Automatic sets of rational numbers

The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.Comment: Previous version appeared in Proc. LATA 2012 conferenc

Diffractive sidewall grating coupler: towards 2D free-space optics on chip.

Silicon photonics has been the subject of intense research efforts. In order to implement complex integrated silicon photonic devices and systems, a wide range of robust building blocks is needed. Waveguide couplers are fundamental devices in integrated optics, enabling different functionalities such as power dividers, spot-size converters, coherent hybrids and fiber-chip coupling interfaces, to name a few. In this work we propose a new type of nanophotonic coupler based on sidewall grating (SIGRA) concept. SIGRAs have been used in the Bragg regime, for filtering applications, as well as in the sub-wavelength regime in multimode interference (MMI) couplers. However, the use of SIGRAs in the radiation regime has been very limited. Specifically, a coarse wavelength division multiplexer was proposed and experimentally validated. In this work we study the use of SIGRAs in the diffractive regime as a mean to couple the light between a silicon wire waveguide mode and a continuum of slab waveguide modes. We also propose an original technique for designing SIGRA based couplers, enabling the synthesis of arbitrary radiation field profile by Floquet- Bloch analysis of individual diffracting elements while substantially alleviating computational load. Results are further validated by 3D FDTD simulations which confirm that the radiated field profile closely matches the target design field.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Kondo effect in multielectron quantum dots at high magnetic fields

We present a general description of low temperature transport through a quantum dot with any number of electrons at filling factor $1<\nu <2$. We provide a general description of a novel Kondo effect which is turned on by application of an appropriate magnetic field. The spin-flip scattering of carriers by the quantum dot only involves two states of the scatterer which may have a large spin. This process is described by spin-flip Hubbard operators, which change the angular momentum, leading to a Kondo Hamiltonian. We obtain antiferromagnetic exchange couplings depending on tunneling amplitudes and correlation effects. Since Kondo temperature has an exponential dependence on exchange couplings, quantitative variations of the parameters in different regimes have important experimental consequences. In particular, we discuss the {\it chess board} aspect of the experimental conductance when represented in a grey scale as a function of both the magnetic field and the gate potential affecting the quantum dot

A Coupled Equations Model for Epitaxial Growth on Textured Surfaces

We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in terms of a few simple atomic scale processes including adatom diffusion, step-edge attachment and detachment, and a net downhill migration of surface adatoms. The continuum model reduces to the linear part of the Kardar-Parisi-Zhang equation with a flux dependent smoothing coefficient in the long wavelength limit.Comment: 11 pages, 4 figures. Submitted to the Journal of Crystal Growt

Curved waveguide grating demultiplexer (CWG) with a flattened response via bimodal output waveguides

We demonstrate a compact wavelength demultiplexer for the silicon-on-insulator platform based on the curved waveguide grating (CWG) architecture. The proposed device uses bi- modal output waveguides to achieve a low-loss flattened spectral response. The device shows insertion loss as low as 1.2 dB and crosstalk below -20 dB.Universidad de Málaga; Ministerio de Educación, Cultura y Deporte (MECD) (FPU16/03401), Ministerio de Ciencia, Innovación y Universidades (MCIU) (PID2019-106747RBI00), Consejería de Economía, Conocimiento, Empresas y Universidad (CECEU) (UMA18-FEDERJA-219, P18-RT1453, P18-RT-793). Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Surface tension of the isotropic-nematic interface

We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsager's density functional theory and computer simulation. When the liquid crystal director is aligned parallel to the interface, the situation of lowest free energy, there is a large tension on the nematic side of the interface and a small compressive region on the isotropic side. By contrast, for perpendicular alignment, the tension is on the isotropic side. There is excellent agreement between theory and simulation both in the forms of the pressure tensor profiles, and the values of the surface tension.Comment: Minor changes; to appear in Phys. Rev.

Subwavelength gratings for sensing and polarization management

Sub-wavelength grating (SWGs) structures are becoming important building blocks in planar waveguide photonic devices [1]. SWG structures have been successfully applied in the design of a range of devices with remarkable performance by using refractive index engineering and dispersion engineering techniques [2]. In this work we explore two new promising applications of these structures, namely in evanescent field waveguide sensing and polarization management. For the evanescent waveguide sensing devices, we show that sub- wavelength patterning of silicon wires can be used to control the delocalization of the waveguide mode and therefore enhance both bulk and surface sensitivities (Fig. 1). We will also discuss the implementation of subwavelength structures in efficient polarization splitter and rotator (PSR) devices [3]. PSR devices based on asymmetrical directional couplers typically exhibit stringent fabrication tolerances. We show that by implementing SWG structures in PSR design both the effective mode index and its derivatives with respect to critical dimensions can be controlled, which significantly improves tolerance to fabrication errors (Fig. 2).Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this "progress report", we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.Comment: Commissioned article for Few-Body Systems, 47 pp, 16 fig

Silicon-on-insulator polarization controller with relaxed fabrication tolerances

Polarization control is essential in applications ranging from optical communications to interferometric sensors. The implementation of in- tegrated polarization controllers is challenging as they require polariza- tion rotating waveguides with stringent fabrication tolerances. Here, we present a fully integrated polarization controller scheme that signi cantly relaxes the requirements on the rotating waveguides, alleviating fabri- cation tolerances. We analytically establish a technology-independent, easily measurable tolerance condition for the rotating waveguides. Po- larization control in the presence of waveguide width errors of 25% is shown through full vectorial simulation.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech