Research Overview

My theoretical research can be classified in terms of the following sub-categories: special functions; canonical solutions; frequency-domain fields in layered media; and packaging applications.  My experimental research has all been directed toward the development of novel techniques for the measurement of EM signals.  A brief overview of my research is given below.

Much of my theoretical research involves the use of a class of special functions called Incomplete Lipschitz-Hankel Integrals (ILHIs).  These special functions have been found to appear in numerous applications in engineering and physics.  However, prior to our work, efficient algorithms were not available to compute the ILHIs.  We have been the pioneers in this area of research, e.g., we have developed new series representations and new applications for ILHIs, and we have also developed new techniques for obtaining solutions in terms of ILHIs.  Our ILHI research has now matured to the point where these special functions are being used to dramatically improve the computational efficiency in a number of important problems in EM, including problems in the areas of electronic packaging, optics, dispersion, diffraction, and propagation. 

Special Functions 

I first encountered the ILHIs of the Bessel type while conducting my doctoral dissertation research.  Since efficient algorithms for the numerical computation of this special function did not exist, we developed new convergent and asymptotic series expansions for the ILHIs [1] (papers are listed under publications and can be accessed by clicking on the reference numbers).  In later research, we also encountered ILHIs of the Hankel form.  Since the recurrence-relation-based techniques that were employed in [1] could not be extended to the ILHIs of the Hankel form, we had to develop new techniques in [17, 19, 42].  Furthermore, in order to extend these algorithms to complex-valued arguments, we also had to develop robust algorithms for the computation of Hankel functions of complex arguments [28, 42]. 

Canonical Solutions

Due to the complexity of Maxwell's equations, there are only a few problems in EM that yield exact, Closed-Form (CF) solutions in terms of special functions.  CF solutions are desirable because in addition to allowing for the efficient computation of the desired field quantities, they provide valuable insight into the physical phenomenology in a problem. The same information is usually very difficult to extract from a purely numerical technique. Because of their superior efficiency and accuracy, CF solutions are also often used to benchmark numerical algorithms. 

Our pioneering work with ILHIs has led to the discovery of new CF solutions for a number of problems in EM [14].  For example, we obtained CF expressions for the near-zone fields associated with a parabolic reflector antenna in [9] and the field distributions for a lens in [18].  Previously, CF expressions were only available in the far zone of the antenna and at the focal point of the lens.  We also developed CF solutions for the near-zone fields associated with physical optics scattering/diffraction from a two-dimensional (2-D) conductive strip/aperture in [13, 40], and for the radiation from a semi-infinite traveling-wave current filament [12].

In addition to appearing in diffraction problems, ILHIs also appear in the CF solutions for a number of transient propagation problems that involve dispersion.  In [11] we used a contour integration technique to find a CF representation for pulse propagation in a waveguide. Later, a simpler differential-equation-based technique was developed to obtain a CF solution for plane-wave propagation through cold plasmas [15].  This technique was later extended to the problems of transient pulse propagation through lossy plasmas [24] and Lorentz media [25], and transient plane waves obliquely incident on a conductive half space [21, 22].  The papers [21, 22] were awarded the Schelkunoff Best Paper Award from the IEEE Transactions on Antennas and Propagations.  The solutions in [21, 22] were also used to study the effects of neglecting displacement currents when studying transient wave propagation in the earth [23].  Techniques similar to those in [15] were used to obtain CF solutions for triangle impulse responses on lossy transmission lines [35] and for the time-domain surface impedance for a homogeneous, lossy half-space [38].  

Frequency-Domain Fields in Layered Media

One of my main research areas has involved the modeling of EM waves in layered media [2, 3, 4, 5, 6, 8, 10, 16, 26, 27, 31, 32].  The results from this research can be applied to problems involving the analysis of interconnects in high-speed digital circuits, microstrip antenna design, development of stealth technologies, studies involving the use of hyperthermia for the treatment of cancer, etc.  In my doctoral dissertation work, we developed analytical techniques that allowed for the accurate and efficient evaluation of the Method of Moment (MoM) reaction integrals [2, 3, 4].  In essence, the angular integrals, in the 2-D MoM reaction integrals (i.e., Sommerfeld integrals), were carried out analytically and represented in terms of rapidly computable ILHIs.  After joining the UA, my first research involved using a combination of numerical techniques (i.e., Fast Fourier Transforms (FFT) and Prony’s method) and analytical techniques to obtain quasi-CF solutions (i.e., similar to complex image theory) for the problem of a vertical electric dipole above the earth [5, 8].  We also investigated the problem of radiation from horizontal wires above earth [6, 10]. 

Packaging Applications

After completing the work in [10], my research direction changed and I focused more of my energy on the previously discussed research areas, i.e., canonical solutions and special functions.  In 1997, I also started a research project involving the accurate and efficient modeling of interconnects in stripline structures.  Whereas we could only analytically evaluate the angular portion of the MoM reaction integrals in open-region structures [2, 3, 4], the presence of the shielding conductors in the stripline removed the branch cuts and allowed the remaining semi-infinite integrals to also be evaluated analytically by using contour integration techniques [26].  These solutions involved ILHIs of the Hankel type [19, 42] instead of the previously encountered ILHIs of the Bessel form [1, 17].  The prototype algorithm that was developed in [28] demonstrated that the CF solutions provided a factor of over 100 improvement in the computational efficiency over standard numerical integration.  Later, these techniques were incorporated into the UA Full-Wave Layered Interconnect Simulator (UA-FWLIS) [27], which can handle more realistic problems involving finite-width interconnects, interconnects in layered dielectrics [31, 32], bends and traveling wave expansion functions (research in progress). 

In addition to the previously discussed full-wave modeling work, we also have research projects involving transient transmission line simulations [33, 35] and macromodels [36, 37, 39, 41].   In [39, 41], we developed a hybrid phase-pole marcromodel, wherein we incorporated the physical time delays, in addition to the poles and residues, into the macromodel.  This leads to a dramatic reduction in the number of terms in the case of electrically long interconnects.   

Experimental Research

I started carrying out experimental research shortly after I came to the UA.  Our first research project involved the use of EM fields for detecting and imaging buried contaminants [7]. During a later project, we found that system drift errors can severely limit the performance of EM instrumentation.  In order to address this source of measurement inaccuracy, we developed a simultaneous calibration technique, which we refer to as the Accurate Real-Time Total Error Suppression Technique (ARTTEST Method).  We have patented this technology, and have applied it to network analyzer measurements [29, 30], phase-noise removal [34], and nonlinear gain compression measurements [43].  Recently, we have extended the ARTTEST Technique to a multipurpose probe (research in progress) that allows for vector signal analysis and vector network analyzer measurements on both frequency-offsetting components (e,g., mixer conversion loss and two-tone amplifier measurements) and non-frequency-offsetting devices (e.g., filters, linear components, and amplifier gain measurements).