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In the International System of Units (SI), distinct physical dimensions were assigned to the electric ( $E$ ) and magnetic ( $H$ ) fields as volt-per-meter and ampere-per-meter, respectively. To save the dimensional balance in the standard Maxwell’s equations (MEs) in SI units, a pair of free-space constants, $\epsilon _{0}$ and ${\mu } _{0}$ , with their dimensions of farad-per-meter and henry-per-meter were installed heuristically. Eventually, every quantity that participated in each ME in SI units has an individual physical dimension distinct from the other terms therein. This situation hampers the control of the dimensional balance in the processes of analytical manipulations with the MEs during the theoretical studies. Reformatting the free-space constants is performed in this article so that one new constant is obtained with its dimension of volt, and the other one has its dimension of ampere. These gave a handle to scale the electric and magnetic fields appropriately. Ultimately, the new fields are obtained with their common dimension of inverse-meter. Meanwhile, the standard differential procedures $\epsilon _{0}\frac {\partial }{\partial t}$ and ${\mu } _{0}\frac {\partial }{\partial t}$ from MEs are obtained in their simple common format of $\frac {\partial }{c\,\partial t}$ , where $c$ is the speed of light. The MEs in the novel format are exhibited for the fields in the free space, plasma, and dielectrics. The content of this article is destined for the researchers who deal with theoretical studies in electrodynamics, and the level of content is appropriate for and realizable by recent graduates, M.Sc. and Ph.D. students, and professionals.

Millimeter-wave (mmWave) bands will be used for the fifth generation communication systems to support high data rates. For the proper characterization of the mmWave propagation channel, it is essential to measure the power angular-delay profile (PADP) of the channel which includes angle-of-departure (AoD) and angle-of-arrival (AoA) of the multipath components (MPCs). In this paper, we first describe in detail our 28 GHz channel sounder where directional horn antennas are placed on rotating gimbals. Then, for this specific sounder class, we describe and address the following two problems in extracting the MPCs from the measurements: 1) For the channel measurements at large distances between the transmitter (TX) and the receiver (RX), it is not possible to generate the triggering signal for the TX and the RX using a single clock (SICL). This necessitates the use of separate clocks (SECLs) which introduces a random timing drift between the clocks. 2) As the positions of the antennas change during the scanning process, total distance traveled by the same MPC differs at each measurement. These two errors together cause missing some of the MPCs and detecting MPCs that do not exist in reality. We propose an algorithm to correct the clock drift and the errors in the MPC delays due to the rotation of the antennas. We compare the MPCs from the SICL measurement and the corrected SECL measurements using a Hungarian algorithm based MPC matching method. We show that the percentage of the matched MPCs increases from 28.36% to 74.13% after the correction process., 15 pages. Submitted to IEEE Transactions on Antennas and Propagation

The aim of this analytical study of a plasma-filled rectangular cavity in time domain is to exhibit the ability of the evolutionary approach to study the electromagnetic fields forced by surge signals in a dynamical system. Maxwell’s equations for the fields and the boundary conditions for the perfect electric conductor rectangular cavity are supplemented with the constitutive relation for the plasma. Two different pulse waveforms were used for modeling of the surge signals exciting the fields. The solution is obtained for the dynamical system in the form of product of two elements. First element that depends on coordinates is a modal basis. The other element depending on time is a modal amplitude. The modal basis is specified as a summation of four subspaces. Two of these subspaces resemble the solenoidal modes, and the other two resemble the irrotational modes. Evolutionary differential equations with initial conditions are obtained and solved analytically for the amplitudes.

The problem of forced oscillations in a cavity filled with a dynamic plasma is solved in the time domain in compliance with the principle of causality. Interaction of the plasma and the cavity field is driven by the motion equation where the field is present in the Lorentz force standing at its right-hand side. The solution has a form of the modal expansions. Every term herein is a product of two multipliers. One is the vector element of the modal basis dependent on coordinates only. The basis is obtained as an eigenvector set of a self-adjoint operator specially selected from Maxwell’s equations. The operator is specified as a merger of the differential procedure $\nabla \times $ and the boundary conditions over perfectly conducting cavity surface. The basis elements are derived with their physical dimensions, i.e., volt per meter and ampere per meter. The other factor is a scalar dimension-free time-dependent modal amplitude. A system of evolutionary equations (i.e., with time derivative) for the modal amplitudes is derived and solved explicitly under the initial conditions. The problem is solved in the Hilbert space of real-valued functions of coordinates and time.

The energetic characteristics of cylindrical medium-free time-domain waveguide fields are solved within the framework of the evolutionary approach to electromagnetics. Solving the boundary-eigenvalue problem for transverse Laplacian yields a configurational basis in the waveguide cross section. Elements of the basis depend on transverse coordinates, whereas the modal amplitudes depend on the longitudinal coordinate, $z,$ and time, $t$. Solving the resulted Klein-Gordon equation yields a basis for analysis of the modal amplitudes. Exact solutions for the amplitudes of TE-modes are obtained, and the energetic field characteristics are derived in accordance with the causality principle.

The relationship between a polarization vector and an electric field applied to a lossy dielectric media of Lorentz type is considered in a novel format of Maxwell’s equations. Dynamic processes are studied via solving Newton’s equation of motion for the polarization vector, where a given applied electric field stands at its right-hand side as a force term. The applied field can have a beginning and an end in time. The causal solution is obtained via solving the motion equation by the method of matrix exponential. Two examples are exhibited where the problem is solved explicitly in the class of the real-valued functions of time.

This paper presents an experimental study of the air-to-ground (AG) propagation channel through ultrawideband(UWB) measurements in an open area using unmanned-aerial-vehicles (UAVs). Measurements were performed using UWB radios operating at a frequency range of 3.1 GHz - 4.8 GHz and UWB planar elliptical dipole antennas having an omni-directional pattern in the azimuth plane and typical donut shaped pattern in the elevation plane. Three scenarios were considered for the channel measurements: (i)two receivers (RXs) at different heights above the ground and placed close to each other in line-of-sight (LOS) with the transmitter (TX) on the UAV and the UAV is hovering; (ii) RXs are in obstructed line-of-sight (OLOS) with the UAV TX due to foliage, and the UAV is hovering; and, (iii) UAV is moving in a circular path. Different horizontal and vertical distances between the RXs and TX were used in the measurements. In addition, two different antenna orientations were used on the UAV antennas (vertical and horizontal) to analyze the effects of antenna radiation patterns on the UWB AG propagation. From the empirical results, it was observed that the received power depends mainly on the antenna radiation pattern in the elevation plane when the antennas are oriented in the same direction, as expected for these omni-azimuth antennas. Moreover, the overall antenna gain at the TX and RX can be approximated using trigonometric functions of the elevation angle., This paper is accepted for publication in Aerospace 2019 Conference

We introduce and investigate a new multi-island bit representation scheme with bit-patterned media (BPM) to increase the tolerance to the reader noise and the media noise compared with the standard BPM with a single island/bit and to granular media. The key idea is to use multiple islands in two dimensions to represent one bit. The redundancy in such a multi-island representation reduces the impact of the write in errors and decreases the effect of the media noise. We show that these multi-island representations offer improved bit error rate (BER), although only one readback sample per bit is used for equalization and detection. Here, a micromagnetic writing model and a read channel including media noise are used for the simulations, where optimized writer and reader architectures with one, two, and three read elements are investigated. Simulations at a 1 ${\rm Tb}/{\rm in}^{2}$ channel bit density, for the target BER of $10^{-2}$ and readback with two readers, indicate that the readback of BPM recording (BPMR) based on 1 ${\rm Tdot}/{\rm in}^{2}$ (1 dot/bit), 2 ${\rm Tdots}/{\rm in}^{2}$ (2 dots/bit), and 4 ${\rm Tdots}/{\rm in}^{2}$ (4 dots/bit) island density can tolerate 1, 3.1, and 3.3 dB more reader noise compared with the granular media. For readback with two readers, at $10^{-2}$ target BER, writing with 4 ${\rm Tdots}/{\rm in}^{2}$ and 2 ${\rm Tdots}/{\rm in}^{2}$ island density can tolerate the media noise (modeled by island position jitter and island size fluctuation) levels of 11% and 8.5% compared with the 1 ${\rm Tdot}/{\rm in}^{2}$ with the media noise level of 5%. When the channel bit density is increased to 1.5 ${\rm Tb}/{\rm in}^{2}$ , such a multi-island approach can still provide improved reader noise and media noise tolerances compared with the standard BPMR with one bit per island and to granular media at the same density.

Analytical solutions of the TE-modal fields for a lossless waveguide are expressed within the framework of the evolutionary approach to electrodynamics (EAE). Electric and magnetic field vectors, which have physical dimensions of volt per meter and amper per meter respectively, are factorized in SI units. Elements of the modal basis that depend on transverse coordinates, r, and the modal amplitudes that depend on longitudinal coordinate, z, and time, t, are obtained via solving the boundary-eigenvalue problem. Exact solutions for mass and momentum are derived and presented graphically.

The problem of propagation is solved for circular waveguide TE-modal waveforms within the framework of the evolutionary approach to electrodynamics (EAE). Physical dimensions of the electric and magnetic intensity vectors, volt per meter and ampere per meter, ingressed in Maxwell's equations are factorized in SI units. Then a system of evolutionary equations for the modal amplitudes dependent on axial coordinate and time are obtained from the Maxwell's equations supplemented with the boundary conditions for perfect electric conductor surfaces. Solutions for the waveguide modal fields and for the energetic field characteristics are presented graphically.

The amplitudes and energetic properties of the TM-modal fields for a lossy waveguide are solved analytically in time-domain. Solving the boundary-eigenvalue for transverse Laplacian problem results a basis in the waveguide cross section. Elements of this basis depend on transverse coordinates, r, and the modal amplitudes depend on the longitudinal coordinate, z, and time, t. Exact solutions are derived and presented graphically.

Statement of the problem involves the system of Maxwell's equations (with the time derivative) and the motion equation for a nonmagnetic quasi-neutral homogeneous plasma simultaneously. The motion equation governs the behavior of the charged particles that is conditioned by their interactions in the plasma with the electromagnetic field, which is governed by the Maxwell's equations, in turn. These processes are considered in a cylindrical cavity bounded by the closed surface of perfect electric conductivity. Within the cavity, an input item is placed that is meant for excitation of the forced oscillations by a given signal applied to that one. The signal has a beginning and an end. The time-domain problem is solved within the framework of the Evolutionary Approach to Electrodynamics (EAE). The EAE was recognized recently as an alternative to the classical time-harmonic field method: (O. A. Tretyakov and F. Erden, “Evolutionary approach to Electromagnetics as an alternative to the time-harmonic field method,” IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Sci. Meeting, 8–14 July, Chicago, US, 2012).

Development of the time-harmonic electromagnetic theory dates back to the end of 19th century stating that all the electromagnetic field quantities vary harmonically in time. This assumption, being formalised in the system of Maxwell's equations (ME) with time derivative, changes the hyperbolic type of the partial differential equation into the elliptic type. Therefore, the time-harmonic solutions to the ME of elliptic type do not satisfy the causality principle and have difficulties with the relativistic transformations. Progress of the time-domain field theory has started via the development of computational electromagnetics in the second part of the 20th century. Numerical techniques are capable of providing huge volumes of numerical data; however, a deep physical insight to the data can be achieved under the presence of analytical results. Nevertheless, analytical theory of time-domain electromagnetics goes through an initial step of its development.

The response of a heat-assisted magnetic recording (HAMR) system is very sensitive to the laser spot position. The response is determined by transition characteristics like the center, curvature, and length. In this paper, by using the thermal Williams-Comstock model and the microtrack model, the effects of laser spot position on transition characteristics are investigated for both longitudinal and perpendicular recording from a read channel systems perspective. The general trend in their variation is determined and used to explain the resultant change in response. By simulation, we determine the post-Viterbi dominant error events for longitudinal HAMR system. Finally, we apply the well-known MTR codes to mitigate such errors and present their bit-error performance

A novel system design for sensing very high density magnetic recording data, such as that envisioned for two-dimensional magnetic recording, is proposed. The key idea is a rotated sense head, so that the shields are aligned down-track, combined with oversampled signal processing to regain the lost down-track resolution. Based on a random Voronoi grain model, simulation indicates that for bits with dimension of 8 nm × 6 nm, 5.5 nm grains, and a reader with 4 nm × 18 nm × 18 nm free layer and 11 nm shield-shield spacing, the bit error rate can drop from 20.9% for a normally positioned head array to 4.2% for a single-rotated single head with sampling period of 2 nm, a minimum mean squared error equalizer, and pattern-dependent noise prediction detector. The user density computed using the Shannon capacity limit is greatly increased to 10.1 Tb/in2.

An outline of the evolutionary approach to time-domain electromagnetics is presented in a compact form available for practical using. A cavity is loaded with a given source of transient signal. The cavity field is presented via expansions in terms of the solenoidal and irrotational modes having time-dependent modal amplitudes. The differential equations with time derivative are derived from Maxwell's equations for the amplitudes jointly with appropriate initial conditions. The frequency-domain theory usually interprets the irrotational modes as some static fields. Graphical results illustrating the time dependence of the irrotational and solenoidal modes will be exhibited in the presentation.

Forced oscillations are studied in a closed resonator filled with a polar dielectric. Time-dependent current density is installed in Maxwell's equations as an externally forced signal source. The latter can be an arbitrary integrable function of time. The system of Maxwell's equations (with partt) is solved simultaneously with Debye equation for the polarization vector, which plays role of a dynamic constitutive relation between the polarization vector and the electric field. The electromagnetic field vectors are presented as modal expansions in terms of the solenoidal and irrotational modes both with time-dependent modal amplitudes. A set of evolutionary differential equations for the modal amplitudes, supplemented with appropriate initial conditions, is derived and solved explicitly. The instantaneous and dynamic component parts of polarization are present in the solutions separately.

In this paper, oversampled timing recovery for magnetic recording channels. Performance comparison using PLL gain parameters were designed. We consider normalized recording density for both longitudinal and perpendicular recording channels with media jitter noise, clock jitter noise, and frequency offset were modelled.

Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such systems by tracing a few rays through them. Determining the location, magnification or scale factor, and field curvature associated with images and Fourier transforms by tracing only two rays is a common skill. In this paper we show how the transform order, scale factor, and field curvature can be determined in a similar manner for the fractional Fourier transform. Our purpose is to develop the understanding and skill necessary to recognize fractional Fourier transforms and their parameters by visually examining ray traces. We also determine the differential equations governing the propagation of the order, scale, and curvature, and show how these parameters are related to the parameters of a Gaussian beam. © 1997 Published by Elsevier Science B.V.

We form optical systems by using only free space portions and cylindrical lenses, and consider these systems as anamorphic fractional Fourier transformers. We dynamically adjust the transform order, scale factor and field curvature of both orthogonal dimensions of anamorphic fractional Fourier transformation by just changing the focal lengths of cylindrical lenses used in the proposed setups. Here, we also consider two approaches for implementing cylindrical lenses with dynamically adjustable focal lengths. There may also be some other methods to obtain cylindrical lenses having adjustable focal lengths which can successfully be used in these proposed setups.

The propagation of mutual intensity through quadratic graded-index media or free space can be expressed in terms of two-dimensional fractional Fourier transforms for one-dimensional systems and in terms of four-dimensional fractional Fourier transforms for two-dimensional systems. As light propagates, its mutual intensity distribution is continually fractional Fourier transformed. These results can also be generalized to arbitrary first-order optical systems. Furthermore, the Wigner distribution associated with a partially coherent field rotates in the same manner as the Wigner distribution associated with a deterministic field. © 1996 Optical Society of America.

Cataloged from PDF version of article. We define the accumulated Gouy phase shift as the on-axis phase accumulated by a Gaussian beam in passing through an optical system, in excess of the phase accumulated by a plane wave. We give an expression for the accumulated Gouy phase shift in terms of the parameters of the system through which the beam propagates. This quantity complements the beam diameter and the wave-front radius of curvature to constitute three parameters that uniquely characterize the beam with respect to a reference point in the system. Measurement of these parameters allows one to uniquely recover the parameters characterizing the first-order system through which the beam propagates. © 1997 Optical Society of America.