Tuning the polarization states of optical spots at the nanoscale on the Poincaré sphere using a plasmonic nanoantenna

It is shown that the polarization states of optical spots at the nanoscale can be manipulated to various points on the Poincaré sphere using a plasmonic nanoantenna. Linearly, circularly, and elliptically polarized near-field optical spots at the nanoscale are achieved with various polarization states on the Poincaré sphere using a plasmonic nanoantenna. A novel plasmonic nanoantenna is illuminated with diffraction-limited linearly polarized light. It is demonstrated that the plasmonic resonances of perpendicular and longitudinal components of the nanoantenna and the angle of incident polarization can be tuned to obtain optical spots beyond the diffraction limit with a desired polarization and handedness.     

The geometry of minimal replacement for the Poincaré group

The constructs of this paper rest on two elementary facts: (1) the Poincaré group P₁₀ is the maximal group of isometries of Minkowski space-time M₄; (2) P₁₀ has a faithful matrix representation as a subgroup of GL(5, R) that maps an affine set into itself. Local action of P₁₀ and Yang-Mills minimal replacement are shown to induce a well-defined minimal replacement operator that maps the tensor algebra over M₄ onto the tensor algebra over a new space-time U₄. The natural frame and coframe fields of M₄ go over into a canonical system of frame and coframe fields of U₄ with both translation and Lorentz-rotation parts. The coframe fields define soldering 1-form fields for U₄ that give rise to the standard geometric quantities through the Cartan equations of structure. This leads to unique determinations of all relevant connection coefficients and the associated 2-forms of curvature and torsion that involve the compensating 1-forms for local action of both the translation and the Lorentz-rotation sectors. The metric tensor of U₄, that is induced by the minimal replacement operator, is shown to satisfy the Ricci lemma; U₄ is necessarily a Riemann-Cartan space. This space admits gauge covariant constant basis fields for the Lie algebra of the Lorentz group and for the Dirac algebra. The induced basis for the Dirac algebra evaluates the images of Dirac operators under minimal replacement, while the induced basis for the Lie algebra of L(4, R) serves to show that the holonomy group of U₄ is the Lorentz group. The minimal replacement operator is extended to include the case of a total gauge group that is the direct product of the Poincaré group and a Lie group of internal symmetries of matter fields. This provides a precise method of lifting any action integral of the matter fields from M₄ up to U₄ so that invariance properties are retained when the total group acts locally. The natural representations afforded by minimal replacement result in curvature being evaluated in terms of first order derivatives of the compensating fields that share many properties in common with the Dirac derivation algebra for spin fields. Direct interpretations of the compensating fields are obtained from the geodesic equations.     

Parameter optimization for a reflective bistable twisted nematic display by use of the Poincar sphereé method

Although reflective bistable twisted nematic (RBTN) displays have potential in low-power-consumption applications, to achieve the optimum conditions for both bistable states simultaneously remains a challenge. We use a geometrical method based on the Poincaré sphere representation to obtain the optimum conditions that can simultaneously satisfy both bistable states for a RBTN structure. With this method, the optimum conditions can be obtained analytically and the operation modes can be clearly visualized and better understood.     

Statistical characteristics of the Poincaré return times for a one-dimensional nonhyperbolic map

Characteristics of the Poincaré return times are considered in a one-dimensional cubic map with a chaotic nonhyperbolic attractor. Two approaches, local one (Kac’s theorem) and global one related with the AP-dimension estimation of return times, are used. The return times characteristics are studied in the presence of external noise. The characteristics of Poincaré recurrences are compared with the form of probability measure and the complete correspondence of the obtained results with the mathematical theory is shown. The influence of the attractor crisis on the return time characteristics is also analyzed. The obtained results have a methodical and educational significance and can be used for solving a number of applied tasks.     

A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold

We define a regularised version of the de Rham operator over the free loop space. We perform a semi-classical approximation of it, such that the index of the limit operator is equal to the “orbit Euler characteristic” of physicists.     

Nontrivial extensions of a massless representation with definite helicity of the Poincaré group in 3+1 dimensions by the tensor product of two other massless representations with definite helicity

Let U _n (a, ) be a massless, helicity n/2, representation of the Poincaré group in 3+1 dimensions. U _n (a, ) is realized in an adapted nuclear space D _n. We explicitly determine the various classes of cohomology for the extension of U _n (a, ) by U _n1 (a, ) U _n2 (a, ).     

The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid–vapour coexistence densities is analysed.     

The thermal–optical effect due to varying the angle of incidence used for designing a tunable filter in photonic crystals

Tunable devices based on photonic-crystal (PhC) structures are employed in optical sources, detectors, and filters. We present the design and optimization of a wavelength-selective tunable filter with potential applications to the wavelength-division-multiplexing (WDM) systems. We analyze the design of a 1D tunable photonic-crystal filter, where tunability is achieved either by changing the temperature or the angle of incidence. The device is designed in a multilayered structure of silicon/silica (Si/SiO₂) with a defect in the middle. Based on the induced variation of optical parameters introduced by an external change of temperature, we analyze the effects of these changes in temperature on the transmission of the optical filter at different angles of incidence. We show that the position of the resonance peak has a linear dependence on temperature and the square of the angle of incidence. A linear regression provides a slope of d??/dT?=?+0.06?nm/°C and d??/d?? ²?=??0.104?nm/degree² around the transmission wavelength ???=?1.55???m. We obtain the corresponding field patterns and the transmission spectra using the transfer-matrix-method (TMM) simulations. We show the ability to tune the optical properties of the photonic-crystal filter elaborated by changing two parameters: the angle of incidence for selecting the wavelength and the temperature for fine tuning of the wavelength, which can be applied in integrated optics.     

Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

ABSTRACT

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entire metastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.     

Influence of charge carriers on magnetic order in lightly doped manganites, detected by μSR: Evidence for a superparamagnetic transition to the antiferromagnetic state

We detected two spontaneous precession frequencies in antiferromagnetic pure LaMnO₃, the end member of different families of charge-doped manganites. The muon site and local field orientation are identified for one frequency, which provides a measure of the staggered magnetization. We present additional zero and longitudinal field muon relaxation data on an LaMnO_3.045 sample in which a new regime appears above an intermediate temperatureT*, where regions of magnetic order coexist with domains of fluctuating moments. These results are discussed in terms of nucleation of the ordered phase in a superparamagnetic matrix.     

New expressions for g—factors of the mixed ground state of 3d^9 ions with a compressional tetragonal symmetry and its application to NaCl：Ni^＋（I）

We deduce new expressions for g-factors of the 3d⁹ ions with a compressional tetragonal symmetry, in which we consider not only the contribution from the spin-orbit coupling of the central transition metal ion but also that of the ligand orbits as well as the admixture of ²B_1g into ²A_1g (ground state). By using the new formulae, the electron paramagnetic resonance g-factors for NaCl:Ni⁺(I) are studied. Thus, the puzzle that the g_‖-shift is positive is reasonably explained.     

The infrared spectrum of 13C2HD between 100 and 2100 cm−1: a global fit for the bending states up to υ 4 + υ 5 = 3

The fundamental bending ro-vibrational bands and a number of overtone, combination and hot bands of ¹³C₂HD have been recorded by Fourier transform infrared spectroscopy in the range 450–2100 cm^?1. In addition, the ν ₅ ← ν ₄ band, centred at 164.65 cm^?1, has been identified in the spectrum of ¹³C₂H₂. The data were analysed simultaneously in a global fit that has provided very accurate rotational and vibrational parameters for the ground and vibrationally excited states.