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Full-Text Articles in Physics

Empirical Validation Of Einstein’S Coefficient For The Deflection Of Light Due To Gravitational Forces, Alexandra R. Mcdowell Mar 2026

Empirical Validation Of Einstein’S Coefficient For The Deflection Of Light Due To Gravitational Forces, Alexandra R. Mcdowell

Honors College Theses

Einstein’s formula to calculate the deflection angle of light through space as it interacts with gravity was introduced in his 1916 publication on general relativity. This was not a new idea, but his equation was, and it was correct. Just 3 years after this publication, it was empirically validated by Sir Arthur Eddington and Sir Frank Dyson. Since that experiment in 1919, at least seven others have been performed that also gave definitive answers in support of Einstein’s deflection constant of 1.751 arcseconds. The two most recent ones made groundbreaking contributions to this effort. The 2017 eclipse showed reproducible results …


Developments And Applications Of Transport Of Intensity Equation Imaging And Optical Diffraction Tomography In Bioimaging, Shane D. Carney Jan 2026

Developments And Applications Of Transport Of Intensity Equation Imaging And Optical Diffraction Tomography In Bioimaging, Shane D. Carney

Electronic Theses & Dissertations (2024 - present)

Non-invasive imaging schemes are highly sought after methodologies in biology and metrology, where maintaining the physical state of a sample is important. Quantitative phase imaging (QPI) techniques non-invasively reconstruct the relative phase delay imparted onto an optical field due to transmission through a sample. Phase delay is proportional to the thickness and refractive index of the sample, but is lost in the intensity measurement process. Digital holographic microscopy (DHM) and transport of intensity equation (TIE) phase imaging are two high-resolution QPI techniques. DHM is a well-researched, accurate, and widely implemented technique, but can be difficult to implement in labs without …


Non-Gaussian Phenomena In Light Scattering And Applications, Shubham Atul Dawda Jan 2026

Non-Gaussian Phenomena In Light Scattering And Applications, Shubham Atul Dawda

Graduate Studies Theses and Dissertations 2026

Physical reality is rarely deterministic; which, when probed by electromagnetic fields that also fluctuate, leads to observables that are most efficiently modelled as statistical processes. At equilibrium, this is usually achieved by invoking the Gaussian statistics of underlying physical processes, however, in practice, one often encounters out-of-equilibrium conditions where Gaussian descriptions may not suffice. Such situations are plentiful in nature– from biology to astronomy. This dissertation addresses several non-Gaussian phenomena associated with light scattering, and includes specific models’ derivations, experimental techniques developments, and demonstrations of potential applications. The systematic presentation will consider circumstances that infringe upon specific assumptions of the …


Investigation Of Laser Based Flow Diagnostics With Metastable Argon, Sterling S. Gordon Dec 2025

Investigation Of Laser Based Flow Diagnostics With Metastable Argon, Sterling S. Gordon

Physics Theses & Dissertations

The overarching motivation of this work is the development of seedless, non-intrusive, laser-based diagnostics for supersonic airflow in wind tunnels. To advance this goal, this dissertation fo-cuses on three-photon excitation in a research-grade argon beam within a tabletop vacuum system, which offers a controlled environment for testing and refining the approach. The chosen excitation scheme drives argon atoms to the 3d[5/2]₃ state using a pulsed Ti:Sapphire laser system, enabling time-of-flight (ToF) measurements on atoms that subsequently undergo a multi-step decay to the metastable 4s[3/2]₂ state. Although full realization of this excitation scheme was hindered by technical …


Growth, Cladding, And Characterization Of Single Crystal Optical Fiber: The Next Evolution In Directed Energy Systems, Allen Benton May 2025

Growth, Cladding, And Characterization Of Single Crystal Optical Fiber: The Next Evolution In Directed Energy Systems, Allen Benton

All Dissertations

High-power fiber lasers are steadily increasing in maximum power and rapidly approaching theoretical maximum power output from a single fiber aperture. The low thermal conductivity of silica fibers is an inherent limitation to the dissipation of heat from the fiber core, and the buildup of heat within the laser gain media is the principal driver of transverse mode instability within fiber systems. This limitation necessitates the exploration of alternate fiber host materials. Due to their high thermal conductivity, excellent transmission range, ability to host most of the optically active rare earth ions, and success as bulk laser materials, single-crystalline YAG …


Atmospheric Characterization For Optical Paths In Lunar Proximity, Patrick D. Carattini Mar 2025

Atmospheric Characterization For Optical Paths In Lunar Proximity, Patrick D. Carattini

Theses and Dissertations

This paper presents a novel technique for estimating the Fried seeing parameter (r0) for optical paths around the Moon, where traditional methods fail due to the Moon's intensity. Using image processing, it derives the atmospheric optical transfer function (OTF) by using the Moon's edge as a step-input. A simulation chain validates the approach, achieving r0 estimation within 0.0012 m. Real-world tests confirm accuracy through visual and statistical analysis, offering an effective alternative for atmospheric characterization of optical paths close to the moon.


Thermal Noise Measurement Below The Standard Quantum Limit, Ronald Pagano Jan 2025

Thermal Noise Measurement Below The Standard Quantum Limit, Ronald Pagano

LSU Doctoral Dissertations

Quantum mechanics places sensitivity restrictions on physical measurements. These limitations manifest themselves in interferometric force and displacement measurements as uncertainty both in the photon number measured at a photodetector (shot noise), and in the quantum radiation pressure applied to the interferometer (quantum back action noise manifested as quantum radiation pressure noise). The balance between shot noise and quantum radiation pressure noise imposes the Standard Quantum Limit (SQL). A large body of work has been dedicated to measuring these quantum effects and mitigating them. Owing to the inherently small scale at which quantum effects are visible, classical effects must be subverted …


Interactions And Applications Of Optical Angular Momentum In Magneto-Optical Material, Seth R. Nelson Jan 2025

Interactions And Applications Of Optical Angular Momentum In Magneto-Optical Material, Seth R. Nelson

Dissertations, Master's Theses and Master's Reports

This dissertation explores the interactions and applications of optical angular momentum within magneto-optical materials. Beginning with a theoretical and experimental analysis of multiple reflection and refraction phenomena within magneto-optical material. We derive and verify the dependence of refractive indices on optical spin angular momentum and magneto-optical magnetization, resulting in nonreciprocal elliptical and linear polarization beam splitting effects and wavevector discretization. We fabricate a magnetless slab waveguide isolator with minimal optical loss. Extending our study to optical orbital angular momentum, we introduce a perturbation to the electronic transition model in bismuth-substituted iron garnets. We demonstrate that this perturbation leads to nonreciprocal …


High-Coherence Kerr-Cat Qubit In 2d Architecture, Ahmed Hajr, Bingcheng Qing, Ke Wang, Gerwin Koolstra, Zahra Pedramrazi, Ziqi Kang, Larry Chen, Long B. Nguyen, Christian Jünger, Noah Goss, Irwin Huang, Bibek Bhandari, Nicholas E. Frattini, Shruti Puri, Justin Dressel, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi Nov 2024

High-Coherence Kerr-Cat Qubit In 2d Architecture, Ahmed Hajr, Bingcheng Qing, Ke Wang, Gerwin Koolstra, Zahra Pedramrazi, Ziqi Kang, Larry Chen, Long B. Nguyen, Christian Jünger, Noah Goss, Irwin Huang, Bibek Bhandari, Nicholas E. Frattini, Shruti Puri, Justin Dressel, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By …


Super-Resolution Magnetic Microscopy And Earth’S Field Magnetometry With Color Centers In Diamond, Nazanin Mosavian Oct 2024

Super-Resolution Magnetic Microscopy And Earth’S Field Magnetometry With Color Centers In Diamond, Nazanin Mosavian

Optical Science and Engineering ETDs

In recent years, the negatively charged nitrogen- vacancy (NV) center has emerged as a promising solid-state color center capable of measuring magnetic fields with high sensi- tivity and spatial resolution under ambient conditions. In this thesis I will discuss how we perform super resolution magnetic microscopy and acquire magnetic field images of nanoparticle samples at 100 nm resolution. I will explain how 3D flux concentrators increase magnetic field amplitude and allows us to measure vector component magnetic fields as low as 50 µT with a diamond magnetometer, without the use of an additional bias magnetic field. I also describe how …


Focused Led Sintering, Dylan Defazio, Nilav Maulik, Branden Majors, Michael Fontillas Jun 2024

Focused Led Sintering, Dylan Defazio, Nilav Maulik, Branden Majors, Michael Fontillas

Mechanical Engineering

This report provides a detailed overview of the final design of our light-emitting diode (LED) focusing system. Our system incorporates a converging lens and a specially designed "glass funnel," which acts as a thick fiber optic that narrows the light to a fine point through internal reflection. The glass components of our system are precisely housed in a part made using advanced computer-numeric controlled (CNC) Mill and CNC Lathe manufacturing processes. This ensures high precision and durability of the overall system. Our LED focusing system is designed with a 60-watt stage light. The decision to use a glass funnel as …


Pt-Symmetry And Eigenmodes, Tamara Gratcheva Jun 2024

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …


New Quantum Information Science Study At Bsu: A Theoretical Study And Research Towards Pic Generation Of Entangled Photons, Peyton Brown May 2024

New Quantum Information Science Study At Bsu: A Theoretical Study And Research Towards Pic Generation Of Entangled Photons, Peyton Brown

Honors Program Theses and Projects

The first part of this thesis explores the abstract quantum state vector space using Dirac formalism, providing a comprehensive analysis of quantum mechanics’ fundamental concepts. Emphasis is placed on the Dirac notation’s pivotal role in elucidating quantum phenomena such as superposition and entanglement. Through detailed examinations of quantum states, polarization, and the CHSH inequality, this study not only reinforces the theoretical foundations of quantum information science but also demonstrates its practical applications in quantum information and quantum computing. The discussion delves into the manipulation of qubits and quantum gates, showing the potential of quantum information theory in enhancing computational efficiencies …


Nonlinear Rogue Wave Generation For All-Optical Switching In Optical Fibers And Photonic Integrated Circuits, Samuel Alexander Bechtold May 2024

Nonlinear Rogue Wave Generation For All-Optical Switching In Optical Fibers And Photonic Integrated Circuits, Samuel Alexander Bechtold

Honors Program Theses and Projects

For my thesis we discuss the history of optics, electronics and photonicsproviding a framework from which I investigate the viability of engineering a Photonic Integrated Circuit (PIC) that takes advantage of the nonlinear optical process known as Rogue Wave Generation (RWG) for an all-optical switching mechanism that is capable of switching speeds in the Peta-Hertz (PHz) frequency regime. This topic is introduced through a discussion of how technological advances such as the transistor, laser and optical fiber made modern computing and telecommunications possible. This is followed by a theoretical explanation of the nonlinear optical phenomena known as supercontinuum generation (SCG) …


Signal Processing Algorithms For Doppler Lidar Sensors, Samantha Grubb May 2024

Signal Processing Algorithms For Doppler Lidar Sensors, Samantha Grubb

Physics and Astronomy Honors Papers

Light detection and ranging (LiDAR) is a remote sensing technology that obtains relative distance and velocity measurements between a sensor and a defined target by using light transmitted and received from the target. FMCW Doppler LiDAR, a particular variant of LiDAR, functions by analyzing the frequency shift in the reflected light to determine the target's range and velocity. This technology plays a crucial role across various sectors including defense, aerospace, and automotive. This paper presents signal processing algorithms designed to optimize data obtained from Doppler LiDAR sensors. By applying various window functions to time domain data, the Signal-to-Noise Ratio (SNR) …


Development Of A High-Resolution Mid-Infrared Spectroscopy Apparatus For The Study Of Methane And Other Astrochemical Molecules., S M Shah Riyadh May 2024

Development Of A High-Resolution Mid-Infrared Spectroscopy Apparatus For The Study Of Methane And Other Astrochemical Molecules., S M Shah Riyadh

Electronic Theses and Dissertations

This research documents steps towards building a novel spectroscopic technique, namely, cavity-enhanced double-resonance (CEDR) spectroscopy, for investigating methane (CH4) and other molecules with significance in astrochemistry. These efforts focus on tackling the complexities of their ro-vibrational energy levels and the inefficiencies in analyzing vibrational spectra, particularly for molecules with high symmetry and strong intramolecular interactions. In the CEDR spectroscopy, the first photon, generated by a continuous-wave optical parametric oscillator (CW-OPO) locked to a Doppler-free saturation absorption line, excites the molecule from its ground level to a selected excited ro-vibrational (rotational-vibrational) level, e.g., that of the asymmetric CH-stretch mode. …


Orbital And Spin Angular Momentum Light Generation, Interactions, Special Photons, And Applications In Liquids, Solids, Vapors And Biological Tissue Media, Sandra Mamani Reyes Jan 2024

Orbital And Spin Angular Momentum Light Generation, Interactions, Special Photons, And Applications In Liquids, Solids, Vapors And Biological Tissue Media, Sandra Mamani Reyes

Dissertations and Theses

Photons possess many characteristics such as wavelength, coherence, speed, polarization and wavefront. The aim of this thesis is the study of two salient properties of light exploring light carrying polarization and space degree of freedom of the wavefront. The wavefront of light is complex with different states of polarization. Special light beams are generated and characterized for interaction with liquids, solids, vapors, and bio- materials to understand fundamental processes such as Transmission, Raman scattering, and Optical Kerr Effect in steady state and temporal domains.

It has been more than hundred years since it is known that light can carry other …


The Weighty Words Of Lord Rayleigh, John Adam Jan 2024

The Weighty Words Of Lord Rayleigh, John Adam

Mathematics & Statistics Faculty Publications

[First paragraph] Lord Rayleigh, a.k.a. John William Strutt, 3rd Baron Rayleigh (1842–1919), was, in my opinion, a quintessential mathematical and experimental physicist and, indeed, a classical applied mathematician of the highest order for his era. Among the many honors he received, the most prestigious was the 1904 Nobel Prize in Physics “for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies.” He was one of the very few members of so-called British “higher nobility” who won fame as an outstanding scientist.


Physics Ii, Kalani Hettiarachchilage Dec 2023

Physics Ii, Kalani Hettiarachchilage

Open Educational Resources

Physics II, class code PHY 156 at College of Staten Island is the second part of two two-semester algebra-based introductory physics courses. This course overlaps of the following topics laws of electricity, magnetism, optics, and modern physics. The important laws of physics in these areas and problem-solving are emphasized. Problem solving is an integral part of the course, all contents are designed to think critically, analytically, and logically. Conceptual understanding is reinforced using interactive computer-based techniques, demonstrations, problem-solving strategies, and laboratory experiences. In this document, all the class materials including lectures, worksheets, homework, group work assignments, quizzes, and conceptual Slido …


Advancements In Time Resolved Spectroscopy And Nonlinear Microscopy, Bryan Semon Dec 2023

Advancements In Time Resolved Spectroscopy And Nonlinear Microscopy, Bryan Semon

Theses and Dissertations

Non-linear optical processes such as coherent anti-Stokes Raman scattering and sum frequency generation offer a view into the chemical and biological interactions of molecules that is distinctly different from linear techniques like near infra-red and fluorescence. This insight comes at a cost: non-linear techniques are more sensitive to external perturbations of the system, increasing the noise and decreasing the repeatability of the data. We work here on both aspects of these non-linear techniques, taking advantage of their power to offer new imaging techniques as well as working to quantify and reduce the non-resonant noise inherent to the system. In pursuit …


Investigating The Effects Of A Southward Flow In The Southeastern Florida Shelf Using Robotic Instruments, Alfredo Quezada Dec 2023

Investigating The Effects Of A Southward Flow In The Southeastern Florida Shelf Using Robotic Instruments, Alfredo Quezada

All HCAS Student Capstones, Theses, and Dissertations

We deployed a Slocum G3 glider fitted with an acoustic Doppler current profiler (ADCP), a Conductivity-Temperature-Depth sensor (CTD), optics sensor channels, and a propeller on the Southeastern Florida shelf. The ADCP and CTD provide continuous measurements of Northern and Eastern current velocity components, salinity, temperature, and density, throughout the water column in a high-current environment. The optics sensor channels are able to provide measurements of chlorophyll concentrations, colored dissolved organic matter (CDOM), and backscatter particle counts. Additionally, for one of the glider deployments, we deployed a Wirewalker wave-powered profiling platform system also fitted with an ADCP and a CTD in …


Quantitative, Photocurrent Multidimensional Coherent Spectroscopy, Adam Halaoui Nov 2023

Quantitative, Photocurrent Multidimensional Coherent Spectroscopy, Adam Halaoui

Electronic Theses and Dissertations

Multidimensional coherent spectroscopy (MDCS) is a quickly growing field that has a lot of advantages over more conventional forms of spectroscopy. These advantages all come from the fact that MDCS allows us to get time resolved correlated emission and absorption spectra using very precisely chosen interactions between the density matrix and the excitation laser. MDCS spectra gives the researcher a lot of information that can be extracted purely through qualitative analysis. This is possible because state couplings are entirely separated on the spectra, and once we know how to read the data, we can see how carriers transport in the …


Broadband Quantum Enhancement Of The Ligo Detectors With Frequency-Dependent Squeezing, D. Ganapathy, W. Jia, M. Nakano, V. Xu, N. Aritomi, T. Cullen, N. Kijbunchoo, S. E. Dwyer, Francisco Llamas, Volker Quetschke Oct 2023

Broadband Quantum Enhancement Of The Ligo Detectors With Frequency-Dependent Squeezing, D. Ganapathy, W. Jia, M. Nakano, V. Xu, N. Aritomi, T. Cullen, N. Kijbunchoo, S. E. Dwyer, Francisco Llamas, Volker Quetschke

Physics & Astronomy Faculty Publications

Quantum noise imposes a fundamental limitation on the sensitivity of interferometric gravitational-wave detectors like LIGO, manifesting as shot noise and quantum radiation pressure noise. Here, we present the first realization of frequency-dependent squeezing in full-scale gravitational-wave detectors, resulting in the reduction of both shot noise and quantum radiation pressure noise, with broadband detector enhancement from tens of hertz to several kilohertz. In the LIGO Hanford detector, squeezing reduced the detector noise amplitude by a factor of 1.6 (4.0 dB) near 1 kHz; in the Livingston detector, the noise reduction was a factor of 1.9 (5.8 dB). These improvements directly impact …


Tunable Linear And Nonlinear Metasurfaces Based On Hybrid Gold-Graphene Plasmons, Matthew Feinstein Sep 2023

Tunable Linear And Nonlinear Metasurfaces Based On Hybrid Gold-Graphene Plasmons, Matthew Feinstein

Dissertations, Theses, and Capstone Projects

Optical Metasurfaces are planar structures that are patterned with subwavelength structures and are very thin compared to the wavelength of light. Despite their thinness, these structured materials can strongly interact with incident light to effect the functionalities of conventional optical components, such as rotation of the polarization state, beam steering, lensing, spectral filtering, and holography, to name a few. Metasurfaces can also facilitate nonlinear optical effects, such as the mixing of beams at different frequencies to generate a beam at a new frequency.

The ability to alter the behavior of a metasurface during operation is highly desired for applications such …


Photon Counting Statistics Of Classical And Quantum Light Sources, Luis Felipe Morales Bultron Aug 2023

Photon Counting Statistics Of Classical And Quantum Light Sources, Luis Felipe Morales Bultron

Graduate Theses and Dissertations

Multiple sources of light, including coherent light, thermal light, light from a degenerate parametric oscillation and resonance fluorescence from a two level coherently driven atom are considered for the analysis of their wait time statistics. We include the second order normalized correlation function and Mandel's Q parameter for brief discussion. A general framework to analyze the generalized conditional and unconditional wait time distributions is also obtained in order to understand the photo-count statistics of the light sources included in this work. Average and variance of wait times with respect to both unconditional and conditional wait time distribution are also obtained …


Tardys Quantifiers: Extracting Temporal And Reversible Dynamical Symmetries, Nhat Vu Minh Nguyen, Arjendu K. Pattanayak, Andres Aragoneses May 2023

Tardys Quantifiers: Extracting Temporal And Reversible Dynamical Symmetries, Nhat Vu Minh Nguyen, Arjendu K. Pattanayak, Andres Aragoneses

2023 Symposium

One of the great challenges in complex and chaotic dynamics is to reveal the details of its underlying determinism. This can be manifest in the form of temporal correlations or structured patterns in the dynamics of a measurable variable. These temporal dynamical structures are sometimes a consequence of hidden global symmetries. Here we identify the temporal (approximate) symmetries of a semiconductor laser with external optical feedback, based on which we define the Temporal And Reversible DYnamical Symmetry (TARDYS) quantifiers to evaluate the relevance of specific temporal correlations in a time series. We show that these symmetries are also present in …


Photonic Monitoring Of Atmospheric Fauna, Adrien P. Genoud Dec 2022

Photonic Monitoring Of Atmospheric Fauna, Adrien P. Genoud

Dissertations

Insects play a quintessential role in the Earth’s ecosystems and their recent decline in abundance and diversity is alarming. Monitoring their population is paramount to understand the causes of their decline, as well as to guide and evaluate the efficiency of conservation policies. Monitoring populations of flying insects is generally done using physical traps, but this method requires long and expensive laboratory analysis where each insect must be identified by qualified personnel. Lack of reliable data on insect populations is now considered a significant issue in the field of entomology, often referred to as a “data crisis” in the field. …


Investigation Of Laser And Nonlinear Properties Of Anderson Localizing Optical Fibers, Cody Ryan Bassett Nov 2022

Investigation Of Laser And Nonlinear Properties Of Anderson Localizing Optical Fibers, Cody Ryan Bassett

Optical Science and Engineering ETDs

In this dissertation, I investigate the possibility of lasing and nonlinear phenomena in completely solid-state transverse Anderson localizing optical fibers (TALOFs). I examine three areas within this range of topics. The research in nonlinear phenomena focuses on four-wave mixing (FWM). FWM is of high interest in TALOFs due to the fact that guided localized modes of the fiber each have different propagation constants, and thus unique possible FWM pairs can be generated from the same input pump beam. I demonstrate the generation of FWM in the TALOF by pumping it with 532 nm light into a localized mode and observing …


Miniaturized Iii-V/ Si Hybrid Laser With An Integrated Modulator, Praveen Kumar Singaravelu Sep 2022

Miniaturized Iii-V/ Si Hybrid Laser With An Integrated Modulator, Praveen Kumar Singaravelu

Theses

Light interaction with microscopic and nanoscopic structures enable manipulation of its characteristics which can be used to detect objects in 3D sensing, propel satellites to space using photonic propulsion and transmit data through optical communication. For optical communication, the basic components are lasers, modulators and photodetectors. The development of CMOS microfabrication foundries helps to manufacture silicon-based photonic devices with high yield that is directly co-integrated with electronics in a single chip. However, the lack of emission of photons efficiently in silicon propelled the necessity of hybrid photonic devices that inherits the combined advantage of different materials i.e. functionality and volume. …


Computational Methods For Propagation Of Optical Fields With The Angle-Impact Wigner Function, Jeremy Wittkopp Aug 2022

Computational Methods For Propagation Of Optical Fields With The Angle-Impact Wigner Function, Jeremy Wittkopp

Legacy Theses & Dissertations (2009 - 2024)

In designing an optical setup for an experiment, one usually turns to simulations first in order to model the propagation of light through the proposed system. This way, the experimenter can determine if the system is operating as intended. In order for these simulations to be useful, they need to properly describe the propagation of light. In order to simplify calculations, most contemporary software makes assumptions on the nature of the light being propagated. Specifically, simulations typically consider optical fields that are beam-like (i.e., most of the rays comprising the field deviate only slightly in angle from the beam's primary …