Nurturing Genius: the Childhood and Youth of Kelvin and Maxwell

William Thomson and James Clerk Maxwell, nineteenth century natural philosophers, were friends and colleagues (Thomson was Maxwell’s senior by seven years). This historical note gives a description of their early lives, with emphasis on the influence of their fathers and of Cambridge on their development

Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure

Phase and transport velocities in particle and electromagnetic beams

In a coherent monoenergetic beam of non-interacting particles, the phase velocity and the particle transport velocity are functions of position, with the strongest variation being in the focal region. These velocities are everywhere parallel to each other, and their product is constant in space. For a coherent monochromatic electromagnetic beam, the energy transport velocity is never greater than the speed of light, and can even be zero. The phase velocities (one each for the non-zero components of the electric and magnetic fields, in general) can be different from each other and from the energy transport velocity, both in direction and in magnitude. The phase velocities at a given point are independent of time, for both particle and electromagnetic beams. The energy velocity is independent of time for the particle beam, but in general oscillates (with angular frequency 2w) in magnitude and direction about its mean value at a given point in the electromagnetic beam. However, there exist electromagnetic steady beams, within which the energy flux, energy density and energy velocity are all independent of time.Comment: 9 pages, 12 figure

Compound transfer matrices: Constructive and destructive interference

Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the compound barrier is simply given by the product of the transmission probabilities of the individual sub-barriers. In contrast if one is scattering waves (whether we are dealing with either purely classical waves or quantum Schrodinger wavefunctions) each sub-barrier contributes phase information (as well as a transmission probability), and these phases can lead to either constructive or destructive interference, with the transmission probability oscillating between nontrivial upper and lower bounds. In this article we shall study these upper and lower bounds in some detail, and also derive bounds on the closely related process of quantum excitation (particle production) via parametric resonance.Comment: V1: 28 pages. V2: 21 pages. Presentation significantly streamlined and shortened. This version accepted for publication in the Journal of Mathematical Physic

Signal Degradation due to Charge Buildup in Noble Liquid Ionization Calorimeters

ATLAS, B physics, R parity, hadron identification high luminosity hadron colliders such as the Large Hadron Collider (LHC) at CER

Theory of reflection: reflection and transmission of electromagnetic, particle and acoustic waves

This book deals with the reflection of electromagnetic and particle waves by interfaces. The interfaces can be sharp or diffuse. The topics of the book contain absorption, inverse problems, anisotropy, pulses and finite beams, rough surfaces, matrix methods, numerical methods,  reflection of particle waves and neutron reflection. Exact general results are presented, followed by long wave reflection, variational theory, reflection amplitude equations of the Riccati type, and reflection of short waves. The Second Edition of the Theory of Reflection is an updated and much enlarged revision of the 1987 monograph. There are new chapters on periodically stratified media, ellipsometry, chiral media, neutron reflection and reflection of acoustic waves. The chapter on anisotropy is much extended, with a complete treatment of the reflection and transmission properties of arbitrarily oriented uniaxial crystals. The book gives a systematic and unified treatment reflection and transmission of electromagnetic and particle waves at interfaces. It is intended for physicists, chemists, applied mathematicians and engineers, and is written in a simple direct style, with all necessary mathematics explained in the text