Azimuthal Index Research Articles

Propagation dynamics of Laguerre-Gaussian beams in the fractional Schrödinger equation with noise disturbance.

The evolution of Laguerre-Gaussian (LG) beams in the fractional Schrödinger equation (FSE) with Gaussian noise disturbance is numerically investigated. Without noise disturbance, the peak intensity of LG beams increases with the increment of radial or azimuthal indices, and the turning point of the peak intensity between different radial indices exists. As propagation distance gets longer, the intensity of the outermost sub-lobe exceeds that of the main lobe. When Gaussian noise is added, for a given noise level, the stability of peak intensity is enhanced as the Lévy index increases, while the center of gravity shows the opposite phenomenon. Moreover, the increment of the radial index can weaken the stability of the center of gravity. We also investigate the stability of the peak intensity of Airy beams in the FSE, and generally, the stability of LG beams is better than that of Airy beams. All these properties show that LG beams modeled by the FSE have potential applications in optical manipulation and communications.

Spatial Synchronization of TE-Modes in a Slit-Type Gyrotron Cavity

We propose a variant of a slitted cavity for gyrotrons based on spatial synchronization of TE-type modes with azimuthal indexes equal to multiples of the slit number and close eigenfrequencies. A simplified theory of such a cavity is presented demonstrating its basic properties. High selectivity of the novel cavity was confirmed by 3-D PIC simulation of a 0.3-THz gyrotron energized by a helical electron beam with an energy of 500 keV and a current of 2 kA. This simulation demonstrates that, using the slit-type cavity, stable single-frequency operation at TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6,4</sub> –TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12,2</sub> mode combined with an output power of more than 80 MW and an efficiency of about 8%. The same arrangement with a conventional solid-wall cavity demonstrates no single-frequency regimes at all.

Superradiant atomic recoil lasing with orbital-angular-momentum light

We analyze the collective light scattering by cold atoms in free space of a pump-laser beam possessing orbital angular momentum. We derive a set of coupled multiparticle equations for the atomic motion in which the vacuum-mode field is adiabatically eliminated. The resulting equations describe collective recoil as due to either transfer of linear momentum or orbital angular momentum. For a transverse annular atomic distribution the initial equilibrium with uniform atomic phases and no scattered field is unstable. The atoms are set in rotation and bunched in phase at different harmonics depending on the pump azimuthal index $\ensuremath{\ell}$ and on the ring radius.

Diffraction grating parameter retrieval using non-paraxial structured beams in coherent Fourier scatterometry

In recent years, a lot of works have been published that use parameter retrieval using orbital angular momentum (OAM) beams. Most make use of the OAM of different Laguerre-Gauss modes. However, those specific optical beams are paraxial beams and this limits the regime in which they can be used. In this paper, we report on the first results on retrieving the geometric parameters of a diffraction grating by analysing the corresponding complex-valued (i.e. amplitude and phase) Helmholtz Natural Modes (HNM) spectra containing both the azimuthal (i.e. n) and radial (i.e. m) indices. HNMs are a set of orthogonal, non-paraxial beams with finite energy carrying OAM. We use the coherent Fourier scatterometry (CFS) setup to calculate the field scattered from the diffraction grating. The amplitude and phase contributions of each HNM are then obtained by numerically calculating the overlap integral of the scattered field with the different modes. We show results on the sensitivity of the HNMs to several grating parameters.

Особенности формы спектра излучения сферического микрорезонатора с люминесцентной оболочкой с высоким показателем преломления, обусловленные поляризацией мод шепчущей галереи

The effect of the thickness and refractive index of the shell on the amplitudes of lines of the TE and TM polarized whispering gallery modes (WGMs) in the emission spectrum of a microcavity structure consisting of a spherical core covered with a luminescent shell with a refractive index greater than that of the core is studied. The luminescence spectra of the shell, the radial distribution of the WGM field, and the mode parameters (wavelength, quality factor, and effective volume) are calculated using the method of spherical wave transfer matrices. It is shown that at certain subwavelength shell thicknesses, the amplitude of the TE mode emission peak is many times greater than the amplitude of the TM mode peak with the same polar, azimuthal, and radial indices. This is explained by the fact that with these parameters of the shell, WGMs propagate inside the shell as waveguide modes.

Features of the shape of the emission spectrum of a spherical microresonator with a high refractive index luminescent shell due to the polarization of the whispering gallery modes

The effect of the thickness and refractive index of the shell on the amplitudes of lines of the TE and TM polarized whispering gallery modes (WGMs) in the emission spectrum of a microcavity structure consisting of a spherical core covered with a luminescent shell with a refractive index greater than that of the core is studied. The luminescence spectra of the shell, the radial distribution of the WGM field, and the mode parameters (wavelength, quality factor, and effective volume) are calculated using the method of spherical wave transfer matrices. It is shown that at certain subwavelength shell thicknesses, the amplitude of the TE mode emission peak is many times greater than the amplitude of the TM mode peak with the same polar, azimuthal, and radial indices. This is explained by the fact that with these parameters of the shell, WGMs propagate inside the shell as waveguide modes. Keywords: spherical microresonator, high refractive index luminescent shell, whispering gallery modes, mode polarization, amplitude of emission lines.

Semiconductor nanotube eigenmodes and the Aharonov–Bohm effect

In the present work, the spectra of electromagnetic eigenmodes of a structure consisting of a semiconductor nanotube filled with a nonmagnetic dielectric are theoretically investigated. This structure is placed in a constant magnetic field parallel to the nanotube axis. The walls of the nanotube are assumed to be infinitely thin. The dispersion equation for eigenmodes in such a structure is derived taking into account the retardation effect. From the dispersion equation it follows that in the general case the bulk-surface and surface eigenmodes can exist in such a structure. These eigenmodes with a nonzero azimuthal mode index are hybrids ones and can experience Aharonov-Bohm oscillations with the magnetic field changes.

Influence of reflections on mode-competition processes in a high-power multimode gyrotron

Reflection of radiation from an output window may strongly affect operation of a gyrotron. In recent years, the control of gyrotron radiation by reflection has become a subject of active study. In this paper, we study the effect of reflection on mode competition in a multimode gyrotron. We consider the interaction of five modes with neighboring azimuthal indexes in a gyrotron with a fixed Gaussian axial field profile. We assume the mode spectrum to be nearly equidistant and set the spectral density parameter value as in high-power gyrotrons used for plasma heating. We analyze the domain of stability of the operating mode on the cyclotron frequency mismatch–normalized beam current parameter plane with and without the reflections. The possibility of suppressing spurious sideband modes and expanding the single-mode oscillation zone of the operating mode by injecting the reflected signal is demonstrated by numerical simulation. The most advantageous situation is when the designed mode is matched with the output window while the reflections of the parasitic modes are rather strong and the reflected waves return into the gyrotron resonator in the adverse phase reducing the Q-factors of the parasitic modes.

Multimode -symmetry thresholds and third-order exceptional points in coupled dielectric waveguides with loss and gain

A pair of coupled dielectric waveguides with balanced loss and gain is the basic system for observing the phenomena of parity-time () symmetry and exceptional points (EPs). We use the multimode analytical approach to study the peculiarities of interaction between the modes excited in such an archetypal structure. With this approach, the conditions for symmetry breaking are obtained in the special case of the hybrid HE and EH modes resulting in the ordinary second-order EPs (or -symmetry thresholds). The coupling of modes with the different azimuthal indices (the TM01 and HE21 modes in our study) generates the uncommon types of EPs. First, there are the so-called multimode -symmetry thresholds due to interaction of hybrid and transverse modes. Second, the third-order EPs appear as a result of three-modes degeneracy of real eigenvalues. It is noteworthy that an increase in the EPs order is achieved without both breaking the symmetry and introducing additional elements into the waveguide structure. The results obtained with the multimode analytical approach are in perfect agreement with the independent full-wave simulations.

Exceptional points in a dielectric spheroid

Evolution of resonant frequencies and resonant modes as dependent on the aspect ratio is considered in a dielectric high index spheroid. Because of rotational symmetry of the spheroid the solutions are separated by the azimuthal index $m$. By the two-fold variation of a refractive index and the aspect ratio we achieve exceptional points (EPs) at which the resonant frequencies and resonant modes are coalesced in the sectors $m=0$ for both TE and TM polarizations and $m=1$.

Quasinormal resonances of rapidly-spinning Kerr black holes and the universal relaxation bound

The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation τ×T≥ħπ. It is known that some perturbation modes of near-extremal Kerr black holes in the regime MTBH/ħ≪m−2 are characterized by normalized relaxation times πτ×TBH/ħ which, in the approach to the limit MTBH/ħ→0, make infinitely many oscillations with a tiny constant amplitude around 1 and therefore cannot be used directly to verify the validity of the TTT bound in the entire parameter space of the black-hole spacetime (Here {TBH,M} are respectively the Bekenstein-Hawking temperature and the mass of the black hole, and m is the azimuthal harmonic index of the linearized perturbation mode). In the present compact paper we explicitly prove that all rapidly-spinning Kerr black holes respect the TTT relaxation bound. In particular, using analytical techniques, it is proved that all black-hole perturbation modes in the complementary regime m−1≪MTBH/ħ≪1 are characterized by relaxation times with the simple dimensionless property πτ×TBH/ħ≥1.

Improvement of the Output Mode Purity of a Complex-Cavity Resonator for a Frequency-Tunable Sub-THz Gyrotron

One way to improve the mode selection in terahertz gyrotrons is the use of stepped cavity resonators that satisfy the resonance condition for two modes with the same azimuthal but different radial indices. Such sectioned resonators, or complex cavities, were analyzed in detail by several authors, recently and in the past. One common problem for such designs is the excitation of unwanted modes by both the stepped cavity structure and the cavity input and output tapers. Mode conversion becomes especially a severe problem for higher-order resonant modes in highly oversized resonators. In this article, we introduce ways to minimize the unwanted mode conversion in both the radial step of the cavity as well as in the tapered sections of the cavity and the up-taper to the collector and output window. Frequency tuning between 391.5 and 393.5 GHz has been achieved by operation at different axial mode numbers of the mode pair TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8,4</sub> /TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8,5</sub> . Due to their intrinsic higher output mode purity, the so-called antiphase modes of the complex cavity have been chosen for this output mode purity study.

Azimuthally and radially polarized orbital angular momentum modes in valley topological photonic crystal fiber

Abstract Artificially tailoring the polarization and phase of light offers new applications in optical communication, optical tweezers, and laser processing. Valley topological physics provides a novel paradigm for controlling electromagnetic waves and encoding information. The proposed fiber has the inner and outer claddings possessing opposite valley topological phases but the same refractive indices, which breaks through the polarization constraints of the traditional fiber. Robust valley edge states exist at the domain walls between the inner and outer claddings because of bulk edge correspondence. The valley topological fiber modes exhibit the unprecedented radial and azimuthal polarization with high-order azimuthal index. Those topological modes are robust against the disorder of the fiber structure. These results enable guide and manipulate the optical polarization and angular momentum in fiber with high fidelity. The proposed fiber has the potential to become a powerful optical spanner for the application of bio-photonics.

Orbital angular momentum transfer in molecular magnets

We study the propagation of probe pulses carrying orbital angular momentum (OAM) in a crystal of molecular magnets characterized by a double-$\mathrm{\ensuremath{\Lambda}}$ light-matter coupling scheme. The model is based on the four-wave mixing (FWM) of applied fields interacting with the magnetic dipole moment of the molecular magnets. We consider the light-matter interaction under the situation where a weak probe field carries an optical vortex and investigate the exchange of optical vortices between different frequencies via the FWM in the microwave region. The propagation of OAM beams with nonzero radial indices is then explored. It is found that the conservation of both azimuthal and radial indices is satisfied over the swapping of OAM states of light. Superimposing two initially weak OAM modes with different topological charges creates specific vortex beams with a very characteristic form. The resulting beam contains a central vortex as well as several singly charged peripheral vortices distributed at the same radial distance from the center of the light beam. This complex pattern of vortices arises because the intensity radius of two interfering OAM modes is different. It is shown that the boundary region of intensity dominance of two OAM modes can be controlled by the molecular magnets parameters and strong cw electromagnetic fields. Our proposed scheme may provide a route to study the solid systems suitable for quantum technologies as well as for OAM exchange devices for quantum information processing.

ENERGY LOSSES OF A POINT MAGNETIC DIPOLE DUE TO INTERACTION WITH A MAGNETIZED PLASMA CYLINDER

In this work, the excitation problem of bulk-surface helicons by a point magnetic dipole moving in a vacuum parallel to the element of magnetized solid-state plasma cylinder is theoretically studied. The external magnetic field is directed parallel to the cylinder axis. The problem is solved in the magnetostatic approximation. It is shown that hybrid modes of the magnetic type with large values of the azimuthal mode index and one field variation along the radius are most efficiently excited at nonrelativistic velocities of magnetic dipole.

Imaging of OAM-entangled photon pairs in the Bessel-Gauss basis with full index control

In this paper, we directly image the orbital angular momentum (OAM) correlations, expressed in the Bessel-Gauss (BG) basis, present in quantum-entangled photon pairs produced by the process of spontaneous parametric downconversion (SPDC). We use a spatial light modulator that displays an appropriate phase mask, followed by coupling into a single-mode fiber, so as to project the signal, or heralding, photon onto a BG mode, and verify that the idler, or heralded, photon is projected non-locally as expected. In contrast with similar experiments relying on Laguerre-Gauss (LG) modes, our current experiment permits, firstly, full index control (allowing the experimenter to define both the azimuthal index ℓ s and the continuous radial index k rs , also referred to as scaling parameter). Importantly, while not resolving the radial index leaves the heralded single photon in a statistical mixture of all available radial modes, the ability to determine both indices allows us to herald single photons in a particular BG mode, described by a quantum-mechanically pure state. Our use of BG modes permits, secondly, the spatially-resolved detection of the heralded single photon, both in the near and far fields, with a time-gated intensified CCD camera, making it possible to experimentally determine both the radial and azimuthal indices of the heralded single photon. Thirdly, the fact that for BG modes the radial index (scaling parameter) is continuous makes it possible to use the scaling parameter as a continuous adjustment in quantum state engineering, for precise mode matching, or for the selection of photon-pair properties such as the spiral bandwidth, as we experimentally demonstrate. We believe that our work opens up interesting new possibilities in the field of quantum communications based on the spatial degree of freedom of photon pairs.

Ultrahigh electric and magnetic near field enhancement based on high-Q whispering gallery modes in subwavelength all-dielectric resonators

Here, we show that whispering gallery modes of subwavelength dielectric resonators can exhibit ultrahigh electric and magnetic field enhancements due to their high-quality factors. The resonators are dielectric disks. The field enhancements are dependent on the height of the disk, the refractive index n and the azimuthal mode index, and they can reach ∼102 inside a subwavelength disk of n = 3.5. For a disk dimer of n = 3.5, the electric field enhancement reaches ∼103 in the small gap. The Purcell factor of an electric and magnetic dipole emitter in the dimer can reach ∼105 and ∼104, respectively.

Cavity quantum electrodynamics design with single photon emitters in hexagonal boron nitride

Hexagonal boron nitride (h-BN), a prevalent insulating crystal for dielectric and encapsulation layers in two-dimensional (2D) nanoelectronics and a structural material in 2D nanoelectromechanical systems, has also rapidly emerged as a promising platform for quantum photonics with the recent discovery of optically active defect centers and associated spin states. Combined with measured emission characteristics, here we propose and numerically investigate the cavity quantum electrodynamics scheme, incorporating these defect-enabled single photon emitters (SPEs) in h-BN microdisk resonators. The whispering-gallery nature of microdisks can support multiple families of cavity resonances with different radial and azimuthal mode indices simultaneously, overcoming the challenges in coinciding a single point defect with the maximum electric field of an optical mode both spatially and spectrally. The excellent characteristics of h-BN SPEs, including exceptional emission rate, considerably high Debye–Waller factor, and Fourier transform limited linewidth at room temperature, render strong coupling with the ratio of coupling to decay rates g/max(γ, κ) predicated as high as 500. This study not only provides insight into the emitter–cavity interaction, but also contributes toward realizing h-BN photonic components, such as low-threshold microcavity lasers and high-purity single photon sources, critical for linear optics quantum computing and quantum networking applications.

768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks.

Beyond orbital angular momentum of Laguerre-Gaussian (LG) modes, the radial index can also be exploited as information channel in free-space optical (FSO) communication to extend the communication capacity, resulting in the LG- shift keying (LG-SK) FSO communications. However, the recognition of radial index is critical and tough when the superposed high-order LG modes are disturbed by the atmospheric turbulences (ATs). In this paper, the convolutional neural network (CNN) is utilized to recognize both the azimuthal and radial index of superposed LG modes. We experimentally demonstrate the application of CNN model in a 10-meter 768-ary LG-SK FSO communication system at the AT of Cn2 = 1e-14 m-2/3. Based on the high recognition accuracy of the CNN model (>95%) in the scheme, a colorful image can be transmitted and the peak signal-to-noise ratio of the received image can exceed 35 dB. We anticipate that our results can stimulate further researches on the utilization of the potential applications of LG modes with non-zero radial index based on the artificial-intelligence-enhanced optoelectronic systems.

Stationary scalar clouds supported by rapidly-rotating acoustic black holes in a photon-fluid model

It has recently been proved that, in the presence of vortex flows, the fluctuation dynamics of a rotating photon-fluid model is governed by the Klein-Gordon equation of an effective massive scalar field in a $(2+1)$-dimensional acoustic black-hole spacetime. Interestingly, it has been demonstrated numerically that the rotating acoustic black hole, like the familiar Kerr black-hole spacetime, may support spatially regular stationary density fluctuations (linearized acoustic scalar `clouds') in its exterior regions. In particular, it has been shown that the composed rotating-acoustic-black-hole-stationary-scalar-field configurations of the photon-fluid model exist in the narrow dimensionless regime $\alpha\equiv\Omega_0/m\Omega_{\text{H}}\in(1,\alpha_{\text{max}})$ with $\alpha_{\text{max}}\simeq 1.08$ [here $\Omega_{\text{H}}$ is the angular velocity of the black-hole horizon and $\{\Omega_0,m\}$ are respectively the effective proper mass and the azimuthal harmonic index of the acoustic scalar field]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the acoustic scalar clouds of the photon-fluid model in the regime $\Omega_{\text{H}}r_{\text{H}}\gg1$ of rapidly-spinning central supporting acoustic black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum $\{\Omega_0(\Omega_{\text{H}},m;n)\}$ which characterizes the stationary bound-state acoustic scalar clouds of the photon-fluid model. Interestingly, it is proved that the critical (maximal) mass parameter $\alpha_{\text{max}}$, which determines the regime of existence of the composed acoustic-black-hole-stationary-bound-state-massive-scalar-field configurations, is given by the exact dimensionless relation $\alpha_{\text{max}}=\sqrt{{{32}\over{27}}}$.