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Articles 1381 - 1410 of 1749

Full-Text Articles in Electromagnetics and Photonics

Freeform Reflector Design With Extended Sources, Florian Fournier Jan 2010

Freeform Reflector Design With Extended Sources, Florian Fournier

Electronic Theses and Dissertations

Reflector design stemmed from the need to shape the light emitted by candles or lamps. Over 2,000 years ago people realized that a mirror shaped as a parabola can concentrate light, and thus significantly boosts its intensity, to the point where objects can be set afire. Nowadays many applications require an accurate control of light, such as automotive headlights, streetlights, projection displays, and medical illuminators. In all cases light emitted from a light source can be shaped into a desired target distribution with a reflective surface. Design methods for systems with rotational and translational symmetry were devised in the 1930s. …


Quantum Dot Based Mode-Locked Semiconductor Lasers And Applications, Jimyung Kim Jan 2010

Quantum Dot Based Mode-Locked Semiconductor Lasers And Applications, Jimyung Kim

Electronic Theses and Dissertations

In this dissertation, self-assembled InAs/InGaAs quantum dot Fabry-Perot lasers and mode-locked lasers are investigated. The mode-locked lasers investigated include monolithic and curved two-section devices, and colliding pulse mode-locked diode lasers. Ridge waveguide semiconductor lasers have been designed and fabricated by wet etching processes. Electroluminescence of the quantum dot lasers is studied. Cavity length dependent lasing via ground state and/or excited state transitions is observed from quantum dot lasers and the optical gain from both transitions is measured. Stable optical pulse trains via ground and excited state transitions are generated using a grating coupled external cavity with a curved two-section device. …


Electro-Optical And All-Optical Switching In Multimode Interference Waveguides Incorporating Semiconductor Nanostructures, Nathan Bickel Jan 2010

Electro-Optical And All-Optical Switching In Multimode Interference Waveguides Incorporating Semiconductor Nanostructures, Nathan Bickel

Electronic Theses and Dissertations

The application of epitaxially grown, III-V semiconductor-based nanostructures to the development of electro-optical and all-optical switches is investigated through the fabrication and testing of integrated photonic devices designed using multimode interference (MMI) waveguides. The properties and limitations of the materials are explored with respect to the operation of those devices through electrical carrier injection and optical pumping. MMI waveguide geometry was employed as it offered advantages such as a very compact device footprint, low polarization sensitivity, large bandwidth and relaxed fabrication tolerances when compared with conventional single-mode waveguide formats. The first portion of this dissertation focuses on the characterization of …


Accelerating Optical Airy Beams, Georgios Siviloglou Jan 2010

Accelerating Optical Airy Beams, Georgios Siviloglou

Electronic Theses and Dissertations

Over the years, non-spreading or non-diffracting wave configurations have been systematically investigated in optics. Perhaps the best known example of a diffraction-free optical wave is the so-called Bessel beam, first suggested and observed by Durnin et al. This work sparked considerable theoretical and experimental activity and paved the way toward the discovery of other interesting non-diffracting solutions. In 1979 Berry and Balazs made an important observation within the context of quantum mechanics: they theoretically demonstrated that the Schrodinger equation describing a free particle can exhibit a non-spreading Airy wavepacket solution. This work remained largely unnoticed in the literature-partly because such …


Misalignment Induced Nodal Aberration Fields And Their Use In The Alignment Of Astronomical Telescopes, Tobias Schmid Jan 2010

Misalignment Induced Nodal Aberration Fields And Their Use In The Alignment Of Astronomical Telescopes, Tobias Schmid

Electronic Theses and Dissertations

Following the foundation of aberration theory for rotationally symmetric optical systems established by Seidel, Schwarzschild, Burch, Conrady, Buchdahl, and in its most useful form H.H. Hopkins, Shack, Buchroeder, Thompson, and Rogers developed a vectorial form of the wave aberration theory that enables addressing optical systems without symmetry. In this research, a vectorial theory is utilized and extended for the alignment of two- and three-mirror astronomical telescopes, including the effects of pointing changes and astigmatic figure errors. Importantly, it is demonstrated that the vectorial form of aberration theory, also referred to as nodal aberration theory, not only provides valuable insights but …


Near-Field Optical Interactions And Applications, David Haefner Jan 2010

Near-Field Optical Interactions And Applications, David Haefner

Electronic Theses and Dissertations

The propagation symmetry of electromagnetic fields is affected by encounters with material systems. The effects of such interactions, for example, modifications of intensity, phase, polarization, angular spectrum, frequency, etc. can be used to obtain information about the material system. However, the propagation of electromagnetic waves imposes a fundamental limit to the length scales over which the material properties can be observed. In the realm of near-field optics, this limitation is overcome only through a secondary interaction that couples the high-spatial-frequency (but non-propagating) field components to propagating waves that can be detected. The available information depends intrinsically on this secondary interaction, …


Epitaxial Growth, Characterization And Application Of Novel Wide Bandgap Oxide Semiconductors, Jeremy Mares Jan 2010

Epitaxial Growth, Characterization And Application Of Novel Wide Bandgap Oxide Semiconductors, Jeremy Mares

Electronic Theses and Dissertations

In this work, a body of knowledge is presented which pertains to the growth, characterization and exploitation of high quality, novel II-IV oxide epitaxial films and structures grown by plasma-assisted molecular beam epitaxy. The two compounds of primary interest within this research are the ternary films NixMg1-xO and ZnxMg1-xO and the investigation focuses predominantly on the realization, assessment and implementation of these two oxides as optoelectronic materials. The functioning hypothesis for this largely experimental effort has been that these cubic ternary oxides can be exploited - and possibly even juxtaposed - to realize novel wide band gap optoelectronic technologies. The …


Micro-Electro-Mechanical Systems (Mems) And Agile Lensing-Based Modules For Communications, Sensing And Signal Processing., Syed Reza Jan 2010

Micro-Electro-Mechanical Systems (Mems) And Agile Lensing-Based Modules For Communications, Sensing And Signal Processing., Syed Reza

Electronic Theses and Dissertations

This dissertation proposes the use of the emerging Micro-Electro-Mechanical Systems (MEMS) and agile lensing optical device technologies to design novel and powerful signal conditioning and sensing modules for advanced applications in optical communications, physical parameter sensing and RF/optical signal processing. For example, these new module designs have experimentally demonstrated exceptional features such as stable loss broadband operations and high > 60 dB optical dynamic range signal filtering capabilities. The first part of the dissertation describes the design and demonstration of digital MEMS-based signal processing modules for communication systems and sensor networks using the TI DLP (Digital Light Processing) technology. Examples of …


Fast Response Dual Frequency Liquid Crystal Materials, Qiong Song Jan 2010

Fast Response Dual Frequency Liquid Crystal Materials, Qiong Song

Electronic Theses and Dissertations

Dual frequency liquid crystal (DFLC) exhibits a positive dielectric anisotropy at low frequencies and negative dielectric anisotropy at high frequencies. The frequency where dielectric anisotropy is zero is called crossover frequency. DFLC can achieve fast rise time and fast decay time with the assistance of applied voltage. However, one drawback of DFLC is that it has dielectric heating effect when driven at a high frequency. Thus, the first part of this dissertation is to develop low crossover frequency DFLC materials. The dielectric relaxation and physical properties of some single- and double-ester compounds were investigated. Experimental results indicate that the double-ester …


Experimental And Theoretical Approaches To Characterization Of Electronic Nonlinearities In Direct-Gap Semiconductors, Claudiu Cirloganu Jan 2010

Experimental And Theoretical Approaches To Characterization Of Electronic Nonlinearities In Direct-Gap Semiconductors, Claudiu Cirloganu

Electronic Theses and Dissertations

The general goal of this dissertation is to provide a comprehensive description of the limitations of established theories on bound electronic nonlinearities in direct-gap semiconductors by performing various experiments on wide and narrow bandgap semiconductors along with developing theoretical models. Nondegenerate two-photon absorption (2PA) is studied in several semiconductors showing orders of magnitude enhancement over the degenerate counterpart. In addition, three-photon absorption (3PA) is studied in ZnSe and other semiconductors and a new theory using a Kane 4-band model is developed which fits new data well. Finally, the narrow gap semiconductor InSb is studied with regard to multiphoton absorption, free-carrier …


Silicon-Sensitized Erbium Excitation In Silicon-Rich Silica For Integrated Photonics, Oleksandr Savchyn Jan 2010

Silicon-Sensitized Erbium Excitation In Silicon-Rich Silica For Integrated Photonics, Oleksandr Savchyn

Electronic Theses and Dissertations

It is widely accepted that the continued increase of processor performance requires at least partial replacement of electronic interconnects with their photonic counterparts. The implementation of optical interconnects requires the realization of a silicon-based light source, which is challenging task due to the low emission efficiency of silicon. One of the main approaches to address this challenge is the use of doping of silicon based matrices with optical centers, including erbium ions. Erbium ions incorporated in various hosts assume the trivalent state (Er3+) and demonstrate a transition at 1.54 μm, coinciding with optical transmission windows in both silicon and silica. …


Technological Challenges Of 1-Dimensional Magnetic Photonic Crystals, Mikhail Vasiliev, Kamal Alameh, Dmitry E. Balabanov, Vladimir I. Burkov, V. V. Koledov, Viacheslav A. Kotov, V. G. Shavrov, Anotoly K. Zvezdin Jan 2010

Technological Challenges Of 1-Dimensional Magnetic Photonic Crystals, Mikhail Vasiliev, Kamal Alameh, Dmitry E. Balabanov, Vladimir I. Burkov, V. V. Koledov, Viacheslav A. Kotov, V. G. Shavrov, Anotoly K. Zvezdin

Research outputs pre 2011

Visible-region magnetic photonic crystals (MPC) designed for higher-order bandgap operation have been proposed to overcome the technological restrictions originating from the strong thickness dependency of the individual magnetic layer properties observed in MPC structures.


Near-Field Radiative Transfer: Thermal Radiation, Thermophotovoltaic Power Generation And Optical Characterization, Mathieu Francoeur Jan 2010

Near-Field Radiative Transfer: Thermal Radiation, Thermophotovoltaic Power Generation And Optical Characterization, Mathieu Francoeur

University of Kentucky Doctoral Dissertations

This dissertation focuses on near-field radiative transfer, which can be defined as the discipline concerned with energy transfer via electromagnetic waves at sub-wavelength distances. Three specific subjects related to this discipline are investigated, namely nearfield thermal radiation, nanoscale-gap thermophotovoltaic (nano-TPV) power generation and optical characterization. An algorithm for the solution of near-field thermal radiation problems in one-dimensional layered media is developed, and several tests are performed showing the accuracy, consistency and versatility of the procedure. The possibility of tuning near-field radiative heat transfer via thin films supporting surface phononpolaritons (SPhPs) in the infrared is afterwards investigated via the computation of …


Nonlinear Fiber Lasers Using Bismuth Based Erbium Doped Fiber Amplifier., Sharifeh Shahi Jan 2010

Nonlinear Fiber Lasers Using Bismuth Based Erbium Doped Fiber Amplifier., Sharifeh Shahi

Student Works (2010-2019)

A thorough study on Bismuth-based Erbium-doped fiber (Bi-EDF) is presented for wide-band amplifiers and multi-wavelength fiber laser applications. This fiber allows high Erbium ions concentration to be doped without a significant concentration quenching effect. The high refractive index characteristic in the Bi-EDF has broadened the emission spectrum of Erbium ions to achieve a broader gain spectrum up to extended L-band region compared to normal silica-based Erbium-doped fiber (EDF). The Bi-EDFA performances have been investigated in terms of power conversion efficiency (PCE), quantum conversion efficiency (QCE), gain and noise figure. The highest QCE and PCE for a 215 cm long of …


Heat And Current Propagation In Buffered Superconducting And Hyper-Conducting Wire, Jesse L. Lynn Dec 2009

Heat And Current Propagation In Buffered Superconducting And Hyper-Conducting Wire, Jesse L. Lynn

Theses and Dissertations

This research models and analyzes the distribution of heat and current in a buffered superconducting or hyper-conducting wire that shows potential for use in different capacities in multiple Air Force systems including the Active Denial System. The thesis includes a brief background of the reaction-diffusion system of partial differential equations provided by AFRL/RZPG and development of the numerical scheme. It then explores solutions to the model. These solutions indicate some of the various heat-related failures that may be observed in such a wire. The nature of the solutions observed depends on the characteristics of the wire, operating temperature and efficiency …


Swept-Frequency Sampled Grating Distributed Bragg Reflector Lasers Optimized For Optical Coherence Tomography Applications, Brandon J. George Dec 2009

Swept-Frequency Sampled Grating Distributed Bragg Reflector Lasers Optimized For Optical Coherence Tomography Applications, Brandon J. George

Master's Theses

Swept Frequency Source Optical Coherence Tomography (OCT) requires high repetition rate and wide spectral width wavelength tunable sources at a low cost. The sampled grating distributed Bragg reflector (SG-DBR) laser provides wide wavelength tuning range while exhibiting a wavelength switching speed that is among the fastest currently available. The SG-DBR laser is used to generate linear frequency ramps with high repetition rates. Since the SG-DBR laser is currently used for the telecommunications industry in high volume, the price of the system is much lower than current OCT sources. Therefore the SG-DBR laser provides a practical solution for Swept Source OCT. …


Focusing Electromagnetic Radiation In Dielectric Media, Mark A. Migliaccio Jr. Oct 2009

Focusing Electromagnetic Radiation In Dielectric Media, Mark A. Migliaccio Jr.

Electrical & Computer Engineering Theses & Dissertations

Bioelectrics and microwave imaging requires an ultra-wideband (UWB) antenna to deliver intense, short electromagnetic pulses into biological targets for the purpose of therapy and imaging. Two antennas with different focal distances, predicted by a two­ dimensional model, have been designed for focusing electromagnetic radiation in the near field.

Focusing is achieved through the use of prolate spheroidal reflector antennas with a conical wave launcher submerged in water. For an ultra-wideband feed signal, with a rise time of 200 picoseconds, the maximum electric field was found to be close to the edge of the reflector, a result that differs from the …


Aerodynamic Analysis Of An Urban Magnetic Levitation Vehicle, John Matthew Wells Oct 2009

Aerodynamic Analysis Of An Urban Magnetic Levitation Vehicle, John Matthew Wells

Mechanical & Aerospace Engineering Theses & Dissertations

This thesis will detail the aerodynamic qualities of a magnetic levitation concept vehicle designed to be installed on Old Dominion University's campus. The vehicle is representative of a class of small, low-speed Maglev systems commonly referred to as Urban Maglev. A 1:12 scale model underwent testing in Old Dominion's low speed wind tunnel. Force and moment coefficients were measured over a wide range of yaw angles. Results give insight into crosswind effects and how these forces affect vehicle dynamics. An analysis of this type is important in understanding the ride quality and safety of the system. Force Coefficients range from …


Dynamic Interaction Of Elevated Guideway With Uncontrolled Maglev Vehicles, Sumanth Reddy Velma Oct 2009

Dynamic Interaction Of Elevated Guideway With Uncontrolled Maglev Vehicles, Sumanth Reddy Velma

Mechanical & Aerospace Engineering Theses & Dissertations

A flexible guideway on an elevated foundation is a key to affordable maglev urban transit. The flexible guideway can undergo significant dynamic motion, either when a vehicle solely relies on an open-loop control system or when a vehicle equipped with feedback control system experiences failure, due to fluctuating magnetic forces between the vehicle and the guideway. In an attempt to understand the effect of the uncontrolled vehicle on the structural response of the guideway, its dynamic interaction with maglev vehicles is investigated under various operating conditions. To this end, two vehicle models using Electrodynamic suspension (EDS) and Electromagnetic suspension (EMS) …


Directional Dual-Band Slot Antenna With Dual-Bandgap High-Impedance-Surface Reflector, Xiulong Bao, Giuseppe Ruvio, Max Ammann Sep 2009

Directional Dual-Band Slot Antenna With Dual-Bandgap High-Impedance-Surface Reflector, Xiulong Bao, Giuseppe Ruvio, Max Ammann

Articles

A compact dual-band high-impedance-surface EBG structure is employed as a reflector for a dual-band annular-slot antenna. The reflector comprises an array of miniaturized EBG cells which utilizes square patches augmented by four S-shaped corrugated arms to reduce the resonant frequency of the proposed EBG structure. In order to broaden the bandwidth and adjust the frequency ratio for the dual-band EBG structure, a log-periodic spacing between the S-shaped strips is introduced. The combination of microstrip-fed annular slot and EBG reflector provides directional properties for both frequency bands with reduced size and low-profile.


Influence Of Solar Heating On The Performance Of Integrated Solar Cell Microstrip Patch Antennas, Maria Roo Ons, S. Shynu, M Seredynski, Max Ammann, Sarah Mccormack, Brian Norton Sep 2009

Influence Of Solar Heating On The Performance Of Integrated Solar Cell Microstrip Patch Antennas, Maria Roo Ons, S. Shynu, M Seredynski, Max Ammann, Sarah Mccormack, Brian Norton

Articles

The integration of microstrip patch antennas with photovoltaics has been proposed for applications in autonomous wireless communication systems located on building façades. Full integration was achieved using polycrystalline silicon solar cells as both antenna ground plane and direct current power generation in the same device. An overview of the proposed photovoltaic antenna designs is provided and the variation characterised of the electromagnetic properties of the device with temperature and solar radiation. Measurements for both copper and solar antennas are reported on three different commercial laminates with contrasting values for thermal coefficient of the dielectric constant.


Design Of Acousto-Optic Chaos Based Secure Free-Space Optical Communication Links, Anjan K. Ghosh, Pramode K. Verma, Samuel Cheng, Robert C. Huck, Monish Ranjan Chatterjee, Mohammed A. Al-Saedi Aug 2009

Design Of Acousto-Optic Chaos Based Secure Free-Space Optical Communication Links, Anjan K. Ghosh, Pramode K. Verma, Samuel Cheng, Robert C. Huck, Monish Ranjan Chatterjee, Mohammed A. Al-Saedi

Electrical and Computer Engineering Faculty Publications

We discuss the design of an acousto-optic cell based free space optical communication link where the data beam is made secure through chaos encryption. Using external signal modulation of the diffracted light from a hybrid acousto-optic cell chaos (or directly via incorporation in the sound-cell driver's bias voltage) encryption of data is possible. We have shown numerically that decryption of the encoded data is possible by using an identical acousto-optic system in the receiver.


Stability Analysis, Modeling, Simulation And Experimental Testing Of An Ems Maglev System With Structural Flexibility, Aravind M. Hanasoge Jul 2009

Stability Analysis, Modeling, Simulation And Experimental Testing Of An Ems Maglev System With Structural Flexibility, Aravind M. Hanasoge

Mechanical & Aerospace Engineering Theses & Dissertations

Vehicle-guideway interaction studies of Magnetically Levitated (Maglev) vehicles indicate that structural flexibility can adversely affect the overall stability and performance of such systems. This is one of the reasons why guideways are generally made very rigid. This in turn leads to increased cost of the overall system since guideway construction forms a significant portion of the overall cost. In this dissertation, the influence of structural flexibility on the stability of Electromagnetic Suspension (EMS) Maglev systems is studied. It is shown how inherently unstable and flexible structure EMS Maglev systems can achieve guaranteed stability by using collocated actuators and sensors, along …


Synthetic Aperture Radar Imaging Simulated In Matlab, Matthew Schlutz Jun 2009

Synthetic Aperture Radar Imaging Simulated In Matlab, Matthew Schlutz

Master's Theses

This thesis further develops a method from ongoing thesis projects with the goal of generating images using synthetic aperture radar (SAR) simulations coded in MATLAB. The project is supervised by Dr. John Saghri and sponsored by Raytheon Space and Airborne Systems. SAR is a type of imaging radar in which the relative movement of the antenna with respect to the target is utilized. Through the simultaneous processing of the radar reflections over the movement of the antenna via the range Doppler algorithm (RDA), the superior resolution of a theoretical wider antenna, termed synthetic aperture, is obtained. The long term goal …


Nondestructive Electromagnetic Material Characterization Using A Dual Waveguide Probe: A Full Wave Solution, Milo W. Hyde Iv, James W. Stewart, Michael J. Havrilla, William P. Baker, Edward Rothwell, Dennis P. Nyquist Jun 2009

Nondestructive Electromagnetic Material Characterization Using A Dual Waveguide Probe: A Full Wave Solution, Milo W. Hyde Iv, James W. Stewart, Michael J. Havrilla, William P. Baker, Edward Rothwell, Dennis P. Nyquist

Faculty Publications

A nondestructive technique for determining the complex permittivity and permeability of a perfect electric conductor backed magnetic shielding material using a dual waveguide probe is presented. The dual waveguide probe allows for the simultaneous collection of reflection and transmission coefficients which distinguishes it from single probe methods common in the literature. Theoretical development of these coefficients, which is accomplished through a coupled magnetic field integral equations formulation using Love's equivalence principle and solved via the method of moments (MOM), is discussed. Evaluation of the resulting MOM impedance matrix elements is performed using complex plane integration leading to enhanced computational efficiency …


Shielding Effectiveness Of Superalloy, Aluminum, And Mumetal Shielding Tapes, Cindy Suit Cheung Apr 2009

Shielding Effectiveness Of Superalloy, Aluminum, And Mumetal Shielding Tapes, Cindy Suit Cheung

Master's Theses

Using MIL-HDBK-419A, MATLAB and Nomographs, Shielding Effectiveness for the Magnetic Field, Electric Field, and Plane Wave were calculated over a frequency range from 10 Hz to 1 GHz. The three shielding tapes used included superalloy, aluminum, and mumetal. Calculations for Shielding Effectiveness involve the computation of Absorption Loss, Reflection Loss, and Re-Reflection Correction Factor. From the outcome of the calculations, it was suitable to conclude that all three metals fulfill the 40 dB Shielding Effectiveness requirements for SGEMP fields for frequencies greater or equal to 1 MHz. Accordingly, all three shielding tapes provide at least 40 dB of shielding to …


Suite Of Standards For Electromagnetic Material Characterization Using Mode Matching Theory, Brian J. Witthoeft Mar 2009

Suite Of Standards For Electromagnetic Material Characterization Using Mode Matching Theory, Brian J. Witthoeft

Theses and Dissertations

The objective of this research is to determine if an acceptable standard can be developed to access the accuracy and precision of measurements taken using waveguide systems. Tiny changes in material fabrication, processing, and environment can cause problems with accuracy and precision in measurement. There is a great deal of research on uncertainty analysis in the literature. A large portion of the effort will be to determine the levels of uncertainty caused by each of the dimensions of the waveguide insert and to develop a suitable standard capable of verifying system performance. The Mode-Matching Technique will be used to extract …


Advanced Radiometry For High Discrimination Explosive Fireball Discrimination, Steven E. Slagle Mar 2009

Advanced Radiometry For High Discrimination Explosive Fireball Discrimination, Steven E. Slagle

Theses and Dissertations

The high explosive fireball phenomenological model for the mid wave infrared spectrum, developed by AFIT, performs classification from spectral signatures was modified to use radiometric intensities. Five bands were sequentially fit to derive the five physical fit parameters describing the fireball's temperature, size, soot absorption coefficient within 16% and emissions from the H2O and CO2 concentrations within 333% of the spectral model. This was improved by changing the model's band sizes, center, and fitting methods where all five fit parameters were matched to within 17% of spectral model. This demonstrated that a combination of radiometric intensities could …


Analysis And Application Of The Bi-Directional Scatter Distribution Function Of Photonic Crystals, Robert B. Lamott Mar 2009

Analysis And Application Of The Bi-Directional Scatter Distribution Function Of Photonic Crystals, Robert B. Lamott

Theses and Dissertations

Photonic crystals (PCs) are periodic structures built from materials with different refractive indices repeated at sub-wavelength intervals, which results in unusual optical characteristics, including narrowband laser protection, and zero reflectance and high absorption anomalies. Most of the research into the optical properties of PCs has concentrated only on the small range of wavelengths and angles where these effects occur. To better understand where all light leaving a PC is scattered, a Complete Angle Scatter Instrument was used to analyze the scatter from three Guided Mode Resonance Filters designed for laser protection. In the plane of incidence, measurements of the scatter …


Retroreflector For Photonic Doppler Velocimetry, Thomas J. Lagoski Mar 2009

Retroreflector For Photonic Doppler Velocimetry, Thomas J. Lagoski

Theses and Dissertations

In order to meet the goals of the Department of Defense (DoD) for smaller and more accurate weapons, the Munitions Directorate of the Air Force Research Laboratory (AFRL/RW) has numerous projects investigating the miniaturization of weapons and munition fuze components. One of these efforts is to characterize the performance of small detonators. The velocity of the flyer, the key component needed to initiate a detonation sequence, can be measured using a photonic Doppler velocimeter (PDV). The purpose of this research was to develop a microelectromechanical system (MEMS) device that would act as an optimal retroreflective surface for the PDV. Two …