A study on refractive index sensors based on optical micro-ring resonators

In this work the behavior of optical micro-ring resonators, especially when functioning as refractive index sensors, is studied in detail. Two configurations are considered, namely a linear waveguide coupled to a circular one and two linear waveguides coupled to each other through a circular one. The optimum coupling conditions are derived and it is shown that in both cases the condition for the resonant wavelength, i.e. the wavelength at which the transmission spectrum exhibits a dip (peak), is the same and depends only on the geometrical characteristics of the circular waveguide and the effective refractive index of the propagating mode. The latter, as well as the corresponding mode profile, can be easily calculated through numerical analysis. The sensitivity of the sensor is defined based on the dependence of the effective refractive index on the refractive index of the environment. Using a result of waveguide perturbation theory, the geometrical characteristics of the core of the circular waveguide that maximize the sensitivity of the system are determined. Both single and dual core configurations are considered. It is found that, when optimally designed, the sensor can detect relative refractive index changes of the order of 10^-4, assuming that the experimental setup can detect relative wavelength shifts of the order of 3x10^-5. Finally, the behavior of the system as bio-sensor is examined by considering that a thin layer of bio-material is attached on the surface of the waveguide core. It is found that, when optimally designed, the system can detect refractive index changes of the order of 10^-3 for a layer thickness of 10 nm, and changes in the layer thickness of the order of 0.24 nm, for a refractive index change of 0.05

Classical multivariate Hermite coordinate interpolation on n-dimensional grids

In this work, we study the Hermite interpolation on n-dimensional non-equally spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. First, we prove the uniqueness of the interpolating polynomial, and we further obtain a compact closed form that uses a single summation, irrespective of the dimensionality, which is algebraically simpler than the only alternative closed form for the n-dimensional classical Hermite interpolation [1]. We provide the remainder of the interpolation in integral form; moreover, we derive the ideal of the interpolation and express the interpolation remainder using only polynomial divisions, in the case of interpolating a polynomial function. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, in the simple case of few points, as well as hundreds of points on 3D-grids using a spline-like interpolation, which compares favorably to state-of-the-art spline interpolation methods

A novel device for controlling the flow of information based on Weyl fermions and a method for manipulating the spatial distribution of Weyl particles

In this work we propose a novel device for controlling the flow of information using Weyl fermions. In more detail, based on a previous work of our group, we show that it is possible to fully control the flow of Weyl fermions on a sequence of different channels, by applying an electric field perpendicular to the direction of motion of the particles on each channel. In this way, we can transmit information, logical bits, depending on the existence or not of a Weyl current on each channel. We also show that the response time of this device is exceptionally low, less than 1 ps, for typical values of the parameters, providing the opportunity to control the flow of information at extremely high rates, of the order of 100 Pbps. This device also offers additional advantages, as low power consumption and robustness against electromagnetic perturbations, and is expected to find important applications in several fields, as telecommunications, signal processing, classical and quantum computing, etc. Finally, we demonstrate that Weyl fermions can be efficiently guided through the proposed device using appropriate magnetic fields

Degenerate solutions to the massless Dirac and Weyl equations and a proposed method for controlling the quantum state of Weyl particles

In a recent work we have shown that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate, in the sense that they remain unaltered under the influence of a wide variety of different electromagnetic fields. In the present article our previous work is significantly extended, providing a wide class of degenerate solutions to the Dirac equation for massless particles. The electromagnetic fields corresponding to these solutions are calculated, giving also some examples regarding both spatially constant electromagnetic fields and electromagnetic waves. Further, some general forms of solutions to the Weyl equation are presented and the corresponding electromagnetic fields are calculated. Based on these results, a method for fully controlling the quantum state of Weyl particles through appropriate electromagnetic fields is proposed. Finally, the transition from degenerate to non-degenerate solutions as the particles acquire mass is discussed.Comment: Keywords: Dirac equation, Weyl equation, Degenerate solutions, Massless particles, Electromagnetic 4-potentials, Electromagnetic fields, Electromagnetic waves, Nearly degenerate solution

A general method for obtaining degenerate solutions to the Dirac and Weyl equations and a discussion on the experimental detection of degenerate states

In this work we describe a general method for obtaining degenerate solutions to the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. In more detail, using four arbitrary real functions, one can automatically construct a spinor which is solution to the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with non-zero mass, the degenerate spinors should be localized, both in space and time. Our method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, we propose two experimental methods for detecting the presence of degenerate states.Comment: In this version of the article we have added a discussion on the experimental detection of degenerate states, proposing two techniques based on electrical and optical measurement

Degenerate wave-like solutions to the Dirac equation for massive particles

In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like electromagnetic fields corresponding to these solutions. We show that the state of the particles does not depend on the intensity of the electromagnetic fields, but only on their frequency, which is proportional to the mass of the particles and lies in the region of Gamma/X-rays for typical elementary charged particles, such as electrons and protons. We have also calculated the electric current density corresponding to the electromagnetic 4-potentials connected to the degenerate solutions and found that it has the same spatial and temporal dependence on the electromagnetic fields, rotating at an exceptionally high frequency. This result indicates that the degenerate states may occur at locations where matter collapses, e.g., in the central region of a black hole. Finally, we have calculated the spin of the particles described by degenerate spinors and found that it rotates in synchronization with the magnetic field and the current density

On the remarkable properties of Weyl particles

In this work we show that Weyl particles can exist at different states in zero electromagnetic field, either as free particles, or at localized states described by a parameter with dimensions of mass. We also calculate the electromagnetic fields that should be applied in order to modify the localization of Weyl particles at a desired rate. It is shown that they are simple electric fields, which can be easily implemented experimentally. Consequently, the localization of Weyl particles in certain materials supporting these particles could also be studied experimentally, in the framework of solid-state physics or in the framework of laser physics, using ions trapped by laser beams. In addition, a particularly important remark is that the localization of the energy of the particles can lead to the generation of gravitational mass, according to Einstein's field equations of general relativity. Furthermore, in the case that the energy and localization of the particles exceeds a critical level, tiny black holes could also be created, potential candidates for the dark matter of the universe.Comment: In this version we have added a remark regarding the potential to study experimentally the behavior of Weyl particles using ions trapped by laser beam