We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anoma...

In this paper we consider the possibility of replacing the diffraction axicon and the conical axicon on the gradient lens with a linear variation of the refractive index. Analytically and numerically using the finite-difference timedomain method we performed a comparative study of the Gaussian beam diffraction on diffraction mikro-axicon, conical axicon and gradient microlens consisting of subw...

Hyperbolic systems of second-order differential equations are considered in a domain with conical points at the boundary; in particular, the equations of elastodynamics are discussed. The asymptotics of solutions near conical points is studied. The “hyperbolic character” of the asymptotics shows itself in the properties of the coefficients (stress intensity factors) depending on time. Some form...

We study a mechanism by which a symmetry-allowed conical intersection is converted to an avoided crossing by external breaking of symmetry. With full quantum dynamics on coupled ab initio potential energy surfaces for an NO(2) molecule under a phase controlled far-infrared femtosecond pulse field, we demonstrate that symmetry breaking thus-introduced can indeed convert the conical intersection ...

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...