Higher Order Evanescent Modes Research Articles

Specificities of Electromagnetic Field Excitation in a Capacitive HF Discharge. III. Symmetric Discharge Partially Filling the Discharge Chamber

Electrodynamic characteristics of a low-pressure (electron collision frequency much lower than the field frequency) capacitive HF discharge maintained by an electromagnetic field with a frequency between 13 and 900 MHz are studied analytically and numerically. It is demonstrated that the field of both the fundamental mode (the field in the metal–space-charge sheath–plasma–space-charge sheath–metal structure) and the field of the higher-order evanescent modes must be taken into account for correct calculation of discharge characteristics under such conditions in a wide range of electron densities. Expressions governing the amplitudes of excited waves, along with expressions governing the discharge impedance in the presence of these waves, are derived by using field expansion in eigenwaves of an empty waveguide and eigenmodes of the three-layer structure. The case in which the size of plasma is smaller than the size of the electrodes is analyzed in detail. In this case, excitation of higher-order types of waves in the plasma column is generated by axial plasma inhomogeneity and is not related to electrodynamic effects near the electrode boundaries. It is demonstrated that the positions of current and voltage resonances related to propagation of surface waves along the three-layer structure becomes substantially modified due to excitation of higher-order field modes of the same structure. In addition, resonances caused by excitation of standing surface waves near the lateral surface (resonances of higher-order modes of the three-layer structure and an empty waveguide) can take place. Variation of relative position of resonances caused by changes in the discharge chamber geometry is investigated. Obtained results qualitatively agree with the results of numerical calculation of the discharge impedance and field propagation in the discharge by COMSOL Multiphysics® software package.

Perfect Conversion of a TM Surface Wave Into a TM Leaky Wave by an Isotropic Periodic Metasurface Printed on a Grounded Dielectric Slab

This article presents an exact solution for a perfect conversion of a TM-polarized surface wave (SW) into a TM-polarized leaky wave (LW) using a reciprocal and lossless penetrable metasurface (MTS) characterized by a scalar sheet impedance, located on a grounded slab. On contrary to the known realizations of LW antennas, the optimal surface reactance modulation which is found here ensures the absence of evanescent higher-order modes of the field Floquet-wave expansion near the radiating surface. Thus, all the energy carried by the SW is used for launching the single inhomogeneous plane wave into space without accumulation of reactive energy in the higher-order modes. It is shown that the resulting penetrable MTS exhibits variation from an inductive to a capacitive reactance passing through a resonance. The present formulation complements a previous article of the authors, in which a perfect conversion from TM-polarized SW to TE-polarized LW was found for impenetrable boundary conditions. Here, the solution takes into account the grounded slab dispersion, and it is convenient for practical implementation.

Chalcogenide fiber loop probe for the mid-IR spectroscopy of oil products.

A theoretical approach based on the electromagnetic theory of optical fibers has been applied in the analysis of the evanescent modes of a chalcogenide fiber bend used as a probe in a fiber-based spectroscopic sensor, by the example of the detection of small amounts of an antigel additive in a diesel fuel. The absorbance of the loop probe calculated for each mode was compared with the results of spectrometer-based measurements. The role of the higher-order evanescent modes of a fiber bend has been revealed. The efficiency of using a loop probe has been shown to depend on conditions of light launching into the probe.

End corrections for double-tuning of the same-end inlet-outlet muffler

Transmission loss spectrum of a simple expansion chamber (SEC) muffler is characterized by periodic domes. In recent years, it has been shown that by extending the inlet pipe and outlet pipe of the SEC inwards by nearly half and quarter lengths (L/2 and L/4) into the chamber, it is possible to raise three-fourths of all the TL-troughs, thereby ensuring a wide-band TL spectrum. This has been called Double-Tuning of the SEC. In practice, physical lengths of the extended inlet and extended outlet are made shorter than L/2 and L/4 by end correction in order to account for the higher-order evanescent modes at the two junctions.In this paper, making use of the three-dimensional (3-D) finite element method (FEM), general parametric expressions have been developed for the end corrections of the two junctions of the same-end inlet-outlet (SEIO) chamber, or flow-reversal chamber, in order to double-tune it on the lines of the co-axial opposite-ends inlet-outlet chamber muffler. The 3-D finite element mesh convergence has been validated against the available experimental TL spectra. This study is perhaps the first known attempt at double-tuning of the same-end inlet-outlet (SEIO) chamber muffler.

Using Higher-Order Modes of Chalcogenide Optical Fibers for the Optimization of Evanescent Wave Mid-IR Spectroscopy

On the basis of a new theoretical approach that is proposed for solving tasks of the evanescent wave mid-IR spectroscopy, it is shown that the dispersion properties of higher-order modes of a multimode chalcogenide optical fiber partly immersed into an absorbing medium can be used for the creation of fiber-optic devices combining the functions of a supercontinuum generator and a sensing element for mid-IR spectroscopic sensors. The propagation of radiation in higher-order modes makes it possible to control the position of zero dispersion of group velocity and to generate supercontinuum with near-IR pumping. Using higher-order evanescent modes in a sensing element, it will be possible to increase its sensitivity and expand the dynamic range.

Exact Solution for Conversion of Surface Waves to Space Waves by Periodical Impenetrable Metasurfaces

We show that there exists an exact solution for a lossless and reciprocal periodic surface impedance which ensures full conversion of a single-mode surface wave propagating along the impedance boundary to a single plane wave propagating along a desired direction in free space above the boundary. In contrast to known realizations of leaky-wave antennas, the optimal surface reactance modulation which is found here ensures the absence of evanescent higher-order modes of the Floquet wave expansion of fields near the radiating surface. Thus, all the energy carried by the surface wave is used for launching the single inhomogeneous plane wave into space, without accumulation of reactive energy in higher-order modes. The results of the study are expected to be useful for creation of leaky-wave antennas with the ultimate efficiency, and, moreover, can potentially lead to novel applications, from microwaves to nanophotonics.

Использование высших мод халькогенидных световодов для оптимизации метода эванесцентной спектроскопии среднего ИК-диапазона

Based on a theoretical approach, new for evanescent wave spectroscopy, it has been shown that the dispersion properties of higher modes of a multimode chalcogenide fiber partially immersed in an absorbing medium can be used to create fiber devices that combine the functions of a supercontinuum generator and a sensing element of a spectroscopic sensor of the mid-IR range. The propagation of radiation in higher modes will allow one to control the position of the group velocity dispersion zero and to obtain a supercontinuum pumped in the near IR range. In the sensing element, the use of higher-order evanescent modes will allow for greater sensitivity and broaden the dynamic range of the sensor.

Improved quantitative circuit model of realistic patch-based nanoantenna-enabled detectors

Improving the sensitivity of infrared detectors is an essential step for future applications, including satellite- and terrestrial-based systems. We investigate nanoantenna-enabled detectors (NEDs) in the infrared, where the nanoantenna arrays play a fundamental role in enhancing the level of absorption within the active material of a photodetector. The design and optimization of nanoantenna-enabled detectors via full-wave simulations is a challenging task given the large parameter space to be explored. Here, we present a fast and accurate fully analytic circuit model of patch-based NEDs. This model allows for the inclusion of real metals, realistic patch thicknesses, non-absorbing spacer layers, the active detector layer, and absorption due to higher-order evanescent modes of the metallic array. We apply the circuit model to the design of NED devices based on Type II superlattice absorbers, and show that we can achieve absorption of ∼70% of the incoming energy in subwavelength (∼λ/5) absorber layers. The accuracy of the circuit model is verified against full-wave simulations, establishing this model as an efficient design tool to quickly and accurately optimize NED structures.

EQUIVALENT CIRCUIT MODEL OF COAXIAL PROBES FOR PATCH ANTENNAS

An equivalent circuit model of coaxial probes is derived directly from the intrinsic via circuit model. As all the higher-order evanescent modes have been included analytically in the parasitic circuit elements, only the propagating mode needs to be considered by the simplest uniform-current model of a coaxial probe in numerical solvers such as flnite element method (FEM) or flnite difierence time domain (FDTD). This avoid dense meshes or sub-gridding techniques and greatly reduces the computational efiorts for accurate calculation of the probe input impedance. The derived equivalent circuit model and the new feeding technique have been validated by both analytical formulas and numerical simulations.

On the Role of Higher-Order Evanescent Modes in End-Offset Inlet and End-Centered Outlet Elliptical Flow-Reversal Chamber Mufflers

This paper deals with the role of the higher-order evanescent modes generated at the area discontinuities in the acoustic attenuation characteristics of an elliptical end-chamber muffler with an end-offset inlet and end-centered outlet. It has been observed that with an increase in length, the muffler undergoes a transition from being acoustically short to acoustically long. Short end chambers and long end chambers are characterized by transverse plane waves and axial plane waves, respectively, in the low-frequency range. The nondimensional frequency limit k(0)(D-1/2) or k(0)R(0) as well as the chamber length to inlet/outlet pipe diameter ratio, i.e., L/d(0), up to which the muffler behaves like a short chamber and the corresponding limit beyond which the muffler is acoustically long are determined. The limits between which neither the transverse plane-wave model nor the conventional axial plane-wave model gives a satisfactory prediction have also been determined, the region being called the intermediate range. The end-correction expression for this muffler configuration in the acoustically long limit has been obtained using 3-D FEA carried on commercial software, covering most of the dimension range used in the design exercise. Development of a method of combining the transverse plane wave model with the axial plane wave model using the impedance Z] matrix is another noteworthy contribution of this work.

Effect of wall thickness on the end corrections of the extended inlet and outlet of a double-tuned expansion chamber

Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss spectrum which drastically lower the overall transmission loss of the muffler. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. These cancellations would not occur unless one altered the geometric lengths for the extended tube in order to incorporate the effect of evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. End corrections of the extended inlet and outlet have been studied by several researchers. However the effect of wall thickness of the inlet/outlet duct on end correction has not been studied explicitly. This has significant effect on the tuning of an extended inlet/outlet expansion chamber. It is investigated here experimentally as well as numerically (through use of 3-D FEM software) for stationary medium.

Complex edge resonance in elastic waveguides

The resonance for different configurations of elastic waveguides with a free edge is studied from the point of view of complex resonance. We determine numerically the variations of the real part and of the imaginary part of the complex resonance frequency as a function of the Poisson ratio. For three different configurations, semi-infinite 2D plates, elastic cylinder and circular hole through a plate, the results show similar behaviours which are: a real resonance frequency for a zero Poisson ratio and a real resonance frequency that corresponds to a Lamé mode at one positive value of the Poisson ratio. In all the configurations, these free edges have complex resonances which have very high quality factors. The two Poisson ratio where the complex resonance frequency has a zero imaginary part (infinite quality factors) corresponds to trapped modes for which there is a decoupling between the propagating waves and the evanescent waves. The first decoupling at zero Poisson ratio is due to the special structure of the elasticity equations there and the second decoupling is due to the decoupling between the propagating Lamé mode and the higher order evanescent modes.

Multimode solution for the reflection properties of an open-ended rectangular waveguide radiating into a dielectric half-space: the forward and inverse problems

Open-ended rectangular waveguides are extensively used in nondestructive dielectric material evaluation. The dielectric properties of an infinite-half space of a material are calculated from the measured reflection properties referenced to the waveguide aperture. This calculation relies on a theoretical and numerical derivation of the reflection coefficient likewise referenced to the waveguide aperture. Most of these derivations assume the dominant mode field distribution across the waveguide aperture. However, when dealing with low permittivity and low loss dielectric materials, there may exist significant errors when calculating the dielectric properties from the measured reflection coefficient. These errors have also shown to be more significant in the upper frequency portion of a waveguide band. More accurate results are obtained when higher order modes are considered in addition to the dominant waveguide mode. However, most studies incorporating higher-order modes have used various approximations when calculating the reflection properties and have not provided a full discussion on the influences of dielectric properties of the infinite-half space and the frequency of operation. This paper gives a rigorous and exact formulation in which the dominant mode and the evanescent higher-order modes are used as basis functions to obtain the solution for the reflection coefficient at the waveguide aperture. The analytic formulation uses Fourier analysis in addition to the forcing of the necessary boundary conditions at the waveguide aperture. The solution also readily accounts for the complex contributions of both TE and TM higher-order modes. Finally, the influences of the dielectric properties of the infinite-half space and the frequency of operation are investigated.

Higher-order mode interaction in planar periodic structures

A method for the inclusion of higher-order evanescent modes in planar periodic structures is presented. The approach utilises the wave matrix method that is extended to account for the nonpropagating orders. As an example, the case of two closely spaced singly periodic gratings is demonstrated. In order to produce suitable data concerning reflection and transmission matrices, an integral equation formulation is used to describe the scattering behaviour of the grating. The application of the theory is intended for the design of multilayer dichroic surfaces.

Higher-order evanescent modes on slow-wave structures

By employing suitable mathematical models, the higher-order evanescent modes on two common slow-wave systems are discussed. It is shown that these closely resemble corresponding modes on related plane-waveguide or coaxial-line structures.