Azimuthal Mode Order Research Articles

Mode-matched phase diffractive optical element for detecting laser modes with spiral phases

A new type of diffractive optical element for detecting and measuring the power distribution of transverse modes emanating from radially symmetric laser resonators is presented. It is based on a relatively simple straightforward design of a phase-only diffractive optical element that serves as a matched filter, which correlates between specific prerecorded transverse modes with a certain azimuthal mode order and those in the incident laser light. Computer simulations supported by experimental results demonstrate how such elements can accurately detect modes with spiral phases and provide quantitative results on the modal power distribution.

Mode degeneracy due to vortex core removal in magnetic disks

The mode spectrum of micrometer-sized ferromagnetic Permalloy disks, exhibiting a vortex ground state, is investigated by means of time-resolved scanning Kerr microscopy. The temporal evolution of the magnetization is probed after application of a fast in-plane field pulse. The lowest order azimuthal mode, a mode with only one diametric node, splits into a doublet as the disk diameter decreases. Theoretical models show that this splitting is a consequence of the interaction of the mode with the gyrotropic motion of the vortex core. Our experiments and micromagnetic simulations confirm that by removing the vortex core from the disk, the mode splitting vanishes.

Traceable 2-D Finite-Element Simulation of the Whispering-Gallery Modes of Axisymmetric Electromagnetic Resonators

This paper explains how a popular commercially available software package for solving partial-differential-equations (PDEs), as based on the finite-element method, can be configured to efficiently calculate the frequencies and fields of the whispering-gallery (WG) modes of axisymmetric dielectric resonators. The approach is traceable; it exploits the PDE-solver's ability to accept the definition of solutions to Maxwell's equations in so-called weak form. Associated expressions and methods for estimating a WG mode's volume, filling factor(s), and in the case of closed (open) resonators, its wall (radiation) loss, are provided. As no transverse approximation is imposed, the approach remains accurate even for quasi-transverse-magnetic/electric modes of low finite azimuthal mode order. The approach's generality and utility are demonstrated by modeling several nontrivial structures, i.e., 1) two different optical microcavities (one toroidal made of silica, the other an AlGaAs microdisk), 2) a third-order sapphire:air Bragg cavity, and 3) two different cryogenic sapphire WG-mode resonators; both 2) and 3) operate in the microwave X-band. By fitting one of 3) to a set of measured resonance frequencies, the dielectric constants of sapphire at liquid-helium temperature have been estimated.

Observation of azimuthal ferromagnetic resonance modes in 1.0μm diameter Permalloy rings

The spin dynamics of thin film Permalloy individual rings in the circulating state is studied in the presence of an in-plane bias field and in response to a transient field applied perpendicular to the ring plane. Only one dominant precessional mode is observed in the remanence state, which corresponds to an angularly uniform excitation. In contrast, when an external bias field is applied, multiple precessional modes are observed, with the number of modes increasing as the field increases. The static magnetic field distorts the circular symmetry of the initial magnetization state. As a result, the precessional torque produced by the pulsed field is inhomogeneous, which promotes the excitation of higher order azimuthal modes.

Acoustic scattering by a spliced turbofan inlet duct liner at supersonic fan speeds

Fan noise is one of the principal noise sources generated by a turbofan aero-engine. At supersonic fan speeds, fan tones are generated by the “rotor-alone” pressure field. In general, these tones can be well absorbed by an inlet duct acoustic liner, apart from at high supersonic fan speeds. However, in practice inlet duct liners contain acoustically hard longitudinal splices which cause scattering. This leads to acoustic energy being scattered into a range of different azimuthal mode orders, similar to the modal content resulting from rotor–stator interactions. The effectiveness of an inlet duct lining is reduced because acoustic energy is scattered into modes that are poorly absorbed by the liner. In this article, the effect of this acoustic scattering is examined by three-dimensional finite-element simulations of sound transmission in a turbofan inlet duct. Results include predictions of the sound power transmission loss with different splice widths, and at different supersonic fan speeds. These results demonstrate how acoustic scattering by liner splices can adversely affect fan tone noise levels at low supersonic fan speeds, but have little adverse affect on noise levels at high supersonic fan speeds. The potential noise benefit that could be achieved by manufacturing thinner splices is also examined.

Interactions of Spin Waves with a Magnetic Vortex

We have investigated azimuthal spin-wave modes in magnetic vortex structures using time-resolved Kerr microscopy. Spatially resolved phase and amplitude spectra of ferromagnetic disks with diameters from 5 microm down to 500 nm reveal that the lowest order azimuthal spin-wave mode splits into a doublet as the disk size decreases. We demonstrate that the splitting is due to the coupling between spin waves and the gyrotropic motion of the vortex core.

Numerical simulation of multistage turbine sound generation and propagation

A numerical method has been developed to calculate the noise within a turbine or a compressor by means of CFD (Time Linearized Euler Code). The noise generation, caused by the interaction of neighbouring cascades, can be calculated as well as the noise propagation within the turbomachine. Numerical results obtained by this method are compared to measurements. The CFD results are qualitatively in good agreement with the measurements. For low azimuthal mode orders at BPF 1, the computed modal sound power levels at the turbine exit are about 5 to 10 dB too high compared with measurements further downstream in the exhaust duct. Especially the cut-on, cut-off behaviour of the modes in the duct is simulated successfully.

Temporal instability of swirling gas jets injected in liquids

A temporal linear stability analysis of an inviscid incompressible swirling gas jet injected into a co-flowing liquid was conducted. The ratio of the tangential velocity to the axial velocity (swirl number) played a significant role in the destabilization of the gas jet. Even at small gas Weber numbers, the presence of swirl caused the higher order azimuthal modes to become unstable; the growth rates, and the dominant and limiting wave numbers of the higher order modes were greater than those of the varicose and sinuous modes. The differences in growth rates, limiting and dominant wave numbers of the various azimuthal modes became significant at large gas Weber numbers. An increase in liquid viscosity resulted in a reduction in the growth rates and the dominant wave numbers. The liquid co-flow velocity controlled the phase velocity of the unstable modes.

Effects of radiation on circular-grating DFB lasers. I. Coupled-mode equations

We derive near-threshold coupled-mode equations that include the effects of radiation for TE fields in circular-grating surface-emitting distributed feedback (DFB) lasers with second-order gratings. The analysis uses an exact description of the periodic grating that is valid for any grating shape and depth. For low-order azimuthal modes, approximate equations are found that are the same as those for a linear DFB laser, though the boundary conditions differ. We solve the coupled-mode equations for a weakly guiding laser numerically for low- and higher-order radial and azimuthal modes and compare these numerical results to previous experimental observations and to the results found for linear gratings. For sufficiently strong coupling, radiative losses have a significant impact on the mode structure of the laser, breaking the radial (longitudinal) mode symmetry otherwise seen for the lowest order azimuthal modes and improving mode selectivity.

Analysis of the zonal and rectangular slots on a conducting spherical cavity

The zonal slot cut on a conducting spherical cavity is analyzed rigorously. The slot is excited asymmetrically, which excites higher order azimuthal modes. The Green's function approach is used to formulate an integral equation for the magnetic current in the slot, which is solved using the moment method (MoM). New recurrence formulas are derived so that within their stable region the admittance integrals can be evaluated without the need for any numerical integration. In this case, the solution is very easy to implement with extremely short computation time. The effects of the latitude angle on the peak resistance and percentage bandwidth are investigated. Furthermore, the cavity resonance modes and their degeneracy are examined by plotting the expansion coefficients of the magnetic current. In addition, the problem of a rectangular slot in the nonequatorial plane is also studied. Measurements are carried out and good agreement between theory and experiment is obtained.

Multimode Analysis of the Hollow Plasma Channel Wakefield Accelerator

The hollow plasma channel is analyzed as an accelerating structure. The excitation of the channel by an ultra-relativistic beam is analyzed. Coupling to the fundamental and all higher order azimuthal modes of the excited electromagnetic fields is derived. Implications of this work for plasma-based accelerators, including beam loading and beam breakup, are discussed. Small initial transverse displacements of the beam are shown to couple to deflecting modes in the channel. The asymptotic growth rate of the resultant beam breakup instability is analyzed and a method for reducing the growth is proposed.

Near- and far-field properties of annular CO_2 waveguide lasers

The theoretical and experimental investigation of field properties of annular waveguide lasers with a Fabry-Perot resonator is presented. Oscillation with high azimuthal mode order leads to an annular intensity distribution in the far field with almost linear dependence of the annular diameter on the mode order. Low-order fields form a distinct focal spot in the far field. A laser device with a discharge area of 6-cm diameter and 53-cm length yields an output power of 600 W.

High-harmonic slotted gyroklystron amplifier: linear theory and nonlinear simulation

A fluid theory and two self-consistent particle-tracing simulation codes are described for designing low voltage, s/sup th/-harmonic slotted gyroklystron amplifiers, in which axis-encircling electron beams are in resonance with the s/sup th/-order azimuthal modes of a series of magnetron-type cavities, allowing the gyrotron amplifier's required magnetic field to be reduced by a factor of s. The linear fluid theory yields a convenient closed-form expression for gain and the nonlinear simulation code determines the large-signal device performance, while the much faster linear simulation code allows thorough, multi-dimensional parameter searches to be performed quickly. The simulation codes self-consistently account for shifts of the cavity's resonant frequency and quality factor due to beam loading. The three theoretical approaches, which agree in the small-signal regime for weak beam loading, were used to design a 95 GHz, three-cavity, slotted twelve-vane, sixth-harmonic gyroklystron amplifier utilizing a 70 kV, 10 A, v/sub /spl perp///v/sub z/=2, axis-encircling beam and a 6.1 kG magnet. The nonlinear self-consistent simulation code predicts that the sixth-harmonic gyrotron amplifier with an ideal beam will yield an electronic efficiency of 20% and a saturated gain of 37 dB, while the more realistic device with a 10% axial velocity spread will generate a peak output power of 84 kW with 12% efficiency, a saturated gain of 27 dB and a 0.2% constant-drive bandwidth. >

Azimuthal mode discrimination of annular resonators

A diffraction formula for annular beam propagation is suggested. Significant computational savings are obtained without restriction to low azimuthal mode orders. Azimuthal mode discrimination is shown to exist in stable annular resonators. High-order azimuthal modes can suffer low diffraction losses with certain mirror parameters. These high-order modes are identified with azimuthal revolving rays that satisfy known geometric relations for multipass resonators.

Optical fiber hybrid-surface plasmon polaritons

When a thin metallic region exists between the core and the cladding regions of a step-index optical fiber, hybrid surface plasma modes can be supported. For each azimuthal mode order two hybrid modes generally occur. Their disperison and attenuation characteristics are studied. The selective influence of the core radius on these is found to be strong only if the radius is small. As the radius increases the modes become degenerate with those of the pure TM polarization.

Circularly symmetric distributed feedback laser: coupled mode treatment of TE vector fields

The vector orientation of transverse electric (TE) fields in deriving coupled mode equations for radially outward- and inward-going modes in a circular waveguide diffraction grating is treated. The equations are derived for cylindrical waves in a system that is translationally invariant along the cylinder axis; the derivation is then extended to the waveguide geometry. The coupled mode equations are used to describe the operation of the circularly symmetric distributed feedback (DFB) laser. While predicting a similar dependence of the laser threshold gain on an azimuthal mode order to that found by a simpler, scalar-field treatment, the vector-field treatment predicts a fundamental difference in the location of the cavity resonances. The circular DFB laser is expected to lase in multiple azimuthal modes but maintain a relatively narrow overall spectral width. >

Mode behaviour in a tapered multimode fibre

A derivation based on ray tracing and the local plane-wave approximation is used to show the behaviour of waveguide modes in a linearly tapered multimode fibre having a step-index profile. The azimuthal mode order l is invariant through the taper, and, for suitably designed tapers, the changes in the radial mode order m and the lateral component u are negligible. A formula for designing such tapers is presented.