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Articles 1 - 30 of 93
Full-Text Articles in Physics
New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne
New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne
Asim Gangopadhyaya
We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission …
Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne
Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne
Asim Gangopadhyaya
The techniques of supersymmetric quantum mechanics are applied to the calculation of the energy difference between the ground state and the first excited state of an asymmetric double well. This splitting, originating from the tunneling effect, is computed via a systematic, rapidly converging perturbation expansion. Perturbative calculations to any order can be easily carried out using a logarithmic perturbation theory. Our approach yield substantially better results than alternative widely used semiclassical analyses.
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne
Asim Gangopadhyaya
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with noncentral vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov – Bohm field and/or in the magnetic field of a Dirac monopole.
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
Asim Gangopadhyaya
We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.
Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow
Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow
Asim Gangopadhyaya
No abstract provided.
Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi
Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi
Asim Gangopadhyaya
A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.
Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang
Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang
Asim Gangopadhyaya
In superspace formulation of supersymmetric gauge theories, gauge invariance requires an infinite set of identities between the infinite set of renormalization constants. Using Ward identities in superspace, the same is derived. These identities at one loop level are also demonstrated.
Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang
Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang
Asim Gangopadhyaya
We discuss some general properties of heterotic conformal field theory in which conformal anomalies c are different for the left-moving and right-moving sectors. It is precisely this type of theory that can be applied immediately to the construction of heterotic string theory. We discuss a general way of constructing such a theory using free fermions. The construction is then applied to generalize Gepner's construction of superstring solutions using the tensor products of N=2 superconformal field theories.
Investigation Of Real-Time Optical Scanning Holography, Bradley D. Duncan
Investigation Of Real-Time Optical Scanning Holography, Bradley D. Duncan
Bradley D. Duncan
Real-time holographic recording using an optical heterodyne scanning technique was proposed by Poon in 1985. The first part of this dissertation provides a detailed theoretical treatment of the technique, based on a Gaussian beam analysis. Topics to be addressed include the derivations of the optical transfer function (OTF) and impulse response of the scanning holographic recording system, reconstructed image resolution and magnification, methods of carrier frequency hologram generation and experimental verification of the recording technique based on careful measurements of a hologram corresponding to a simple transmissive slit. Furthermore, computer simulations are presented pertaining to the incoherent nature of the …
Imaging Diffractometer With Holographic Encoding Enhancements For Laser Sensing And Characterization, Joesph Binford, Bradley Duncan, Jack Parker, Elizabeth Beecher, Mark Delong
Imaging Diffractometer With Holographic Encoding Enhancements For Laser Sensing And Characterization, Joesph Binford, Bradley Duncan, Jack Parker, Elizabeth Beecher, Mark Delong
Bradley D. Duncan
What is believed to be a novel holographic optical encoding scheme has been developed to enhance the performance of laser sensors designed for the measurement of wavelength and angular trajectory. A prototype holographic imaging diffractometer has been created to reconstruct holographic cueing patterns superimposed in the focal plane of wide-angle scene imagery. Based on experimental pattern metric measurements at the focal plane, a theoretical model is used to compute the laser source wavelength and its apparent propagation direction within the sensor's field of view. The benefits of incorporating holographic enhancements within an imager-based sensor architecture are discussed.
Review: 'Optical Fiber Communications' (2nd Edition), By Gerd Keiser, Bradley D. Duncan
Review: 'Optical Fiber Communications' (2nd Edition), By Gerd Keiser, Bradley D. Duncan
Bradley D. Duncan
If first impressions are worth anything (and they usually are), I would have to admit that my first impression of the second edition of Gerd Keiser's now popular text Optical Fiber Communications was quite good. My compliments are hereby extended to the publisher for choosing a rather handsome cover and dust jacket. It stands in strong contrast to the text's first edition, which still ranks as probably the ugliest book I own, with color choices ranging from dull cream and "baby" blue to pale pink! I am now happy to say that this older version has been discretely·retired to the …
Optical Sparse Aperture Imaging, Nicholas Miller, Matthew Dierking, Bradley Duncan
Optical Sparse Aperture Imaging, Nicholas Miller, Matthew Dierking, Bradley Duncan
Bradley D. Duncan
The resolution of a conventional diffraction-limited imaging system is proportional to its pupil diameter. A primary goal of sparse aperture imaging is to enhance resolution while minimizing the total light collection area; the latter being desirable, in part, because of the cost of large, monolithic apertures. Performance metrics are defined and used to evaluate several sparse aperture arrays constructed from multiple, identical, circular subapertures. Subaperture piston and∕or tilt effects on image quality are also considered. We selected arrays with compact nonredundant autocorrelations first described by Golay. We vary both the number of subapertures and their relative spacings to arrive at …
Monte Carlo Simulation Of Multiple Photon Scattering In Sugar Maple Tree Canopies, Michael Greiner, Bradley Duncan, Matthew Dierking
Monte Carlo Simulation Of Multiple Photon Scattering In Sugar Maple Tree Canopies, Michael Greiner, Bradley Duncan, Matthew Dierking
Bradley D. Duncan
Detecting objects hidden beneath forest canopies is a difficult task for optical remote sensing systems. Rather than relying upon the existence of gaps between leaves, as other researchers have done, our ultimate goal is to use light scattered by leaves to image through dense foliage. Herein we describe the development of a Monte Carlo model for simulating the scattering of light as it propagates through the leaves of an extended tree canopy. We measured several parameters, including the gap fraction and maximum leaf-area density, of a nearby sugar maple tree grove and applied them to our model. We report the …
Improving Mid-Frequency Contrast In Sparse Aperture Optical Imaging Systems Based Upon The Golay-9 Array, Andrew Stokes, Bradley Duncan, Matthew Dierking
Improving Mid-Frequency Contrast In Sparse Aperture Optical Imaging Systems Based Upon The Golay-9 Array, Andrew Stokes, Bradley Duncan, Matthew Dierking
Bradley D. Duncan
Sparse aperture imaging systems are capable of producing high resolution images while maintaining an overall light collection area that is small compared to a fully filled aperture yielding the same resolution. This is advantageous for applications where size, volume, weight and/or cost are important considerations. However, conventional sparse aperture systems pay the penalty of reduced contrast at midband spatial frequencies. This paper will focus on increasing the midband contrast of sparse aperture imaging systems based on the Golay-9 array. This is one of a family of two-dimensional arrays we have previously examined due to their compact, non-redundant autocorrelations. The modulation …
Periodic, Pseudo-Noise Waveforms For Multi-Function Coherent Ladar, Matthew Dierking, Bradley Duncan
Periodic, Pseudo-Noise Waveforms For Multi-Function Coherent Ladar, Matthew Dierking, Bradley Duncan
Bradley D. Duncan
We report the use of periodic, pseudonoise waveforms in a multifunction coherent ladar system. We exploit the Doppler sensitivity of these waveforms, as well as agile processing, to enable diverse ladar functions, including high range resolution imaging, macro-Doppler imaging, synthetic aperture ladar, and range-resolved micro-Doppler imaging. We present analytic expressions and simulations demonstrating the utility of pseudonoise waveforms for each of the ladar modes. We also discuss a laboratory pseudonoise ladar system that was developed to demonstrate range compression and range-resolved micro-Doppler imaging, as well as the phase recovery common to each of the coherent modes.
Holographic Aperture Ladar, Bradley Duncan, Matthew Dierking
Holographic Aperture Ladar, Bradley Duncan, Matthew Dierking
Bradley D. Duncan
Holographic aperture ladar is a variant of synthetic aperture ladar that seeks to increase cross-range scene resolution by synthesizing a large effective aperture through the motion of a smaller receiver and through the subsequent proper phasing and correlation of the detected signals in postprocessing. Unlike in conventional synthetic aperture ladar, however, holographic aperture ladar makes use of a two- dimensional translating sensor array, not simply a translating point detector. Also unlike in conventional synthetic aperture ladar, holographic aperture images will be formed in the two orthogonal cross-range dimensions parallel and perpendicular to the sensor platform’s direction of motion. The central …
Experimental Demonstration Of A Stripmap Holographic Aperture Ladar System, Jason Stafford, Bradley Duncan, Matthew Dierking
Experimental Demonstration Of A Stripmap Holographic Aperture Ladar System, Jason Stafford, Bradley Duncan, Matthew Dierking
Bradley D. Duncan
By synthesizing large effective apertures through the translation of a smaller imaging sensor and the subsequent proper phasing and correlation of detected signals in postprocessing, holographic aperture ladar (HAL) systems seek to increase the resolution of remotely imaged targets. The stripmap HAL process was demonstrated in the laboratory, for the first time to our knowledge. Our results show that the stripmap HAL transformation can precisely account for off-axis transmitter induced phase migrations. This in turn allows multiple pupil plane field segments, sequentially collected across a synthetic aperture, to be coherently mosaiced together. As a direct consequence, we have been able …
Review: 'Theory Of Dielectric Optical Waveguides,' 2nd Edition, By Dietrich Marcuse, Bradley D. Duncan
Review: 'Theory Of Dielectric Optical Waveguides,' 2nd Edition, By Dietrich Marcuse, Bradley D. Duncan
Bradley D. Duncan
I suppose I ought to say up front that while preparing this review I often found myself feeling very much like a student evaluating his teacher. After all, it was, in part, the first edition of Dietrich Marcuse's Theory of Dielectric Optical Waveguides (among a handful of other similar texts) from which I first studied the principles of optical waveguide theory under the demanding, yet patient and graceful guidance of Dr. Ahmad Safaai-Jazi. Thus with the utmost respect for a teacher whom I have never met, I shall try to faithfully share my thoughts and feelings regarding the second edition …
Modal Interference Techniques For Strain Detection In Few-Mode Optical Fibers, Bradley D. Duncan
Modal Interference Techniques For Strain Detection In Few-Mode Optical Fibers, Bradley D. Duncan
Bradley D. Duncan
Interference between the modes of an optical fiber results in specific intensity patterns which can be modulated as a function of disturbances in the optical fiber system. These modulation effects are a direct result of the difference in propagation constants of the constituent modes. In this presentation it is shown how the modulated intensity patterns created by the interference of specific mode groups in few-mode optical fibers (V < 5.0) can be used to detect strain. A detailed discussion of the modal phenomena responsible for the observed strain induced pattern modulation is given and it is shown that strain detection sensitivities …
Effects Of Spatial Modes On Ladar Vibration Signature Estimation, Douglas Jameson, Matthew Dierking, Bradley Duncan
Effects Of Spatial Modes On Ladar Vibration Signature Estimation, Douglas Jameson, Matthew Dierking, Bradley Duncan
Bradley D. Duncan
Ladar-based vibrometry has been shown to be a powerful technique in enabling the plant identification of machines. Rather than sensing the geometric shape of a target laser vibrometers sense motions of the target induced by moving parts within the system. Since the target need not be spatially resolved, vibration can be sensed reliably and provide positive identification at ranges beyond the imaging limits of the aperture. However, as the range of observation increases, the diffraction-limited beam size on the target increases as well, and may encompass multiple vibrational modes on the target's surface. As a result, vibration estimates formed from …
Bidirectional Scattering Distribution Functions Of Maple And Cottonwood Leaves, Michael Greiner, Bradley Duncan, Matthew Dierking
Bidirectional Scattering Distribution Functions Of Maple And Cottonwood Leaves, Michael Greiner, Bradley Duncan, Matthew Dierking
Bradley D. Duncan
We present our investigations into the optical scattering properties of both sugar maple (Acer saccarum) and eastern cottonwood (Populus deltoides) leaves in the near-IR wavelength regime. The bidirectional scattering distribution function (BSDF) describes the fractions of light reflected by and transmitted through a leaf for a given set of illumination and observation angles. Experiments were performed to measure the BSDF of each species at a discrete set of illumination and observation angles. We then modeled the BSDFs in such a way that other researchers may interpolate their values for scattering in any direction under illumination at any angle.
Demonstrated Resolution Enhancement Capability Of A Stripmap Holographic Aperture Ladar System, Samuel Venable, Bradley Duncan, Matthew Dierking, David Rabb
Demonstrated Resolution Enhancement Capability Of A Stripmap Holographic Aperture Ladar System, Samuel Venable, Bradley Duncan, Matthew Dierking, David Rabb
Bradley D. Duncan
Holographic aperture ladar (HAL) is a variant of synthetic aperture ladar (SAL). The two processes are related in that they both seek to increase cross-range (i.e., the direction of the receiver translation) image resolution through the synthesis of a large effective aperture. This is in turn achieved via the translation of a receiver aperture and the subsequent coherent phasing and correlation of multiple received signals. However, while SAL imaging incorporates a translating point detector, HAL takes advantage of a two-dimensional translating sensor array. For the research presented in this article, a side-looking stripmap HAL geometry was used to sequentially image …
Saturated Semiconductor Optical Amplifier Phase Modulation For Long Range Laser Radar Applications, Jennifer Carns, Bradley Duncan, Matthew Dierking
Saturated Semiconductor Optical Amplifier Phase Modulation For Long Range Laser Radar Applications, Jennifer Carns, Bradley Duncan, Matthew Dierking
Bradley D. Duncan
We investigate the use of a semiconductor optical amplifier operated in the saturation regime as a phase modulator for long range laser radar applications. The nature of the phase and amplitude modulation resulting from a high peak power Gaussian pulse, and the impact this has on the ideal pulse response of a laser radar system, is explored. We also present results of a proof-of-concept laboratory demonstration using phase-modulated pulses to interrogate a stationary target.
Review: 'Integrated Optics: Design And Modeling,' By Reinhard Marz, Bradley D. Duncan
Review: 'Integrated Optics: Design And Modeling,' By Reinhard Marz, Bradley D. Duncan
Bradley D. Duncan
My overall impression is that Integrated Optics: Design and Modeling will make a fine addition to almost anyone's collection of books on integrated optics. It will, however, serve its readers better as a reference book than as a text from which to first learn the basic concepts of integrated optics. I say this because the book is written at a fairly sophisticated technical level, though the author often moves rather quickly to the "bottom line" without providing material much beyond what is first necessary to introduce a problem or concept, and then a statement of the results and/or implications. It …
Index-Matched Boundary Techniques For The Elimination Of Acoustical Resonances, Jack H. Parker, Bradley D. Duncan
Index-Matched Boundary Techniques For The Elimination Of Acoustical Resonances, Jack H. Parker, Bradley D. Duncan
Bradley D. Duncan
We extend the principle of optical index of refraction to apply the concept of acoustical index for transverse acoustical wave propagation in strings. The relationship between acoustical index and mass density of the acoustic material is developed. With this theoretical link established, classic index-matching techniques are explored at acoustical boundaries. Proper selection of boundary interface segments leads to the elimination of resonant vibrationalmodes that occur in rigidly supported strings, while maintaining the nonresonant vibration response.
Coupling Efficiencies For General Target Illumination Ladar Systems Incorporating Single Mode Optical Fiber Receivers, Christopher Brewer, Bradley Duncan, Kenneth Barnard, Edward Watson
Coupling Efficiencies For General Target Illumination Ladar Systems Incorporating Single Mode Optical Fiber Receivers, Christopher Brewer, Bradley Duncan, Kenneth Barnard, Edward Watson
Bradley D. Duncan
A rigorous method for modeling received power coupling efficiency (ηF/R) and transmitted power coupling efficiency (ηF/T) in a general-target-illumination ladar system is presented. For our analysis we concentrate on incorporating a single-mode optical fiber into the ladar return signal path. By developing expressions for both ηF/R and ηF/T for a simple, diffuse target, our model allows for varying range, beam size on target, target diameter, and coupling optics. Through numerical analysis ηF/R is shown to increase as the range to target increases and decrease as target diameter increases, and ηF/T is shown to decrease with target range. A baseline signal-to-noise …
Parametric Extension Of The Classical Exposure Schedule Theory For Angle-Multiplexed Photorefractive Recording Using The Common-Aperture Beam Geometry, Mark Delong, Bradley Duncan, Jack Parker
Parametric Extension Of The Classical Exposure Schedule Theory For Angle-Multiplexed Photorefractive Recording Using The Common-Aperture Beam Geometry, Mark Delong, Bradley Duncan, Jack Parker
Bradley D. Duncan
The gradual reorientations in crystal geometry encountered during angle-multiplexed holographic recording with obliquely incident recording beams can create significant parametric exposure-time and recording-angle dependencies in both grating writing- and erasure-time constants. We present a parametric extension of the classically derived backward-recursion algorithm that compensates for the intermingling effects of recording geometry, writing-beam intensity variations, and unique crystal behavior. We present experimental data for a sequence of 301 holograms recorded with the goal of equal hologram strength and, separately, the same sequence recorded with the goal of equal hologram reconstruction intensity—which are different cases for a steeply incident readout beam.
Heterodyne Ladar System Efficiency Enhancement Using Single-Mode Optical Fiber Mixers, Donald K. Jacob, Martin B. Mark, Bradley D. Duncan
Heterodyne Ladar System Efficiency Enhancement Using Single-Mode Optical Fiber Mixers, Donald K. Jacob, Martin B. Mark, Bradley D. Duncan
Bradley D. Duncan
A theoretical performance analysis of a heterodyne ladar system incorporating a single-mode fiber receiver has been performed. For our purposes, the performance parameters of interest are the coupling and mixing efficiency of the ladar receiver, as they relate to the overall system carrier-to-noise ratio. For a receiver incorporating a single-mode fiber mixer, the received and local-oscillator fields are matched both spatially and temporally at the detector, yielding 100% mixing efficiency. We have therefore focused our efforts on determining an expression for the efficiency with which a diffuse return from a purely speckle target can be coupled into the receiving leg …
Space-Bandwidth Product Enhancement Of A Monostatic, Multi-Aperture Infrared Image Upconversion Ladar Receiver Incorporating Periodically Polled Linbo3, Christopher Brewer, Bradley Duncan, Phillip Maciejewski, Sean Kirkpatrick, Edward Watson
Space-Bandwidth Product Enhancement Of A Monostatic, Multi-Aperture Infrared Image Upconversion Ladar Receiver Incorporating Periodically Polled Linbo3, Christopher Brewer, Bradley Duncan, Phillip Maciejewski, Sean Kirkpatrick, Edward Watson
Bradley D. Duncan
We investigate the space-bandwidth product of a ladar system incorporating an upconversion receiver. After illuminating a target with an eye-safe beam, we direct the return into a piece of periodically poled LiNbO3 where it is upconverted into the visible spectrum and detected with a CCD camera. The theoretical and experimental transfer functions are then found. We show that the angular acceptance of the upconversion process severely limits the receiver field of regard for macroscopic coupling optics. This limitation is overcome with a pair of microlens arrays, and a 43% increase in the system’s measured space-bandwidth product is demonstrated.
Real-Time Non-Linear Image Processing Using An Active Optical Scanning Technique, Bradley Duncan, Ting-Chung Poon, Ron Piper
Real-Time Non-Linear Image Processing Using An Active Optical Scanning Technique, Bradley Duncan, Ting-Chung Poon, Ron Piper
Bradley D. Duncan
Real-time non-linear image processing has been achieved using an active optical scanning technique. This paper reports experimental results in edge extraction for both binary and grey-scale transmissive objects. Binary edge extraction is achieved using morphological transformations, while grey-scale edge extraction is achieved using a threshold decomposition technique. Advantages and limitation of both techniques are identified.