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At levels of laser intensity below threshold for multiphoton ionization, the parametric generation of optical harmonics in gases and other isotropic media is subject to selection rules with origins in angular momentum conservation. The recently developed optics of vector polarization modes provides an unprecedented opportunity to exploit these principles in the production of high harmonic beams with distinctive forms of transverse intensity profile, comprising discrete sub-wavelength filaments in crown-like arrays. A detailed analysis of the fundamental electrodynamics elicits the mechanism, and delivers results illustrating the transverse structures and spatial dimensions of harmonic output that can be achieved., Comment: 2 figures

There is recurrent interest in the orbital angular momentum (OAM) conveyed by optical vortices, which are structured beams with a helically twisted wavefront. Particular significance is attached to the issue of how, in its interactions with matter, light conveying OAM might prove sensitive to the relative handedness and degree of twist in the associated optical wavefront. As a result of recent experimental and theoretical studies, the supposition that beams with OAM might enable discrimination between oppositely handed forms of matter has become a renewed focus of attention. Some of the tantalizing conclusions that are beginning to emerge from this research have, however, not yet established a definitive basis for a supporting mechanism. To resolve this problem requires the development of theory to support a faithful representation, and a thorough understanding, of the fundamental molecule-photon physics at play in such optical processes, even for processes as basic as absorption. The present analysis establishes mechanisms at play that entail a novel manifestation of optical spin-orbit interactions (SOI), engaging transition electric quadrupole moments. Moreover, powerful symmetry principles prove to render distinctively different criteria governing the exhibition of 2D and 3D chirality. The new results elucidate the operation of such effects, identifying their responsibility for discriminatory optical interactions of various forms in both chiral and achiral media., Comment: 18 pages, 1 figure

The multipolar Hamiltonian of quantum electrodynamics (QED) is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground., Comment: 10 pages, 123 references. (in press)