Physics Commons^™

A Model For The Multi-Virus Contact Process, Xu Huang

Rose-Hulman Undergraduate Mathematics Journal

We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of infections the node carries at the moment when it gets another infection. In this paper, we show that on any finite graph, any positive value of infection rate $\lambda$ will result in the death of the process almost surely. In the case of $d$-regular infinite trees, We also give a lower bound on the infection rate in order for …

Design Of A Resonant Optical Cavity For Imaging Magneto-Optically Active Thin Film Samples, Cody Robert Brelage

Graduate Theses - Physics and Optical Engineering

This document describes the design and fabrication of an optical resonator system to investigate magneto-optic properties of thin film samples. This system uses an open-air optical resonator to enable photons to make multiple passes through each thin film and thus increase the magnitude of the Faraday rotation that each sample imposes onto the light that exits the system. This system promises many future experiments to study the magneto-optic properties of thin film and nano-particle samples. Using an optical resonator to enhance Faraday rotation should enable an improved signal-to-noise ratio in taking measurements and images with a photodetector.

Human And Technical Factors In The Adoption Of Quantum Cryptographic Algorithms, Alyssa Pinkston

Mathematical Sciences Technical Reports (MSTR)

The purpose of this research is to understand what factors would cause users to choose quantum key distribution (QKD) over other methods of cryptography. An Advanced Encryption Standard (AES) key can be exchanged through communication using the Rivest, Shamir, Adleman (RSA) cryptographic algorithm, QKD, or post-quantum cryptography (PQC). QKD relies on quantum physics where RSA and PQC use complex mathematics to encrypt data. The BB84 quantum cryptographic protocol involves communication over a quantum channel and a public channel. The quantum channel can be technically attacked by beamsplitting or intercept/resend. QKD, like other forms of cryptography, is vulnerable to social attacks …

Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi

Mathematical Sciences Technical Reports (MSTR)

This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x² − ny² = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …

Using Differential Equations To Model A Cockatoo On A Spinning Wheel As Part Of The Scudem V Modeling Challenge, Miles Pophal, Chenming Zhen, Henry Bae

Rose-Hulman Undergraduate Mathematics Journal

For the SCUDEM V 2020 virtual challenge, we received an outstanding distinction for modeling a bird perched on a bicycle wheel utilizing the appropriate physical equations of rotational motion. Our model includes both theoretical calculations and numerical results from applying the Heaviside function for the swing motion of the bird. We provide a discussion on: our model and its numerical results, the overall limitations and future work of the model we constructed, and the experience we had participating in SCUDEM V 2020.

Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden

Rose-Hulman Undergraduate Mathematics Journal

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares …

Metasurfaces For Nano-Illumination In Lidar And Lighting Applications, Sehyeon Kim

Graduate Theses - Physics and Optical Engineering

The development of a non-scanning laser-based imaging lidar system based on a diffractive optical element with potential applications in advanced driver assistance systems, autonomous vehicles, drone navigation, and mobile devices is reported. The proposed lidar utilizes image processing with homography. The emphasis in the design approach has been on compactness and cost of the final system for it to be deployable both as standalone or complementary to existing lidar sensors, enabling fusion sensing in the applications. This work describes the basic elements of the proposed lidar system. It presents the potential ranging mechanisms, along with their experimental results demonstrating the …

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

Distributed Feedback Master Oscillator Power Amplifier Using Interface Polaritons, Dongwon Jang

Graduate Theses - Physics and Optical Engineering

Characterization and simulation of an innovative solid-state distributed feedback master oscillator power amplifier (solid-state DFB MOPA) are presented, using interface polaritons (IPs) that enhance wave propagations at gain-loss interfaces in active layers. The author set up the design of the fabricated device, and a company, Freedom photonics, collaborated with us, allowing me to modify some of their designed MOPA systems. The master oscillator (MO) consists of a patterned grating on a waveguiding region to transfer only a single mode of 1.550 μm wavelength. The power amplifier (PA) is fabricated with the MO to reduce power loss and tapered to amplify …

Design And Fabrication Of Biaxial Hyperbolic Metamaterials, Changkee Hong

Graduate Theses - Physics and Optical Engineering

This thesis describes a new method for fabrication of biaxial hyperbolic metamaterials (BHMMs) using layered structures consisting of oblique angle deposited (OAD) titanium dioxide (TiO2) and copper (Cu). An oblique angle deposition (OAD) technique was utilized to deposit dielectric layer composed of nanocolumnar structures in order to provide biaxial property. The biaxial hyperbolic dispersion of the fabricated BHMM was characterized via profilometer and variable angle spectroscopic ellipsometry (VASE) measurements for wavelength between 381 nm and 894 nm. For the fabricated BHMM, a noticeable difference of 0.13 - 0.001 between the in-plane permittivity components and dual epsilon-near-zero (ENZ) regions which are …

Modeling And Characterization Of A Ring-Resonator Based Silicon Photonic Sensor On Silicon-On-Insulator (Soi), Gwangho Choi

Graduate Theses - Physics and Optical Engineering

The purpose of this work is to build silicon photonic devices and verify their functionalities. In particular, the structure of a ring resonator (RR) is analyzed and applied to various silicon photonic application in sensing. Silicon waveguides, grating couplers, directional couplers, and RRs are fabricated on the silicon-on-insulator (SOI) wafer. Geometrical parameters and optical properties of the silicon devices are studied and also applied to the design of the aforementioned devices. The waveguide dimensions and, optical properties of the silicon waveguide such as dispersion and effective-index are examined. The RRs are made of a series of straight and bent waveguides …

Design, Fabrication, And Characterization Of Multilayer Hyperbolic Metamaterials, James Dilts

Graduate Theses - Physics and Optical Engineering

Hyperbolic metamaterials (HMMs) show extreme anisotropy, acting as metals and dielectrics along orthogonal directions. They are designed using the effective medium theory (EMT) and can be fabricated using standard semiconductor processing techniques. Current techniques used to characterize the optical behavior of HMMs have a high complexity or are unable to robustly determine the complex permittivity tensor. We describe the details of a procedure to obtain a very low mean-squared-error (MSE) for extraction of permittivity from hyperbolic metamaterials using spectroscopic ellipsometry. We have verified our procedure by fabricating three different samples of various materials and fill factors designed to have a …

Hybrid Optical Integrator Based On Silicon-On-Insulator Platform, Taewon Huh

Graduate Theses - Physics and Optical Engineering

A hybrid optical integrator is a recirculating loop that performs oversampling typically for analog input, using the cross-gain modulation (XGM) in a semiconductor optical amplifier (SOA). The modulated input signal changes the gain of the loop through XGM and thus modifies the loop accumulation. This thesis presents hybrid optical integrator for an all-optical analog-to-digital converter based on a silicon photonics platform. The device consists of silicon waveguides of dimension 220 × 500 nm (thick × width) and approximately 5 m optical loop length including fiber length, input and output grating couplers for 1550 nm signal, directional couplers, and external components …

Tilt Measurements Using A Monolithic Cyclic Interferometer, Joseph Porter

Graduate Theses - Physics and Optical Engineering

Measurement applications globally are demanding higher resolution measurements within a smaller footprint. The cyclic interferometer is a proven means of high-resolution tilt measurements while maintaining fringe stability. However, the cyclic interferometer commonly has many optical elements over a large surface area. In this thesis, a monolithic cyclic interferometer has been designed, constructed, and characterized. The monolithic system contains all the functionality of a typical cyclic interferometer, yet the optical elements are contained within a single glass optic. In doing so, the system attains a compact form factor and it is possible to complete measurements within a broader field of application.

Coupling Light Into Siliconwaveguide Using Surface Plasmon Polaritons, Jeong Rok Kim

Graduate Theses - Physics and Optical Engineering

No abstract provided.

Probabilities Involving Standard Trirectangular Tetrahedral Dice Rolls, Rulon Olmstead, Doneliezer Baize

Rose-Hulman Undergraduate Mathematics Journal

The goal is to be able to calculate probabilities involving irregular shaped dice rolls. Here it is attempted to model the probabilities of rolling standard tri-rectangular tetrahedral dice on a hard surface, such as a table top. The vertices and edges of a tetrahedron were projected onto the surface of a sphere centered at the center of mass of the tetrahedron. By calculating the surface areas bounded by the resultant geodesics, baseline probabilities were achieved. Using a 3D printer, dice were constructed of uniform density and the results of rolling them were recorded. After calculating the corresponding confidence intervals, the …

Design, Fabrication, And Characterization Of A One-Dimensional Single-Material Polarizing Photonic Crystal, Ehsan Ordouie

Graduate Theses - Physics and Optical Engineering

We examine a multilayered one-dimensional (1D) polarizing photonic crystal designed and fabricated out of a single material. This polarizer is designed for high reflection of the s polarization and low reflection of p polarization at the wavelength of 632.8 nm. This device is fabricated implementing the oblique angle deposition technique to produce six-bilayers of alternating high to low indices of titanium dioxide using e-beam PVD for depositing on top of a fused silica substrate. For modeling, we used transfer-matrix method and numerical finite-difference time-domain analysis to simulate behavior of the 1D photonic bandgap structure. Both model and simulation predict better …

Gain Modeling Of Erbium-Doped Fiber Amplifiers Pumped At 980nm, Deepak Charles Baskar

Graduate Theses - Physics and Optical Engineering

Erbium-Doped Fiber Amplifiers (EDFA) are one of the most widely used optical amplifiers in the field of optical communications and fiber lasers. Theoretical models based on the rate equations, therefore, were developed to predict the performance of such amplifiers. The goal of this thesis is to provide a numerical model for EDFAs and verify its validity through experimental measurements. Two computer programs based on two different numerical methods (the Finite Difference method and the 4th Order Runge-Kutta Method) to solve differential equations were written. The different fiber parameters to build the model including absorption and emission crosssections and scattering losses …

The Simulation, Design, And Fabrication Of Optical Filters, John-Michael Juneau

Graduate Theses - Physics and Optical Engineering

The purpose of this thesis is to create a model for designing optical filters and a method for fabricating the designed filters onto a multitude of substrates, as well as to find ways to optimize this process. The substrates that were tested were quartz, glass slides, polycarbonate, and polyethylene terephthalate (PET). This work will account for variations in the deposition process and substrate cleaning method, in order to optimize the performance of the final optical filter. Several different filters were simulated and then fabricated. These filters included 3, 5, and 7-layer Bragg reflectors, 11-layer narrowband filters, and some variations of …

Fabrication And Characterization Of Thermo-Optic Mach-Zehnder Silicon Modulator, Yeongho Park

Graduate Theses - Physics and Optical Engineering

This thesis focuses on the modeling, design, and fabrication of the Thermo-Optic Mach-Zehnder Modulator, which is one of the simple active devices in silicon photonics. The Mach-Zehnder interferometer (MZI) was formed as an optical path on a silicon on insulator (SOI) wafer of 2040±80 nm thick, and the thermo-optic effect was used to modulate the infrared light of 1553 nm wavelength by controlling the temperature of the one arm of the MZI. To fabricate and understand the Si photonic device, the whole process from theory to the measurement setup is introduced. Additionally, all the fabrication details and some informative experiments …

Construction And Passive Q-Switching Of A Ring-Cavity Erbium-Doped Fiber Laser Using Carbon Nanotubes As A Saturable Absorber, Austin Scott

Graduate Theses - Physics and Optical Engineering

The purpose of this thesis is to design, build, test, and achieve pulsed operation of a ring-cavity erbium-doped fiber laser using carbon nanotubes as a saturable absorber. The erbium-doped fiber is characterized first, cross-sections are calculated, and the gain value is determined. Subsequently, the ring cavity is constructed and the laser is operated in the continuous wave regime. Much time is then spent trying to characterize and utilize the carbon nanotubes successfully. Many dispersions are made using multiple solvents and dispersing media, various images are taken with both scanning electron and Raman microscopy, and attempts at purification are made. Saturable …

Nanoscale Tilt Measurement Using A Cyclic Interferometer With Phase Stepping And Multiple Reflections, Tahereh Naderishahab

Graduate Theses - Physics and Optical Engineering

High accuracy tilt or roll angle measurement is required for a variety of engineering and scientific applications. Optical interferometry is normally used because it is non-contact and can measure tilt with a very high degree of accuracy. In this thesis, a cyclic interferometer has been developed with four mirrors to measure tilt angles as small as a few nanoradians. To measure the phase, a novel and simple method of phase shift by polarization was developed to enhance measurement sensitivity and accuracy. Since the cyclic interferometer is insensitive to external vibrations and turbulences, polarization phase step was accomplished with relative ease. …

Design And Implementation Of A Microscope Based On Magneto-Optic Effects, Yuxuan Liu

Graduate Theses - Physics and Optical Engineering

When light passes through a medium that is subjected to a strong magnetic field, its polarization state may change due to magneto-optic effects such as Faraday rotation. An imaging system based on this polarization change is designed and constructed. The imaging system is built around a magnetic pulse field generator and able to detect polarization change of the incident light due to magneto-optic effects. An automated scheme is implemented using LabView. The program is developed to integrate all hardware and conduct multiple measurements automatically to enhance sensitivity. Basic testing measurements are conducted to evaluate the performance of the system. A …

Study Of Cu/Sio2/Cu Metamaterials: Design, Simulation, Fabrication, Testing, And Optical Applications, Minsu Oh

Graduate Theses - Physics and Optical Engineering

In the past few years, “metamaterials” have grabbed attention of researchers in both science and engineering. They have revealed great potentials to realize unusual optical applications such as flat lenses or frequency-selective performances with their unusual electromagnetic properties. In this project, Cu/SiO2/Cu metamaterials of diverse designs and parameters were studied towards discovering their unknown optical applications. From simulation work, it was found that some metamaterials exhibit a performance of a rectangle-shaped bandpass at optical frequencies. Their operational wavelength region can be adjusted by having a different scale of the structure or a different thickness of the constituent materials. This indicates …

Designs And Reliability Evaluations Of A Scattered Light Measurement System, Kang-Min Lee

Graduate Theses - Physics and Optical Engineering

The purpose of my work was to develop an in-plane stray light measurement system having the advantage of being easily applicable in both motion control and optical configurations. First of all, mechanical designs were conducted based on both 3D modeling and structural analysis through a finite element method (FEM). Optical configurations for both the incident source and the detector were designed to achieve minimum observed source convergence angle of the system. The control panel and micro stepping system were programmed for automated measurement. Finally, the designed system was calibrated and aligned. In order to evaluate the system reliability for scatter …

Surface Roughness Effects On Light Propagation In Optical Light Pipes, Youngjin Park

Graduate Theses - Physics and Optical Engineering

Solid- and hollow-core light pipes are commonly employed to shape the intensity profile of high power lasers for applications in various technology industries such as the automobile, medical, and communications. There are several loss mechanisms present in solid-core glass and polymer light pipes, including absorption, bulk scattering in the material, surface scattering at the material-air interface, and Fresnel Loss at the material-air interface. Fresnel reflection and surface scattering losses typically dominate over other loss mechanisms in solid-core light pipes made of high quality optical materials. In order to analyze the losses in the light pipe, an approximate model is developed …

Optical Bistability In A Vcsel Coupled To Serially-Connected Pin Photodiodes Quantizer Device, Sanaz Faryadras

Graduate Theses - Physics and Optical Engineering

In this work we investigated the structure and performance of vertical cavity surface emitting lasers (VCSEL) which will be used in building an optical quantizer. In any p-i-n structure, capacitance is the most important factor in deciding the highest modulation speed. Therefore, components with smaller capacitance would show higher switching speed. A novel electrical quantizer was constructed using two identical 850 nm Finisar VCSELs, which could manifest electrical switching up to 1.4 MHz. Also, a new electrical quantizer was built with two Eudyna PIN photodiodes (PD-PD), which works at higher frequencies up to 8 MHz, comparing to previous works. The …

Development And Validation Of An Empirical Temperature-Dependent Voltage Model For Diode Laser Characterization, Grant Matthew Brodnik

Graduate Theses - Physics and Optical Engineering

This work investigates the effects of temperature on the operation and performance of indium-phosphide (InP) based high-power broad-area laser (BAL) diodes operating in the eye-safe regime (1.5 μm – 2.0 μm). Low temperature (-80C to 0C) operation using a cryogenically cooled system enables investigation of temperature-dependent parameters such as threshold current, slope efficiency, diode voltage, and power conversion efficiency (PCE) of devices. Building upon established empirical models that describe threshold current and slope efficiency as functions of temperature, a key additional parametric model is developed to describe diode voltage incorporating a temperature dependence. With the inclusion of this temperature-dependent voltage …

Bending Loss Mitigation By Surface Plasmon Resonance, Daniel Steven Spoor

Graduate Theses - Physics and Optical Engineering

Surface plasmon resonance can be used to confine a wave within a thin metal film. The resultant wave is very well-confined by the extreme refractive index difference between the metal and the ambient medium. Such confinement can be used to guide waves under extreme conditions such as subwavelength channels or through extremely tight bends where radiation losses would normally dissipate the wave.

A nichrome thin film was deposited and etched as a shadow alongside a series of multi-mode SU-8 slab waveguides with extremely sharp angled bends. Light from a Helium-Neon laser was coupled into these waveguides and the power transmitted …

Study Of Surface Plasmon Resonance In Metal And Alloy Nanofilms Using Maxwell Description And Metamaterial Simulation In Comsol, Heesoo Park

Graduate Theses - Physics and Optical Engineering

Metamaterials are artificial metallic structures having, possibly, simultaneously negative permittivity and negative permeability which is called a double negative medium. To achieve a visible light range of the metamaterial, the unit cell of the metamaterial units should be 10-200nm. It is a much bigger structure than a size of normal atom. Still, the resolution of fabrication, which is difficult part, should typically be a few nanometers to achieve a nano-level unit. We study Ag thin-film as a convenient candidate for metamaterial over a specific frequency range. Because, the thin film metal is composed of disk shape island structures itself. These …