Mathematical Modelling of Material Transfer to High-Density Lipoprotein (HDL) upon Triglyceride Lipolysis by Lipoprotein Lipase: Relevance to Cardioprotective Role of HDL.

High-density lipoprotein (HDL) contributes to lipolysis of triglyceride-rich lipoprotein (TGRL) by lipoprotein lipase (LPL) via acquirement of surface lipids, including free cholesterol (FC), released upon lipolysis. According to the reverse remnant-cholesterol transport (RRT) hypothesis recently developed by us, acquirement of FC by HDL is reduced at both low and extremely high HDL concentrations, potentially underlying the U-shaped relationship between HDL-cholesterol and cardiovascular disease. Mechanisms underlying impaired FC transfer however remain indeterminate. We developed a mathematical model of material transfer to HDL upon TGRL lipolysis by LPL. Consistent with experimental observations, mathematical modelling showed that surface components of TGRL, including FC, were accumulated in HDL upon lipolysis. The modelling successfully reproduced major features of cholesterol accumulation in HDL observed experimentally, notably saturation of this process over time and appearance of a maximum as a function of HDL concentration. The calculations suggested that the both phenomena resulted from competitive fluxes of FC through the HDL pool, including primarily those driven by FC concentration gradient between TGRL and HDL on the one hand and mediated by lecithin-cholesterol acyltransferase (LCAT) and cholesteryl ester transfer protein (CETP) on the other hand. These findings provide novel opportunities to revisit our view of HDL in the framework of RRT.

Optical Momentum, Spin, and Angular Momentum in Dispersive Media.

We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector k_{p}>ω/c, and a transverse spin, which can change its sign depending on the frequency ω.

Singular skeleton of a Laguerre-Gaussian beam transformed by the double-phase-ramp converter.

We analyze transformations of circular Laguerre-Gaussian beams with zero radial index after passage through the double-phase-ramp (DPR) converter and study the behavior of optical vortices in the propagating transformed beam. Direct and inverse DPR converters are considered, and informative features of the complete set of optical vortices are revealed. For the input beam with even azimuthal index, such a reaction may cause the sign reversal of the axial optical vortex. The results can be used for creation of light beams with prescribed singular skeleton, for the beam diagnostics, and in high-resolution metrology.

Transverse energy circulation and the edge diffraction of an optical vortex beam.

Edge diffraction of a circular Laguerre-Gaussian beam represents an example of the optical vortex symmetry breakdown in which the hidden "vortex" energy circulation is partially transformed into the visible "asymmetry" form. The diffracted beam evolution is studied in terms of the irradiance moments and the moment-based parameters. In spite of the limited applicability of the moment-based formalism, we show that the "vortex" and "asymmetry" parts of the orbital angular momentum can still be reasonably defined for the hard-edge diffracted beams and retain their physical role of quantifying the corresponding forms of the transverse energy circulation.

Extraordinary momentum and spin in evanescent waves.

Momentum and spin represent fundamental dynamic properties of quantum particles and fields. In particular, propagating optical waves (photons) carry momentum and longitudinal spin determined by the wave vector and circular polarization, respectively. Here we show that exactly the opposite can be the case for evanescent optical waves. A single evanescent wave possesses a spin component, which is independent of the polarization and is orthogonal to the wave vector. Furthermore, such a wave carries a momentum component, which is determined by the circular polarization and is also orthogonal to the wave vector. We show that these extraordinary properties reveal a fundamental Belinfante's spin momentum, known in field theory and unobservable in propagating fields. We demonstrate that the transverse momentum and spin push and twist a probe Mie particle in an evanescent field. This allows the observation of 'impossible' properties of light and of a fundamental field-theory quantity, which was previously considered as 'virtual'.

Mie scattering and optical forces from evanescent fields: a complex-angle approach.

Mie theory is one of the main tools describing scattering of propagating electromagnetic waves by spherical particles. Evanescent optical fields are also scattered by particles and exert radiation forces which can be used for optical near-field manipulations. We show that the Mie theory can be naturally adopted for the scattering of evanescent waves via rotation of its standard solutions by a complex angle. This offers a simple and powerful tool for calculations of the scattered fields and radiation forces. Comparison with other, more cumbersome, approaches shows perfect agreement, thereby validating our theory. As examples of its application, we calculate angular distributions of the scattered far-field irradiance and radiation forces acting on dielectric and conducting particles immersed in an evanescent field.

Internal energy flows and instantaneous field of a monochromatic paraxial light beam.

It is known that the orbital angular momentum of a paraxial light beam is related to the rotational features of the instantaneous optical-frequency oscillation pattern within the beam cross section [J. Opt. A 11, 094004 (2009)]. Now this conclusion is generalized: any identifiable directed motion of the instantaneous two-dimensional pattern of the field oscillations ("running" behavior of the instant oscillatory pattern) corresponds to the transverse energy flow in the experimentally observable time-averaged field. The transverse orbital flow density can be treated as a natural geometric and kinematic characteristic of this running behavior.

Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons.

Paraxial beams whose transverse structure rotates upon free propagation (spiral beams) can be treated as analogs of azimuthons recently found in nonlinear media [Phys. Rev. Lett.95, 203904 (2005)]. These linear azimuthons have essentially a nonlocalized character and can possess an almost arbitrary rotation rate independent of the angular momentum of the beam. Such beams can be assimilated into fluent mechanical bodies with intrinsic mass flows determined by transverse energy redistribution over the beam cross section.