-harmonic conical waves generated in an annular periodically poled nonlinear photonic crystal. We show that the conical beams are formed as a result of the cascading effect involving two parametric processes that satisfy either the transverse and/or longitudinal phase-patching conditions. This is the first experimental observation of third-harmonic ...

We report on the observation of second-harmonic conical waves generated in a novel geometry of the transverse excitation of an annular periodically poled nonlinear photonic structure by a fundamental Gaussian beam. We show that the conical beams are formed as a result of the higher-order nonlinear Bragg diffraction involving two parametric processes in which an ordinary fundamental wave is conv...

We study spectral properties of Dirichlet Laplacian on the conical layer of the opening angle π − 2θ and thickness equal to π. We demonstrate that below the continuum threshold which is equal to one there is an infinite sequence of isolated eigenvalues and analyze properties of these geometrically induced bound states. By numerical computation we find examples of the eigenfunctions. Spectrum of...

This paper presents a series of approaches for discrete time-domain synthesis of conical bore instrument sounds. The generation of steady, selfsustained oscillations using conical waveguides is complicated by properties inherent to truncated conic frusta. Two different physical structures are discussed which can be characterized by the same circuit diagram. A more abstract and flexible “virtual...

A novel S-band monopulse antenna with four conical helix antennas on a microstrip substrate comparator is designed, fabricated and measured. Conical helix antenna height is 3λ, and comparator size is 130mm × 150mm. The bandwidth (SWR < 2 dB) of the antenna is 21.3% with an operating frequency range of 2.7GHz–3.35 GHz. The maximum gain of the sum pattern is 17.4 dB, and the null depths of the di...

In [7], a notion of noncommutative tangent space is associated with a conical pseudomanifold and the Poincaré duality in K-theory is proved between this space and the pseudomanifold. The present paper continues this work. We show that an appropriate presentation of the notion of symbols on a manifold generalizes right away to conical pseudomanifolds and that it enables us to interpret the Poinc...

Experimental evidence is presented that shows that the conical emission often found surrounding a near-resonant laser beam after it passes through an atomic vapor is due to nondegenerate four-wave mixing enhanced by the ac Stark effect. We demonstrate self-trapping of a pulsed dye-laser beam in sodium vapor for wavelengths 0.04 to 10 A shorter than that of the D(2) resonance and show that the f...

This paper studies the normalized Ricci flow on surfaces with conical singularities. It’s proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it’s shown that they admit Ricci soliton metric. MSC 2...