Publications

Abbreviated version

Billy Cheek, Mieczyslaw Dabkowski, Amr El Nagdi, Louis R. Hunt, Tim P. LaFave Jr., Ke Liu, Duncan L. MacFarlane, & Viswanath Ramakrishna, "Analysis of a Polynomial System Arising in the Design of an Optical Lattice Filter Useful in Channelization", Acta Applicandae Mathematicae, to be published.

Abstract (tentative)
In this work, we consider design questions for an active optical filter, which is being manufactured at the University of Texas at Dallas, and which has proven to be useful in the signal processing task of RF channelization. The filter can be described by a linear, discrete time state space model. The controlling agents, the gains, are embedded in the matrices intervening in this state space model. Consequently, techniques from linear feedback control theory do not apply. We concentrate on the question of finding real valued gains so that the A matrix of the state model has a prescribed characteristic polynomial. We find that three of the coefficients can be arbitrarily picked, but that the remaining are constrained by these and the other system parameters. Our techniques use methods from constructive algebraic geometry.

Duncan L. MacFarlane¹, Marc P. Christensen², Ke Liu¹, Tim P. LaFave Jr.¹, Gary A. Evans², Nahid Sultana¹, T. W. Kim†, Jiyoung Kim†, Jay B. Kirk², Nathan Huntoon², Andrew J. Stark‡, Mieczyslaw Dabkowski³, Louis R. Hunt¹, and Viswanath Ramakrishna³ "Four-Port Nanophotonic Frustrated Total Internal Reflection Coupler " Photonics Technology Letters, to be published.

¹Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 75083.
²Department of Electrical Engineering, Southern Methodist University, Dallas, TX 75275-0338.
³Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083.
†Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, TX 75083.
‡Electrical and Computer Engineering Department at Georgia Institute of Technology, Atlanta, GA 30332.

Abstract (tentative)
Four-port frustrated total internal reflection couplers in InP based GaInAsP quantum well substrates are realized and characterized. Each coupler forms an “X” at the perpendicular intersection of two ridge waveguides and is aligned 45° to the optical path. The 180nm-wide couplers are fabricated by dry etching deep trenches through the quantum wells and backfilling with alumina (n=1.71) by atomic layer deposition. Coupling coefficients for the fabricated coupler are in good agreement with a three-dimensional finite difference time domain theory, and an 82% coupler efficiency is estimated.

Duncan L. MacFarlane¹, Marc P. Christensen², Amr El Nagdi¹, Gary A. Evans², Louis R. Hunt¹, Nathan Huntoon², Jiyoung Kim†, T. W. Kim†, Jay Kirk², Tim P. LaFave Jr.¹, Ke Liu¹, Viswanath Ramakrishna³, Mieczyslaw Dabkowski³, and Nahid Sultana¹ "Experiment and Theory of an Active Optical Filter", IEEE Journal of Quantum Electronics, to be published.

¹Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 75083.
²Department of Electrical Engineering, Southern Methodist University, Dallas, TX 75275-0338.
³Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083.
†Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, TX 75083.

Abstract (tentative)


The role of gain in an optical filter is advanced by good agreement between theory and experiment presented herein. The particular integrated photonic filter is comprised of four semiconductor optical amplifiers and one four-port coupler located at the intersection of the amplifiers. The four-port coupler is realized using frustrated total internal reflection off a very thin slab of alumina embedded in the substrate. The delta function response of the filter is measured using an ultra-fast laser and cross-correlator, and the measured transfer functions agree well with a z-transform based description of the device.

Tim LaFave Jr. "Discrete Charge Dielectric Model of Electrostatic Energy" Journal of Electrostatics 69(5) 414-418 (2011).

Abstract
Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external source: Coulomb repulsion among point charges, direct polarization between point charges and their associated surface charge elements, and indirect polarization between point charges and surface charge elements formed by other point charges. The model yields the potential energy, U(N), stored in a general N point charge system differing from conventional integral formulations, 1/2∫E⋅DdV and 1/2∫ρΦdV, in a manner significant to the treatment of few-electron systems.

A. El Nagdi, K. Liu, Tim P. LaFave Jr., L. R. Hunt, V. Ramakrishna, M. Dabkowski, D. L. MacFarlane, M. P. Christensen, “Active integrated filters for RF-photonic channelizers,” Sensors 11(2) 1297-1320 (2011).

Abstract
A theoretical study of RF-photonic channelizers using four architectures formed by active integrated filters with tunable gains is presented. The integrated filters are enabled by two- and four-port nano-photonic couplers (NPCs). Lossless and three individual manufacturing cases with high transmission, high reflection, and symmetric couplers are assumed in the work. NPCs behavior is dependent upon the phenomenon of frustrated total internal reflection. Experimentally, photonic channelizers are fabricated in one single semiconductor chip on multi-quantum well epitaxial InP wafers using conventional microelectronics processing techniques. A state space modeling approach is used to derive the transfer functions and analyze the stability of these filters. The ability of adapting using the gains is demonstrated. Our simulation results indicate that the characteristic bandpass and notch filter responses of each structure are the basis of channelizer architectures, and optical gain may be used to adjust filter parameters to obtain a desired frequency magnitude response, especially in the range of 1–5 GHz for the chip with a coupler separation of ~9 mm. Preliminarily, the measurement of spectral response shows enhancement of quality factor by using higher optical gains. The present compact active filters on an InP-based integrated photonic circuit hold the potential for a variety of channelizer applications. Compared to a pure RF channelizer, photonic channelizers may perform both channelization and down-conversion in an optical domain.

Tim LaFave Jr & Raphael Tsu, "Capacitance: A property of nanoscale materials based on spatial symmetry of discrete electrons" Microelectronics Journal 39 617-623 (2008). The 6th International Conference on Low Dimensional Structures and Devices – LDSD’07.

Abstract
Capacitance is a measure of the ability to store electrons and is conventionally considered to be a constant dependent upon the shape of metal contacts and the dimensions of the system. In general, however, equipotentials of dielectric systems without metal contacts take the shape of very complex three-dimensional surfaces resulting from the spatial distribution of discrete electrons. The fundamental definition of capacitance, C≡Q/V, in which V is the potential within which electrons are confined, requires that the total capacitance take into account local capacitances of every electron and all cross-capacitances. To circumvent this complexity, the average total electrostatic potential experienced by each electron is utilized to obtain a capacitance expression generally appropriate to dielectric systems consisting of few excess electrons without metallic contacts. The capacitance may then be expressed as an exact function of the total electrostatic potential energy of the system. The integrity of this expression is demonstrated using a representative system of N excess electrons confined to a dielectric sphere. The capacitance expression is shown to be consistent with the conventional capacitance for a single electron dielectric sphere and with C=4πε₀ε'a for metallic spheres. A relatively large sphere size is chosen such that the magnetic moment interaction energy is negligibly small. The capacitance exhibits a non-uniform relationship with respect to N coincident with shell-filling patterns of the natural atomic system. This classical electrostatic interactions approach is particularly appealing to the practical development of nanoscale materials and devices as it circumvents immediate recourse to often unintuitive and complicated quantum mechanical descriptions.

Tim LaFave Jr & Raphael Tsu, “A new definition of capacitance of few electron systems” PIERS, Hangzhou, China 1269-1274 (2008).

Abstract
Due to the discreteness of electronic charges in a nanoscale system, capacitance is defined in terms of the total interaction energy of N-electrons confined in a dielectric sphere. Specifically, the distribution of N-electrons is obtained from minimization of the total interaction energy including Coulomb, polarization and the self-polarization terms. And recently, by including the formation energy, the work done on the system, the capacitance agrees with the case when N = 1 and N = ∞. While Schrödinger equation is crucial in dealing with kinetic energy, it is the Poisson equation that allows properly accounting for spatial symmetry properties resulting from the discrete nature of electrons.

Tim LaFave Jr & Raphael Tsu, “The value of monophasic capacitance of few-electron systems” Microelectronics Journal 40 791-795 (2009). European nano Systems (ENS 2007); International Conference on Superlattices, Nanostructures and nanodevices (ICSNN 2008).

Abstract
Due to the discreteness of electronic charges in a nanoscale system, capacitance is defined in terms of the total interaction energy of N-electrons confined in a dielectric sphere. Specifically, the distribution of N-electrons is obtained from minimization of the total Coulomb and polarization interaction energy and the formation energy, the work done on the system. Our discrete charge dielectric (DCD) model gives rise to an electrostatic capacitance agreeing with the N=1 and ∞ cases. For nanometer-size devices, the Schrodinger equation should be used; however, for size greater than 10nm, the Poisson equation accounts for spatial symmetry properties resulting from the discrete nature of interacting electrons. Without metallic components, the equal potential landscape does not coincide with our spherical boundary except for the N=1 case. There is a special configuration associated with each N. Hence, the capacitance defined is monophasic, representing a single electrostatic phase. The most important application of this work may lie in optoelectronics and biological systems.

Tim LaFave Jr The Classical Electrostatic Periodic Table, Capacitance of Few Electron Dielectric Spheres and a Novel Treatment of One- and Two-Electron Finite Quantum Wells PhD Dissertation, University of North Carolina, Charlotte, 2006

Abstract
The centerpiece of this dissertation is the discovery of the classical electrostatic periodic table of elements through non-linear ground state energies coincident with atomic shell-filling resulting from symmetry properties of discrete electrons constrained by a spherically-symmetric system. The time-independent electrostatic equilibrium configuration of few electrons confined to a large classical dielectric sphere is obtained by minimization of the total interaction energy. The interactions model yields more than twice the energy predicted by the classical Gauss model. Each N-electron system is proposed as a unique phase characterized by its symmetry properties. A new mono-phasic capacitance definition of dielectric spheres is derived from the fundamental relation Q=CV. Large differences from the Gauss model are obtained for few-electron systems, but convergence is found in the metallic limit. Of particular significance is the means by which symmetry-dependent properties of atomic-scale devices may be exploited by controlling the internal architecture of charge distributions. This work will be useful to modeling of many-electron chemical and biological systems, such as macromolecules, owing largely to symmetry differences between the Gauss model and the interactions model. The foundation upon which all Nature rests is the symmetry of fundamental particles.