Physics Commons^™

Doing 'True Science': The Early History Of The 'Institutum Divi Thomae,' 1935-1951, John Alfred Heitmann

John A. Heitmann

This essay focuses on the origins and early history of the Institutum Divi Thomae (hereafter referred to as the IDT or Institutum), thus describing one particularly rich episode illustrating the relationship between American Catholicism and science during the middle of the twentieth century. The IDT was established by the Archdiocese of Cincinnati in 1935; its faculty and students, while working in the area of cancer research, published hundreds of scientific and technical papers, developed a number of commercial products, and received considerable publicity in both the religious and secular press during the first two decades of its existence. However, with …

Role Of Diffusive, Photovoltaic, And Thermal Effects In Beam Fanning In Linbo3, Jaw-Jueh Liu, Partha P. Banerjee, Q. W. Song

Partha Banerjee

We analyze the steady-state (Gaussian) beam fanning in LiNbO3 from the nonlinearly coupled Kukhtarev equations by including both diffusive and photovoltaic effects and by adding the thermal effect in the calculation. There is good agreement between theory and experiment. The results show a symmetric beam-fanning pattern whose size depends on the beam waist and the power. Possible applications of our results in nondestructive testing of material parameters and optical limiting are discussed.

Simulation Of Two-Dimensional Nonlinear Envelope Pulse Dynamics By A Two-Step Spatiotemporal Angular Spectrum Method, H. K. Sim, Adrianus Korpel, Karl E. Lonngren, Partha P. Banerjee

Partha Banerjee

We present an extension of our previous nonlinear beam-simulation method to the propagation and interaction of pulse envelopes. The extra time dimension is applied in the context of a dispersive nonlinear medium that is described by a Klein–Gordon equation with an added cubically nonlinear, self-focusing term. Pulse propagation in this medium is modeled as the evolution of a spatiotemporal spectrum—i.e., the frequency-dependent angular spectrum of the pulse envelope—traversing a sequence of self-induced, thin, weak phase filters. Preliminary simulation experiments show agreement with known behavior in the absence of nonlinearity, confirm the existence of an (apparently unstable) stationary solution, and demonstrate …

Theoretical And Experimental Studies Of Propagation Of Beams Through A Finite Sample Of A Cubically Nonlinear Material, Partha P. Banerjee, Raj M. Misra, M. Maghraoui

Partha Banerjee

Propagation of an externally focused or defocused Gaussian beam in a cubically nonlinear material is studied analytically and experimentally. The theoretical analysis is applied to determine the sign and magnitude of n2 for a material by means of a single-beam experiment with a finite nonlinear sample within which propagational diffraction cannot be neglected. Experimental results for a solution of chlorophyll in ethanol are reported. Based on available theory, an average n2 can be defined for a nonlinearity of thermal origin, and this value is found to be in good agreement with experimental results. Finally, the theoretical analysis and …

On A Simple Derivation Of The Fresnel Diffraction Formula And A Transfer Function Approach To Wave Propagation, Partha P. Banerjee, Ting-Chung Poon

Partha Banerjee

The Fresnel diffraction formula is straightforwardly obtained by solving a partial differential equation (PDE) for envelope propagation using Fourier transform techniques. The PDE, in turn, can be derived from the dispersion relation of a linear medium by employing a simple operator formalism. The transfer function and impulse response of propagation follows as a spin‐off and is used to solve illustrative problems. Huygens’ principle is visualized as a consequence of the convolution property of linear systems.

Notch Spatial Filtering With An Acousto-Optic Modulator, Partha P. Banerjee, Dongqing Cao, Ting-Chung Poon

Partha Banerjee

The role of acousto-optic (AO) modulators in programmable real-time image processing has recently been demonstrated. For fully investigating the image-processing capabilities of the AO modulator, general techniques to derive spatial transfer functions are needed for a variety of physical situations. We develop a technique to determine the spatial transfer functions numerically for various cases of beam incidence on an AO modulator. Normal incidence and incidence at twice the Bragg angle are investigated as examples for which double-sided and single-sided notch spatial filtering, respectively, are achieved. The observed spatial-filtering characteristics are reconciled with simple intuitive physical arguments.

Nonlinear Transverse Effects In Second-Harmonic Generation, Pawel Pliszka, Partha P. Banerjee

Partha Banerjee

We study a three-dimensional model of interaction of fundamental-frequency and second-harmonic beams in a quadratically nonlinear medium. Numerical simulations of the three-dimensional propagation problem in the presence of diffraction and anisotropy are performed under the paraxial approximation. The role of the transverse effects in various regimes is investigated. We demonstrate the effect of phase modulation and an induced nonlinear focusing during the interaction of the fundamental frequency with the generated second harmonic.

Multiwave Coupling In A High-Gain Photorefractive Polymer, Kenji Matsushita, Partha P. Banerjee, S. Ozaki, Daisuke Miyazaki

Partha Banerjee

The characteristics of a new high-gain photorefractive polymer composite with a PNP chromophore are investigated. Competition between beam fanning and two-wave coupling (TWC) is predicted and verified experimentally. The intensity dependence of TWC gain is studied. Higher diffraction order and forward phase conjugation in a TWC geometry are observed and explained.

Linear And Nonlinear Propagation In Negative Index Materials, Partha P. Banerjee, George Nehmetallah

Partha Banerjee

We analyze linear propagation in negative index materials by starting from a dispersion relation and by deriving the underlying partial differential equation. Transfer functions for propagation are derived in temporal and spatial frequency domains for unidirectional baseband and modulated pulse propagation, as well as for beam propagation. Gaussian beam propagation is analyzed and reconciled with the ray transfer matrix approach as applied to propagation in negative index materials. Nonlinear extensions of the linear partial differential equation are made by incorporating quadratic and cubic terms, and baseband and envelope solitary wave solutions are determined. The conditions for envelope solitary wave solutions …

Application Of Up-Sampling And Resolution Scaling To Fresnel Reconstruction Of Digital Holograms, Logan Williams, George Nehmetallah, Rola Aylo, Partha P. Banerjee

Partha Banerjee

Fresnel transform implementation methods using numerical preprocessing techniques are investigated in this paper. First, it is shown that up-sampling dramatically reduces the minimum reconstruction distance requirements and allows maximal signal recovery by eliminating aliasing artifacts which typically occur at distances much less than the Rayleigh range of the object. Second, zero-padding is employed to arbitrarily scale numerical resolution for the purpose of resolution matching multiple holograms, where each hologram is recorded using dissimilar geometric or illumination parameters. Such preprocessing yields numerical resolution scaling at any distance. Both techniques are extensively illustrated using experimental results.

Achieving Enhanced Gain In Photorefractive Polymers By Eliminating Electron Contributions Using Large Bias Fields, C. M. Liebig, S. H. Buller, Partha P. Banerjee, S. A. Basun, Pierre-Alexandre Blanche, J. Thomas, Cory W. Christenson, N. Peyghambarian, Dean R. Evans

Partha Banerjee

Photorefractive polymers have been extensively studied for over two decades and have found applications in holographic displays and optical image processing. The complexity of these materials arises from multiple charge contributions, for example, leading to the formation of competing photorefractive gratings. It has been recently shown that in a photorefractive polymer at relatively moderate applied electric fields the primary charge carriers (holes) establish an initial grating, followed by a subsequent competing grating (electrons) resulting in a decreased two-beam coupling and diffraction efficiencies. In this paper, it is shown that with relatively large sustainable bias fields, the two-beam coupling efficiency is …

3d Visualization Using Pulsed And Cw Digital Holographic Tomography Techniques, George Nehmetallah, Partha P. Banerjee, D. Ferree, R. Kephart, Sarat C. Praharaj

Partha Banerjee

We outline the use of digital holographic tomography to determine the three-dimensional (3D) shapes of falling and static objects, such as lenslets and water droplets. Reconstruction of digitally recorded inline holograms is performed using multiplicative and Radon transform techniques to reveal the exact 3D shapes of the objects.

Reply To “Comment On Gravitational Slingshot,” By C. L. Cook [Am. J. Phys. 73 (4), 363 (2005)], Asim Gangopadhyaya, Asim Gangopadhyaya, Robert Cacioppo, John Dykla

Asim Gangopadhyaya

No abstract provided.

Kl−Ks Mass Difference And Supersymmetric Left-Right-Symmetric Theories, Asim Gangopadhyaya

Asim Gangopadhyaya

The supersymmetric contributions to the K_L−K_S mass difference makes the previously obtained bounds on the right-handed scale (M_R>1.6 TeV) much weaker. This raises the interesting possibility that the left-right model could be tested as an alternative to SU_L(2)⊗U(1) at low energies. Also we find that to demand that the supersymmetric contribution to the K_L−K_S mass difference be less than 3.5×10⁻¹⁵ GeV requires that scalar-quark masses be more than 400 GeV.

Approaching A Universal Scaling Relationship Between Fracture Stiffness And Fluid Flow, David Nolte, Laura Pyrak-Nolte

David D Nolte

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 …

Generation Of A Complete Set Of Additive Shape-Invariant Potentials From An Euler Equation, Jonathan Bougie, Asim Gangopadhyaya, Jeffrey Mallow

Asim Gangopadhyaya

In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ħ can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ħ explicitly.

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.

Magnet Traveling Through A Conducting Pipe: A Variation On The Analytical Approach, Benjamin Irvine, Matthew Kemnetz, Asim Gangopadhyaya, Thomas Ruubel

Asim Gangopadhyaya

We present an analytical study of magnetic damping. In particular, we investigate the dynamics of a cylindrical neodymium magnet as it moves through a conducting tube. Owing to the very high degree of uniformity of the magnetization for neodymium magnets, we are able to provide completely analytical results for the electromotive force generated in the pipe and the consequent retarding force. Our analytical expressions are shown to have excellent agreement with experimental observations.

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

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

Asim Gangopadhyaya

No abstract provided.

Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne

Asim Gangopadhyaya

The semiclassical WKB approximation method is reexamined in the context of nonrelativistic quantum-mechanical bound-state problems with broken supersymmetry (SUSY). This gives rise to an alternative quantization condition (denoted by BSWKB) which is different from the standard WKB formula and also different from the previously studied supersymmetric (SWKB) formula for unbroken SUSY. It is shown that to leading order in ħ, the BSWKB condition yields exact energy eigenvalues for shape-invariant potentials with broken SUSY (harmonic oscillator, Pöschl-Teller I and II) which are known to be analytically solvable. Further, we show explicitly that the higher-order corrections to these energy eigenvalues, up to …

Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods, Asim Gangopadhyaya, Darwin Chang

Asim Gangopadhyaya

We apply the superfield method with the spurion technique to derive the renormalization-group equations in broken supersymmetric theories. We point out some possible ambiguities in this procedure and show that it is in general necessary to express the supersymmetry-breaking terms in explicit D-type form. We also found that it is possible to construct broken supersymmetric theories where some of the symmetry-breaking parameters do not receive any infinite renormalization.

Comment On ‘‘The Hidden Symmetry For A Quantum System With An Infinitely Deep Square-Well Potential By Shi-Hai Dong And Zhong-Qi Ma [Am. J. Phys. 70 (5) 520-521 (2002)], Asim Gangopadhyaya, Jeffrey Mallow

Asim Gangopadhyaya

No abstract provided.

Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya

Asim Gangopadhyaya

The slingshot effect is an intriguing phenomenon that has been used effectively by NASA to send spacecraft to outer edges of the solar system. This phenomenon can be satisfactorily explained by Newtonian physics. However, if it is presented as a problem involving four-momentum conservation, the methods of relativistic kinematics easily lead to the conditions necessary for an accelerating as well as a retarding scenario. This problem provides an example that showcases the frequent utility of relativistic methods to analyze problems of Newtonian mechanics.

Magnetic Transitions In Disordered Gdal2, D. Williams, Paul Shand, Thomas Pekarek, Ralph Skomski, Valeri Petkov, Diandra Leslie-Pelecky

Thomas M. Pekarek

The role of disorder in magnetic ordering transitions is investigated using mechanically milled GdAl2. Crystalline GdAl2 is a ferromagnet while amorphous GdAl2 is a spin glass. Nanostructured GdAl2 shows a paramagnetic-to-ferromagnetic transition and glassy behavior, with the temperature and magnitude of each transition dependent on the degree and type of disorder. Disorder is parametrized by a Gaussian distribution of Curie temperatures TC with mean TC and breadth Δ TC. A nonzero coercivity is observed at temperatures more than 20 K above the highest TC of any known Gd-Al phase; however, the coercivity decreases with decreasing temperature over the same temperature …

New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne

Asim Gangopadhyaya

We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.

Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne

Asim Gangopadhyaya

Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.

Disorder-Induced Depression Of The Curie Temperature In Mechanically Milled Gdal2, Marco Morales Torres, D. Williams, Paul Shand, C. Stark, Thomas Pekarek, L. Yue, Valeri Petkov, Diandra Leslie-Pelecky

Thomas M. Pekarek

The effect of disorder on the ferromagnetic transition is investigated in mechanically milled GdAl2. GdAl2is a ferromagnet when crystalline and a spin glass when amorphous. Mechanical milling progressively disorders the alloy, allowing observation of the change from ferromagnetic to a disordered magnetic state. X-ray diffraction and pair-distribution-function analysis are used to determine the grain size, lattice parameter, and mean-squared atomic displacements. The magnetization as a function of temperature is described by a Gaussian distribution of Curie temperatures. The mean Curie temperature decreases with decreasing lattice parameter, where lattice parameter serves as a measure of defect concentration. Two different rates of …