Provable properties of asymptotic safety in f(R) approximation

We study an f(R) approximation to asymptotic safety, using a family of non-adaptive cutoffs, kept general to test for universality. Matching solutions on the four-dimensional sphere and hyperboloid, we prove properties of any such global fixed point solution and its eigenoperators. For this family of cutoffs, the scaling dimension at large n of the nth eigenoperator, is λn ∝ b n ln n. The coefficient b is non-universal, a consequence of the single-metric approximation. The large R limit is universal on the hyperboloid, but not on the sphere where cutoff dependence results from certain zero modes. For right-sign conformal mode cutoff, the fixed points form at most a discrete set. The eigenoperator spectrum is quantised. They are square integrable under the Sturm-Liouville weight. For wrong sign cutoff, the fixed points form a continuum, and so do the eigenoperators unless we impose square-integrability. If we do this, we get a discrete tower of operators, infinitely many of which are relevant. These are f(R) analogues of novel operators in the conformal sector which were used recently to furnish an alternative quantisation of gravity.

Extraordinary optical transmission in silicon nanoholes

In this work, for the first time, a study was conducted of the existence of Extraordinary Optical Transmission (EOT) in Silicon (Si) thin films with subwavelength holes array and high excess carrier concentration. Typically EOT is studied in opaque perforated metal films. Using Si would bring EOT and its many applications to the silicon photonics realm and the mid-IR range. Since Si thin film is a semi-transparent film in mid-IR, a generalization was proposed of the normalized transmission metric used in literature for EOT studies in opaque films. The plasma dispersion effect was introduced into the studied perforated Si film through either doping or carriers’ generation. Careful consideration for the differences in optical response modeling in both cases was given. Full-wave simulation and analysis showed an enhanced transmission when using Si with excess carriers, mimicking the enhancement reported in perforated metallic films. EOT was found in the mid-IR instead of the visible range which is the case in metallic films. The case of Si with generated excess carriers showed a mid-IR EOT peak reaching 157% around 6.68 µm, while the phosphorus-doped Si case showed a transmission enhancement of 152% around 8.6 µm. The effect of varying the holes’ dimensions and generated carriers’ concentration on the transmission was studied. The analogy of the relation between the fundamental mode cutoff and the EOT peak wavelength in the case of Si to the case of metal such as silver was studied and verified. The perforated Si thin film transmission sensitivity for a change in the refractive index of the holes and surroundings material was investigated. Also, a study of the device potential in sensing the hole and surroundings materials that have almost the same refractive index yet with different absorption fingerprints was performed as well.

Gyro-devices – natural sources of high-power high-order angular momentum millimeter-wave beams

The Orbital Angular Momentum (OAM) carried by light beams with helical phasefront (vortex beams) has been widely employed in many applications such as optical tweezers, optical drives of micro-machines, atom trapping, and optical communication. OAM provides an additional dimension (diversity) to multiplexing techniques, which can be utilized in addition to conventional multiplexing methods to achieve higher data rates in wireless communication. OAM beams have been thoroughly studied and used in the optical regime but in the mm-wave and THz-wave region, they are still under investigation. In these frequency bands, there are difficulties associated with beam-splitting and beam-combining processes as well as with the use of spiral phase plates and other methods for OAM generation, since the wavelength is much larger compared to those at optical frequencies, leading to higher diffraction losses. The present paper describes the natural generation of high-power OAM modes by gyro-type vacuum electron devices with cylindrical interaction circuit and axial output of the generated rotating higher-order transverse electric mode TEm,n, where m > 1 and n are the azimuthal and radial mode index, respectively. The ratio between the total angular momentum (TAM) JN and total energy WN of N photons is given by m/ω, where ω is the angular frequency of the operating mode, which in a gyrotron oscillator is close to the TEm,n-mode cutoff frequency in the cavity. Therefore, m/ω = Rc/c, where Rc is the caustic radius and c the velocity of light in vacuum. This means that the OAM is proportional to the caustic radius and at a given frequency the same for all modes with the same azimuthal index m. Right-hand rotation (co-rotation with the electrons) corresponds to a positive value of m and left-hand rotation to negative m. The corresponding OAM mode number (topological charge) is l = m – 1. Circularly polarized TE1n modes only possess a Spin Angular Momentum (SAM: s = ±1). TE0n modes have neither SAM nor OAM. This is the result of the photonic (quasi-optical) approach to derive the TAM of modes generated in gyrotrons. The same result follows from the electromagnetic (EM) wave approach for the TAM within a given waveguide volume per total energy of the EM wave in the same volume. Such high-power output beams with very pure higher-order OAM, generated by gyrotron oscillators or amplifiers (broadband) could be used for multiplexing in long-range wireless communications. The corresponding mode and helical wavefront sensitive detectors for selective OAM-mode sorting are available and described in the present paper.

Different Graded Refractive Index Fiber Profiles Design for the Control of Losses and Dispersion Effects

This paper has presented the basic infrastructure of different multilayer graded index fiber profiles design. The optimum graded refractive index fiber profile design for the control of total Losses and dispersion effects are considered. The trade-off between different refractive index fiber profiles is realized in order to achieve loss and dispersion effects management. It is evident that the proposed first optical fiber has presented lower dispersion and splice loss than other proposed fibers. As well as the proposed third optical fiber outlines lower effective mode field diameter and micro bending loss than other proposed fibers. Dominant mode, cutoff wavelength and international telecommunication union-telecommunication (ITU-T) values for each fiber are examined based on finite difference method.

Effect of Chirality on Dispersion Characteristics of Uniaxial Anisotropic Chiral Elliptical Waveguide

In this paper, the dispersion characteristic of elliptical waveguide consisting of uniaxial anisotropic chiral medium is investigated. The eigenvalue equation for the waveguide that is to be studied is deduced by solving the Mathieu and modified Mathieu functions. The cutoff frequencies for several lower order even modes have been calculated and their dispersion characteristics are correspondingly plotted. The effects of elliptical eccentricity and chirality on the mode cutoff frequencies and mode transmission are examined numerically.