Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals

Transverse-periodic-oriented nematic liquid crystals (LCs) are a special type of optical axis grating that are capable of very high efficiency diffraction (theoretically, 100%) in thin layers of materials with thickness comparable to the radiation wavelength. In particular, they fully diffract linearly polarized input beam into circularly polarized +1st and -1st diffraction orders. We experimentally demonstrate switching between diffraction orders of such gratings when the polarization of the incident beam changes from right-circular to left-circular and vice versa with the aid of an electrically controlled LC phase retarder. Such a setup in which the diffraction efficiency and direction are controlled externally, without application of an electric field to the transverse-periodic grating, provides additional control opportunities and does not compromise the quality of the grating. The grating used in the experiment was 1.5 microm thick and had a period of 4 microm. The contrast ratio of switching between the +1st and -1st orders was as high as 267:1 for a He-Ne laser beam with a switching time of 6.6 ms.     

Effects of coupled vibrations on the parameters of tangentially polarized stripe-electroded piezoelectric cylinders (L)

The effects of coupled vibrations on the piezoelectric properties and electroacoustic transducer performance of radially polarized hollow cylindrical elements as a function of the choice of height-to-diameter ratio have been well documented [J. Acoust. Soc. Am. 120(3), 1374-1380 (2006); J. Acoust. Soc. Am. 122(6), 3419-3427 (2007)]. This letter presents experimental work on the effects of coupled (circumferential, axial, and flexural) vibrations on the resonance frequencies, effective electromechanical coupling coefficient, and acoustical performance of tangentially polarized piezoceramic cylindrical elements. Comparisons are made with analytical predictions of the properties of uniformly circumferentially polarized cylinders.     

Stability of solitons in parity-time-symmetric couplers

Families of analytical solutions are found for symmetric and antisymmetric solitons in a dual-core system with Kerr nonlinearity and parity-time (PT)-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of gain, loss, and intercore coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").     

Unveiling the correlation between non‐diffracting tractor beam and its singularity in Poynting vector

This paper investigates the singular optics of nonparaxial light beams in the near field when the light behaves as a tractor beam. New insights into the optical pulling force, which is usually represented by integrating the stress tensor at a black box enclosing the object, are interpreted by the optical singularity of the Poynting vector. The negative nonconservative pulling force originates from the transfer of the azimuthal Poynting vector to the longitudinal component partly owing to the presence of a scatterer. The separatrice pattern and singularity shifts of the Poynting vector unanimously exhibit a differentiable near‐field distribution in the presence of optical pulling force. A new method is established to calculate the near‐field optical force using the differential Poynting vector in the far field. The results obtained provide a clear physical interpretation of the light–matter interaction and manifest the significance of singular optics in manipulating objects.

     

Unitary representations of superconformal algebra

superconformal algebra is algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of algebra are discussed. A new approach to construction of algebras from rational conformal field theories is proposed.     

Gap soliton dynamics in a nonuniform resonant structure

A model for the propagation of coherent pulses along a one-dimensional, resonantly absorbing Bragg grating that includes localized inhomogeneous population inversion at its center is presented. The long-range coupling between the optical field and resonant atoms allows for controllable trapping of a gap soliton by the local inversion, thus opening new opportunities for control of signal transmission and localization of light.     

Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging

We describe a novel microscopy technique for quantitative phase-contrast imaging of a transparent specimen. The technique is based on depth-resolved phase information provided by common path spectral-domain optical coherence tomography and can measure minute phase variations caused by changes in refractive index and thickness inside the specimen. We demonstrate subnanometer level path-length sensitivity and present images obtained on reflection from a known phase object and human epithelial cheek cells.     

Endomorphisms of the Separated Product of Lattices

To describe the evolution of separated entities remaining separated, we proposeto study endomorphisms (join-preserving maps, sending atoms to atoms) of theseparated product of cao lattices (complete, atomistic orthocomplementedlattices). Morphisms have been used successfully to describe the evolution ofentities, and the separated product is a model for the property lattice of separatedsystems; its set of atoms is the Cartesian product of each atom space. Let L bethe separated product of two cao lattices having the covering property and f anendomorphism of L. We prove that the center F(L) of L is the power set of₁ × ₂ where _i is the atom space ofF(L _i ) (Theorem 1), f preserves irreduciblecomponents (Theorem 2), and if L is irreducible there exist two endomorphismsf ¹ and f ² and a permutation such that the restriction of f to atoms is given byf(p ₁, p ₂) = (f ¹(p ₍₁₎), f ²(p ₍₂₎))(Theorem 3). For generalizations of these resultsto separated products of families of cao lattices, we develop new general argumentsinvolving a topology we define on the set of atoms of a cao lattice.     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.