arXiv subjects

Masud Mansuripur

Publications and source records attributed to Masud Mansuripur.

At least 19 recordsLinked to original sources

arXiv2025

A rigorous coupled-wave analysis of birefringent holographic gratings with periodically-modulated dielectric tensor along an in-plane direction and tensor variations in the thickness direction

Diffraction of light upon interaction with thick slabs of a dielectric material having a periodic modulation of its refractive index (or dielectric tensor) is typically studied with the aid of the method known as the rigorous coupled-wave analysis (RCWA). The method involves solving Maxwell's equations for a large number of coupled electromagnetic plane-waves inside the dielectric slab, then matching the boundary conditions at the interface between the incidence medium and the slab, as well as those at the interface between the slab and the transmittance medium. In this way, one obtains the E-field and H-field amplitudes for all the reflected and transmitted plane-waves (i.e., diffraction orders as well as evanescent waves) that emerge within the incidence and transmittance media. If the refractive index (or dielectric tensor) of the holographic slab happens to vary in the thickness direction, one treats the slab as a number of thin layers stacked upon each other, then computes and combines the scattering matrices of these layers to arrive at the complete solution for the entire stack. The goal of the present paper is to extend the standard RCWA method to the case where the hologram's dielectric tensor varies in the thickness direction (in addition to being periodically modulated along an in-plane axis), without slicing up the thick hologram into a number of thin layers. The reflected and transmitted plane-waves in this case exhibit a large degree of degeneracy, but our numerical results confirm the validity and the accuracy of our proposed algorithm for handling such degeneracies.

physics.optics↗

arXiv2025

Quantization of the electromagnetic field, entropy of an ideal monoatomic gas, and the birth of Bose-Einstein statistics

In 1924, Einstein received a short manuscript in the mail from the Indian physicist S.N. Bose. He quickly translated Bose's manuscript to German and submitted it to Zeitschrift für Physik. Within a few weeks, Einstein presented his own findings (using a generalization of Bose's counting method) to a session of the Prussian Academy of Sciences. Whereas Bose had suggested a new counting method for the quanta of the electromagnetic field -- one that yielded Planck's blackbody radiation formula -- Einstein applied Bose's method to an ideal monoatomic gas. Shortly afterward, Einstein presented to the Academy a follow-up paper in which he described the Bose-Einstein condensation for the first time. The present paper describes some of the fascinating issues that Einstein struggled with as he attempted to unify the quantum-statistical properties of matter with those of the electromagnetic field.

physics.hist-ph↗

arXiv2024

The continuum limit of k-space cavity angular momentum is controlled by an infinite range difference operator

A wavepacket (electromagnetic or otherwise) within an isotropic and homogeneous space can be quantized on a regular lattice of discrete k-vectors. Each k-vector is associated with a temporal frequency omega; together, k and omega represent a propagating plane-wave. While the total energy and total linear momentum of the packet can be readily apportioned among its individual plane-wave constituents, the same cannot be said about the packet's total angular momentum. One can show, in the case of a reasonably smooth (i.e., continuous and differentiable) wave packet, that the overall angular momentum is expressible as an integral over the k-space continuum involving only the Fourier transform of the field and its k-space gradients. In this sense, the angular momentum is a property not of individual plane-waves, but of plane-wave pairs that are adjacent neighbors in the space inhabited by the k-vectors, and can be said to be localized in the k-space. Strange as it might seem, this hallmark property of angular momentum does not automatically emerge from an analysis of a discretized k-space. In fact, the discrete analysis shows the angular momentum to be distributed among k-vectors that pair not only with nearby k-vectors but also with those that are far away. The goal of the present paper is to resolve the discrepancy between the discrete calculations and those performed on the continuum, by establishing the conditions under which the highly non-local sum over plane-wave pairs in the discrete k-space would approach the localized distribution of the angular momentum across the continuum of the k-space.

physics.class-ph↗

arXiv2024

Fundamental principles and applications of nonlinear optical phenomena in classical and quantum electrodynamics

Nonlinear optical phenomena play important roles in the vast emerging fields of micro- and nano-technology. This paper describes the general characteristics of nonlinear optical materials and systems, with a focus on parametric amplification, frequency-doubling with pump depletion, quantum noise accompanying attenuation and amplification of light beams, and parametric fluorescence.

physics.optics↗

arXiv2024

Quantum fluctuations and noise in interferometry and photodetection: Applications in optical sensing and micromanipulation

Accurate optical sensing and micromanipulation requires sensitive measurements of the position, orientation, and dynamics of small particles--and sometimes even large objects--under consideration. The signals acquired in the process, including those needed for the feedback control of these particles and objects, are inevitably contaminated by quantum fluctuations and noise that accompany the physical processes of optical interference and photodetection (or photon counting). This paper explores the origins of signal fluctuation and quantum noise that are inevitably associated with such sensitive measurements.

quant-ph↗

arXiv2024

Does one still need to "shut up and calculate"?

In learning quantum mechanics, an essential question has always been: How does one go about developing a "physical feel" for quantum phenomena? Naturally, one needs a basis or ground zero to start from, and that basis must be unlike anything with which we are already familiar in consequence of our experiences with the world of classical physics. We argue (channeling Richard Feynman) that the most elementary and the least cumbersome concept to build upon is the existence of complex probability amplitudes for physical events. An event that can take place in multiple alternative ways should be treated by adding the corresponding amplitudes when the paths are, in principle, indistinguishable, and by adding the probabilities themselves when the paths are distinguishable. Once we accept this principle and hone our intuition by examining quantum phenomena in its light, we will be on the path to "understanding" quantum mechanics. Elementary examples from the field of quantum optics demonstrate how adherence to Feynman's principle could lead to a better, more "intuitive" appreciation for the magic of quantum mechanics.

quant-ph↗

arXiv2023

Electromagnetic angular momentum of quantized wavepackets in free space

A single electromagnetic plane-wave propagating in free space possesses neither spin nor orbital angular momentum. Both types of angular momentum arise from interference between pairs of plane-waves having the same temporal frequency ω but differing k-vectors k_1 and k_2. While it is fairly straightforward to evaluate a wavepacket's spin and orbital angular momenta in the (k,ω) continuum by means of Fourier transformation, obtaining the same results by discretizing the (k,ω) space, then attempting to approach the continuum limit via an infinite enlargement of the spatial volume under consideration, is fraught with danger.

physics.optics↗

arXiv2023

On the quantum theory of light interacting with nano-materials

The fundamental processes of absorption, stimulated and spontaneous emission, and elastic as well as inelastic scattering involving light and atoms, molecules, and nano-particles have been studied for decades using both classical and quantum theories. While providing an overview of the subject, this paper presents a streamlined approach to studying atom-photon interactions in the context of modern quantum optics in the hope of providing guidance for applications in the general area of molecular and nano-photonic machines.

physics.optics↗

arXiv2023

Spin and orbital angular momenta of electromagnetic waves in classical and quantum electrodynamics

A plane, monochromatic electromagnetic wave propagating in free space can have a certain amount of spin angular momentum but cannot possess any orbital angular momentum. Even the spin angular momentum of the plane-wave is difficult to evaluate without resort to certain mathematical limit arguments. Both spin and orbital angular momenta can be computed for a wavepacket of finite duration and finite cross-sectional area using standard methods of classical electrodynamics. Extending these results to finite wavepackets in quantum electrodynamics requires subtle arguments in conjunction with the multimodal structure of the wavepacket. This paper presents some of the nuances of classical as well as quantum-optical methods for analyzing the spin and orbital angular momenta of electromagnetic waves.

physics.optics↗

arXiv2023

Fundamental properties of beam-splitters in classical and quantum optics

A lossless beam-splitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the magnitudes and phases of these probability amplitudes. Proceeding to examine a pair of (nearly) single-mode wavepackets in the number-states |n1> and |n2> that simultaneously arrive at the splitter's input ports, we find the distribution of photon-number states at the output ports using an argument inspired by Feynman's scattering analysis of indistinguishable Bose particles. The result thus obtained coincides with that of the standard quantum-optical treatment of beam-splitters via annihilation and creation operators a and a†. A simple application of the Feynman method provides a form of justification for the Bose enhancement implicit in the well-known formulas a|n>=sqrt(n)|n-1> and a†|n>=sqrt(n+1)|n+1>.

quant-ph↗

arXiv2022

Spin-1 photons, spin-1/2 electrons, Bell's inequalities, and Feynman's special perspective on quantum mechanics

The Einstein-Podolsky-Rosen (EPR) paradox that argues for the incompleteness of quantum mechanics as a description of physical reality has been put to rest by John Bell's famous theorem, which inspired numerous experimental tests and brought about further affirmations of quantum reality. Nevertheless, in his writings and public presentations, Richard Feynman never acknowledged the significance of Bell's contribution to the resolution of the EPR paradox. In this paper, we discuss several variants of the Bell inequalities (including one that was specifically espoused by Feynman), and explore the ways in which they demolish the arguments in favor of local hidden-variable theories. We also examine the roots of Feynman's attitude toward Bell's theorem in the context of Feynman's special perspective on quantum mechanics.

quant-ph↗

arXiv2022

Linear and angular momenta of photons in the context of "which path" experiments of quantum mechanics

In optical experiments involving a single photon that takes alternative paths through an optical system and ultimately interferes with itself (e.g., Young's double-slit experiment, Mach-Zehnder interferometer, Sagnac interferometer), there exist fundamental connections between the linear and angular momenta of the photon on the one hand, and the ability of an observer to determine the photon's path through the system on the other hand. This paper examines the arguments that relate the photon momenta (through the Heisenberg uncertainty principle) to the "which path" (German: welcher Weg) question at the heart of quantum mechanics. We show that the linear momenta imparted to apertures or mirrors, or the angular momenta picked up by strategically placed wave-plates in a system, could lead to an identification of the photon's path only at the expense of destroying the corresponding interference effects. We also describe a thought experiment involving the scattering of a circularly-polarized photon from a pair of small particles kept at a fixed distance from one another. The exchange of angular momentum between the photon and the scattering particle in this instance appears to provide the "which path" information that must, of necessity, wipe out the corresponding interference fringes, although the fringe-wipe-out mechanism does not seem to involve the uncertainty principle in any obvious way.

quant-ph↗

arXiv2022

Insights into the behavior of certain optical systems gleaned from Feynman's approach to quantum electrodynamics

Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability amplitude. The sum of the amplitudes over all these paths then yields the overall probability amplitude that the system starting at A would end up at B. We apply Feynman's method to several optical systems of practical interest and discuss the nuances of the method as well as instances where the predicted outcomes agree or disagree with those of classical optical theory. Examples include the properties of beam-splitters, passage of single photons through Mach-Zehnder and Sagnac interferometers, electric and magnetic dipole scattering, reciprocity, time-reversal symmetry, the optical theorem, the Ewald-Oseen extinction theorem, far field diffraction, and the two-photon interference phenomenon known as the Hong-Ou-Mandel effect.

quant-ph↗

arXiv2021

Ubiquity of Fourier Transformation in Optical Sciences (Part II)

This paper contains a transcript of my presentation at the Wyant Tribute Symposium on August 2, 2021 at SPIE's Optics & Photonics conference in San Diego, California. The technical part of the paper has no overlap with a previous article of mine that was published in Applied Optics last year, bearing the same title as this one.1 The applications of Fourier transformation described in the present paper include the central limit theorem of probability and statistics, the Shannon-Nyquist sampling theorem, and computing the electromagnetic field radiated by an oscillating magnetic dipole.

physics.class-ph↗

arXiv2021

Fresnel reflection and transmission in the presence of gain media

When a monochromatic electromagnetic plane-wave arrives at the flat interface between its transparent host (i.e., the incidence medium) and an amplifying (or gainy) second medium, the incident beam splits into a reflected wave and a transmitted wave. In general, there is a sign ambiguity in connection with the k-vector of the transmitted beam, which requires at the outset that one decide whether the transmitted beam should grow or decay as it recedes from the interface. The question has been posed and addressed most prominently in the context of incidence at large angles from a dielectric medium of high refractive index onto a gain medium of lower refractive index. Here, the relevant sign of the transmitted k-vector determines whether the evanescent-like waves within the gain medium exponentially grow or decay away from the interface. We examine this and related problems in a more general setting, where the incident beam is taken to be a finite-duration wavepacket whose footprint in the interfacial plane has a finite width. Cases of reflection from and transmission through a gainy slab of finite-thickness as well as those associated with a semi-infinite gain medium will be considered. The broadness of the spatio-temporal spectrum of our incident wavepacket demands that we develop a general strategy for deciding the signs of all the k-vectors that enter the gain medium. Such a strategy emerges from a consideration of the causality constraint that is naturally imposed on both the reflected and transmitted wavepackets.

physics.optics↗

arXiv2021

Electromagnetic force and torque derived from a Lagrangian in conjunction with the Maxwell-Lorentz equations

Electromagnetic force and torque are typically derived from a stress tensor in conjunction with Maxwell's equations of classical electrodynamics. In some instances, the Principle of Least Action (built around a Lagrangian) can be used to arrive at the same mathematical expressions of force and torque as those derived from a stress tensor. This paper describes some of the underlying arguments for the existence of a Lagrangian in the case of certain simple physical systems. While some formulations of electromagnetic force and torque admit a Lagrangian, there are other formulations for which a Lagrangian may not exist.

physics.optics↗

arXiv2021

The Talbot Effect

The Talbot effect, also referred to as self-imaging or lensless imaging, was originally discovered in the 1830's by Henry Fox Talbot. Over the years, various investigators have found different aspects of this phenomenon, and a theory of the Talbot effect capable of explaining the various observations based on the classical theory of diffraction has emerged. Unfortunately, many of the standard Optics textbooks do not discuss the Talbot effect. The goal of the present paper is to bring to the reader's attention the essential features as well as an elementary explanation of this wonderful phenomenon.

physics.optics↗

arXiv2020

A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium's optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

physics.optics↗