Comment on the paper: Evanescent waves do contribute to the far field

Abstract

In a series of papers [1], it has been claimed that evanescent waves contribute to the far field of a radiating dipole, i.e. that the amplitude of the sum of the evanescent waves decreases as 1/r with increasing distance, r, from the dipole. In spite of the fact that three recent papers [2] have demonstrated that these claims are incorrect and that they contradict well-established results relating to the farzone behavior of the angular spectrum representation of wavefields [3], the author continues to repeat this claim, most recently in a note with the title ‘Evanescent waves do contribute to the field’. It is the purpose of this note to point out an error in the previous publications [1] which has led to this erroneous conclusion.     

Grain boundary and fracture surface analysis of Fe–C–P steel

Abstract

The present paper investigates the distribution of grain boundary types and fracture surface crystallography in an Fe–C–P alloy. It is shown that electron backscatter diffraction (EBSD) is an effective technique with which to conduct these investigations. The proportions of both Σ1 and particularly Σ3 (in coincidence site lattice notation)present after various heat treatments were higher than would have been expected for random generation. There was limited evidence that both higher annealing temperatures and longer annealing times promoted generation of Σ3 type boundaries. The standard EBSD technique was modified and extended to encompass both the novel ‘matched fracture’ specimen approach and direct mapping from fracture surfaces to provide crystallographic information. A correlation was noted between higher aging temperatures and proportions of cleavage fracture. Furthermore, there was a strong correlation between cleavage fracture surfaces exhibiting river markings and an {001} surface orientation.     

Dissipative atom optics

Abstract

We present an experiment where a cloud of cold caesium atoms is dropped onto an atomic mirror formed by a laser evanescent wave, and is cooled during the reflection. This cooling is due to a single Sisyphus process, transferring atoms from one ground-state hyperfine level to another, less coupled to the evanescent wave. We compare our results with a simple one-dimensional theoretical model. We also give the first experimental evidence for a large increase in the confinement lifetime of the atoms in this ‘gravitational cavity’ because of the cooling process.     

High-sensitivity Diffraction-compensated Moiré Deflectometry

Abstract

The spatial resolution and angular sensitivity of conventional moiré deflectometry are known to obey a conjugate relationship reminiscent of the uncertainty principle so that one cannot be improved without deteriorating the other. This paper looks at the origin of this relationship and suggests ways by which this ‘uncertainty principle’ can be violated. It is shown that a ‘projection’ of the grating which is free from diffraction effects and which, at the same time, contains the deflection information amplified by the ‘optical lever’ distance D between the gratings can be formed if the diffracted beams of order + 1 and ? 1 are separated from other orders and are recombined in certain ways. As a result, the angular sensitivity, which depends on the ratio of the pitch d of the grating to the distance D between the two gratings, can be improved without losing the spatial resolution by multiple diffraction orders. One of the diffraction compensation schemes is experimentally illustrated. It is shown that the ‘uncertainty product’ is improved by more than two orders of magnitude.     

The information content of weakly scattered fields: Implications for near-field imaging of three-dimensional structures

Abstract

The structural information carried by the homogeneous and evanescent components of the scattered field is investigated for the case of a single plane wave, either homogeneous or evanescent, incident on a weakly scattering three-dimensional medium. For homogeneous plane wave incidence, it is shown that, unlike the one-to-one mapping that exists in the case of scattering from thin (i.e. two-dimensional) structures, the evanescent components of the scattered field are related to the three-dimensional Fourier transform of the dielectric susceptibility through a generalized Radon transform. For evanescent plane wave incidence, a reciprocal relationship exists between the homogenous components of the scattered field and the three-dimensional Fourier transform of the susceptibility. Inversion techniques are outlined for these two cases, as well as other experimental modalities, which explicitly require, except for separable media, complete (i.e. multiple view) measurement data. These results have direct bearing on total internal reflection microscopy (TIRM), and they yield insight into the limitations of more general near-field imaging techniques.     

Pulse Propagation in a Gaseous Laser Amplifier

Abstract

It is shown that some transversal profile modifications, such as ‘overshoot’ at the edges of laser pulses propagating through gaseous laser amplifiers, can be qualitatively explained when diffusion of the active centres of the amplifier is taken into account. The necessary conditions for this situation to occur are also discussed and numerical results are presented which are in good agreement with previously obtained experimental results.     

Comment: There is no unmet requirement of optical coherence for continuous-variable quantum teleportation

Abstract

It has been argued that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not ‘truly coherent’. Here it is shown that ‘true coherence’ is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. A laser is as good a clock as any other, even in principle, and this objection to teleportation experiments is baseless.     

Travelling and evanescent parts of the optical near field

Abstract

The optical near field of a localized source has been studied by means of the angular spectrum representation of the electromagnetic Green's tensor. This Green's tensor can be expressed in terms of four auxiliary functions, which depend on the field point through the dimensionless radial distance q to the source, or origin of coordinates, and the polar angle ρ with the z axis. Each function separates into a part containing travelling (radiative) waves and a part which is a superposition of evanescent (decaying) waves. We have derived series expansions in q of the four functions, both for the travelling and for the evanescent parts. It is shown that the travelling waves are finite at the origin of coordinates, and that all singular behaviour of the radiation field is governed by the evanescent waves. It is illustrated numerically that the series expansions are applicable up to about five wavelengths from the origin. In order to extend the range to also cover larger values of q, we have derived series expansions of the auxiliary functions which converge rapidly near the x-y plane, and a full asymptotic expansion with the z coordinate as the large variable. Finally, from the properties of the Taylor coefficients we have derived simple new integral representations for the auxiliary functions.     

Model for growth and coarsening of two phase systems under diffusional control

Abstract

A model is described which is capable of simulating the two-dimensional evolution of microstructure in two phase systems undergoing diffusion controlled growth and surface tension driven coarsening. To solve the diffusion equation in the matrix phase, an integral equation method is employed. Thus, although it is necessary to describe the shapes of the second phase particles using a number of elements, it is not necessary to discretise the matrix phase as the particles evolve. This allows the computation times to be kept within reasonable limits. The boundary condition at the interface and the variation of the interfacial concentration with interface curvature are accounted for in a rigorous fashion. It is shown that the method can handle the ‘soft’ impingement of overlapping diffusion fields. A treatment of the ‘hard'’ physical impingement of particles is developed. To demonstrate the accuracy and stability of the method, the results from the model are compared with the exact solution for a spherical particle growing in a circular domain; it is shown that the agreement is reasonable. The results from a number of example computations are presented, which include (a) growth of a single particle in a finite domain, (b) soft and hard impingement of two particles in a finite domain, (c) coarsening of a significant number of particles at constant volume fraction, and (d) simultaneous nucleation, growth, and coarsening of second phase particles. Where appropriate, the results are compared with those from other models which have been published in the literature. The advantages and disadvantages of the present model are discussed.     

Union Cases Based on Designs by Bertel Thorvaldsen

Abstract

The recent article¹ on the use of Thorvaldsen's medallion designs by Peck for the decoration of two of the Peck and Hdvorsen cases made no reference to its use by other manufacturers. We have a case (see illustration), not recorded by Rinhart², nominally of quarter plate size, of fine quality and bearing the moulded legend contained within an oval ‘SMITH'S PATENT. 1860’. (Indicated ‘A’ on illustration.) It bears the title ‘Morning’ and there appears to be no indication of the engraver of the die. The paper label contained within is merely printed     

Indicating Surface of Natural Reflectance

Abstract

To study the behaviour of anisotropic media in reflection when illuminated by natural light, an ‘indicating surface of natural reflectance’ is defined. The use of such a surface is proposed, and its statistical parameters are given. The expressions that relate these parameters to the refractive indices of the incident medium and to the principal indices of the medium under observation have been deduced for the case of uniaxial media. Those corresponding to uniaxial transparent substances are presented here.     

Metal Surface Treatment and Reduction in Pitting Corrosion of 304L Stainless Steel by Excimer Laser

Abstract

The use of excimer lasers to produce thin rapidly quenched melts on metal surfaces is discussed. Results obtained using a XeCl laser on a variety of metal samples are given. The surface refinement and smoothing induced by laser treatment, giving improved resistance to pitting corrosion and higher etch resistance suggest significant potential for this method as a means of ‘micro-engineering’ surfaces.     

A systematized theory of creative concept generation in design: first-order and high-order concept generation

This paper aims to develop a systematized theory on the thinking process at the ‘very early stage of design.’ Here, ‘very’ is used to exaggerate the beginning of design, which includes the time just prior to or the precise beginning of the so-called conceptual design. First, concept generation is segregated into two phases—the problem-driven phase and the inner sense-driven phase. With regard to theoretical approach, the concept generation process is discussed by comparing metaphor, abduction, and general design theory from the perspective of similarities and dissimilarities. In addition, property mapping, concept blending, and concept integration in thematic relation are explained methodologically. So far, these theories and methods have been discussed independently, and the relations among them have not been clarified. As a result, it was found that the concept generation process could be categorized into two types: first-order concept generation and high-order concept generation. Furthermore, it was shown that high-order concept generation is related to the inner sense-driven phase, whereas first-order concept generation is related to the problem-driven phase.     

Propagating and evanescent waves associated with inhibited reflection in uniaxial crystals: Extraordinary incidence

Abstract

When an extraordinary wave under inhibited reflection conditions is incident on an interface between a uniaxial crystal and an isotropic medium, the reflected extraordinary wave is evanescent and the polarization of the refracted wave changes from linear to elliptical. In the present paper it is shown that the refracted ray undergoes a shift which is not only longitudinal (as the Goos—Hänchen effect in total reflection in isotropic interfaces) but also transversal. The structure of the evanescent reflected wave is studied and the polarization of the transmitted wave is analysed.     

The asymmetric lossy near-perfect lens

We extend the ideas of the perfect lens recently proposed [J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)] to an alternative structure. We show that a slab of a medium with negative refractive index bounded by media of different positive refractive index also amplifies evanescent waves and can act as a near-perfect lens. We examine the role of the surface states in the amplification of the evanescent waves. The image resolution obtained by this asymmetric lens is more robust against the effects of absorption in the lens. In particular, we study the case of a slab of silver, which has a negative dielectric constant, with air on one side and other media such as glass or GaAs on the other side as an ‘asymmetric’ lossy near-perfect lens for p-polarized waves. It is found that retardation has an adverse effect on the imaging due to the positive magnetic permeability of silver, but we conclude that subwavelength image resolution is possible in spite of it.     

Optically induced non-radiative fast pulses in metals

Abstract

We describe new experiments in which the signals induced inside a solid conductor by external excitation using nanosecond long pulsed laser radiation are detected using a pyro-electric material. From the data obtained, it is shown that there is a previously unreported ‘early’ or ‘fast’ signal which propagates inside the solid at a speed greater than that reported for sound in the same media. This signal is observed in addition to the usually observed thermal and acoustic waves that travel at the speed of sound in the same media. We demonstrate that this signal cannot be adequately accounted for by existing theories of thermo-elastic wave propagation in solids.     

A new view on the Peřina-Mišta form of the Glauber-Sudershan P function

Abstract

The ‘regularized’ form of the Glauber-Sudershan P function in terms of a series of Laguerre polynomials proposed by Perina and Mista is reconsidered. It is shown that the corresponding expansion coefficients result from averaging sampling functions well known from optical homodyne tomography with respect to the quadrature distribution of the signal field. An illustrative example of a nonclassical state is considered.     

Effect of oxygen concentration on diffusion length in Czochralski and magnetic Czochralski silicon

Abstract

This paper reports some new results on the influence of oxygen aggregation phenomena in the 450-850°C range on the diffusion length of minorities in both Czochralski (Cz) and magnetic Czochralski silicon. Thefeatures of the oxygen aggregation phenomena were studied by infrared spectroscopy at 20 K and the effect of these processes on the diffusion length was monitored by surface photovoltage measurements at 300 K. The results show that in Cz silicon the formation of thermal donors at 450°C is not associated with a detectable increase of the recombination activity, but that thermal donors are the precursors of other oxygen species, which grow during any further heat treatment. It was shown, moreover, that selfinterstitials injected from a surface oxide inhibit the oxygen segregation, in good agreement with predictions in the literature concerning the ‘volume exigency’ of oxygen segregation processes. Marked evidence of the influence of the cooling rate on the diffusion length was observed at 850°C, where the lifetime of heat treated Cz silicon was shown to be longer for a slow cooling process.     

Second Harmonic Generation in Optical Fibres: Multiphoton Absorption and Translation-inversion Symmetry

Abstract

Multiphoton absorption provides a route to x ₍₂₎ grating formation in optical fibres. It explains the efficacy of ‘seeding’ the fibre with green light to induce fibre second harmonic generation. The process depends on absorption sites with spatially inverted configurations having different multiphoton absorption rates.     

Superluminal tunnelling times as weak values

Abstract

We consider the tunnelling particle as a pre- and post-selected system and prove that the tunnelling time is the expectation value of the position of a ‘clock’ degree of freedom weakly coupled to it. Such a value, called a ‘weak value’, typically falls outside the eigenvalue spectrum of the operator. The appearance of unusual weak values has been associated with a unique interference structure called ‘superoscillations’ (band-limited functions which on a finite interval, approximate functions with spectra well outside their band). It is proposed that superoscillations play an important role in the interferences which give rise to superluminal effects. To demonstrate that, we consider a certain simple tunnelling barrier which allows a wave packet to travel in zero time and negligible distortion, a distance arbitrarily longer than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Similar reasoning applies to the dwell time. For this system, both the Wigner time (related to the group velocity) and a clock time correspond to superluminal velocities.