The interplay between light polarization and matter is the basis of many fundamental physical processes and applications. However, the electromagnetic wave nature of light in free space sets a fundamental limit on the three-dimensional polarization orientation of a light beam. Although a high numerical aperture objective can be used to bend the wavefront of a radially polarized beam to generate the longitudinal polarization state in the focal volume, the arbitrary three-dimensional polarization orientation of a beam has not been achieved yet. Here we present a novel technique for generating arbitrary three-dimensional polarization orientation by a single optically configured vectorial beam. As a consequence, by applying this technique to gold nanorods, orientation-unlimited polarization encryption with ultra-security is demonstrated. These results represent a new landmark of the orientation-unlimited three-dimensional polarization control of the light–matter interaction.

This Letter presents a scheme to embed both angular/spectral surface plasmon resonance (SPR) in a unique far-field rainbow feature by tightly focusing (effective NA=1.45) a polychromatic radially polarized beam on an Au (20 nm)/SiO2 (500 nm)/Au (20 nm) sandwich structure. Without the need for angular or spectral scanning, the virtual spectral probe snapshots a wide operation range (n=1-1.42; λ=400-700 nm) of SPR excitation in a locally nanosized region. Combined with the high-speed spectral analysis, a proof-of-concept scenario was given by monitoring the NaCl liquid concentration change in real time. The proposed scheme will certainly has a promising impact on the development of objective-based SPR sensor and biometric studies due to its rapidity and versatility.

We describe a procedure for determining the generalised scaling functions f n (g) at all the values of the coupling constant. These functions describe the high spin contribution to the anomalous dimension of large twist operators (in the sl(2) sector) of N = 4 SYM. At fixed n, f n (g) can be obtained by solving a linear integral equation (or, equivalently, a linear system with an infinite number of equations), whose inhomogeneous term only depends on the solutions at smaller n. In other words, the solution can be written in a recursive form and then explicitly worked out in the strong coupling regime. In this regime, we also emphasise the peculiar convergence of different quantities ('masses', related to the f n (g)) to the unique mass gap of the O(6) nonlinear sigma model and analyse the first next-to-leading order corrections.ArXiv ePrint: 0808.1886 Furthermore, the same linear integral equation (2.11) still controls this next-to-leading order (nlo), f (0) (g, j). Now, similarly, we may imagine that the dots should initially be inverse integer powers of ln s, with coefficients, at each power, depending on g and j. Afterwards, inverse integer powers of s should also enter the stage, but they are determined by the complete non-linear integral equation (NLIE) of [18]. 1 However, in this paper we will constrain ourselves to the leading Sudakov factor f (g, j), leaving the analysis of its corrections for future publications.Actually, in [19] we have initiated the study of the strong coupling regime of the first generalised scaling function f 1 (g) and have shown the proportionality of its leading order to the mass gap m(g) (see (3.13) below) of the O(6) nonlinear sigma model (NLSM). This gives a first positive test, in the strong coupling regime j ≪ m(g) of the NLSM, for the Alday-Maldacena proposal [11]. This claims that as long as g ≫ j the quantity f (g, j) + j should coincide with the O(6) NLSM energy density. The latter was expanded and checked for the first orders in the perturbative regime j ≫ m(g) of the NLSM by [11]. Hence, our test was a first indication in another valuable region of the NLSM, i.e. j ≪ m(g), where the free energy series is, besides, convergent [22]. Afterwards, the embedding of the O(6) NLSM into N = 4 SYM at large g was brilliantly shown in a formal way by [20], where the leading strong coupling contribution of f 3 (g) was computed too. In a contemporaneous paper [21], starting from the our linear integral equation [19], we have set down the initial ideas for a systematic study of all the f n (g) and confined our study to the first four f 1 (g), f 2 (g), f 3 (g) and f 4 (g), by finding for them some analytic relations and expressions. These have been then evaluated numerically with additional analytic results for large g, finding agreement with the suitable results from the O(6) NLSM [22]. Furthermore, the agreement on f 4 (g) is highly nontrivial, since it contains the details of the specific interaction in the O(6) NLSM. For completeness sake, all these results will be reported in the f...

We report on the concept, generation, and observation of versatile excited surface plasmon polariton ͑SPP͒ patterns via focused split polarization. Unlike the conventional subwavelength features such as holes array, grating, or other protrusion to satisfy the phase matching condition for SPP excitation, we utilized a structured focus to form either counterpropagating interference or a multiple casting plasmonic pattern by means of the arrangement of split polarization and corresponding focus position. The characteristics of the near-field SPP image are in close agreement with the finite-difference time-domain calculation and confirm its feasibility associated with SPP excitations in many areas.