Review of theoretical models of electromagnetic NDT and their applications

There is an increasing interest in modelling electromagnetic methods of NDT - particularly eddy currents. A collaboration within the International Institute of Welding led to a survey intended to explain to non mathematicians the present scope of modelling. The present review commences with this survey and then points out some of the developments and some of the outstanding problems in transferring modelling into industry.

A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

Synthesis of broadband anti-reflection coatings for spaceflight infrared optics

A synthesis method is outlined for the design of broadband anti-reflection coatings for use in spaceborne infrared optics. The Golden Section optimisation routine is used to make a search, using designated non-absorptive dielectric thin film combinations, for the coating design which fulfils the required spectral requirements using the least number of layers and different materials. Three examples are given of coatings designed by this method : (I) 1µm to 12µm anti-reflection coating on Zinc Sulphide using Zinc Sulphide and Yttrium Fluoride thin film materials. (ii) 2µm to 14µm anti-reflection coating on Germanium using Germanium and Ytterbium Fluoride thin film materials. (iii) 6µm to 17µm anti-reflection coating on Germanium using Lead Telluride, Zinc Selenide and Barium Fluoride. The measured spectral performance of the manufactured 6µm to 17µm coating on Germanium is given. This is the anti-reflection coating for the germanium optics in the NASA Cassini Orbiter CIRS instrument.

Do in vivo terahertz imaging systems comply with safety guidelines?

Techniques for the coherent generation and detection of electromagnetic radiation in the far infrared, or terahertz, region of the electromagnetic spectrum have recently developed rapidly and may soon be applied for in vivo medical imaging. Both continuous wave and pulsed imaging systems are under development, with terahertz pulsed imaging being the more common method. Typically a pump and probe technique is used, with picosecond pulses of terahertz radiation generated from femtosecond infrared laser pulses, using an antenna or nonlinear crystal. After interaction with the subject either by transmission or reflection, coherent detection is achieved when the terahertz beam is combined with the probe laser beam. Raster scanning of the subject leads to an image data set comprising a time series representing the pulse at each pixel. A set of parametric images may be calculated, mapping the values of various parameters calculated from the shape of the pulses. A safety analysis has been performed, based on current guidelines for skin exposure to radiation of wavelengths 2.6 µm–20 mm (15 GHz–115 THz), to determine the maximum permissible exposure (MPE) for such a terahertz imaging system. The international guidelines for this range of wavelengths are drawn from two U.S. standards documents. The method for this analysis was taken from the American National Standard for the Safe Use of Lasers (ANSI Z136.1), and to ensure a conservative analysis, parameters were drawn from both this standard and from the IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields (C95.1). The calculated maximum permissible average beam power was 3 mW, indicating that typical terahertz imaging systems are safe according to the current guidelines. Further developments may however result in systems that will exceed the calculated limit. Furthermore, the published MPEs for pulsed exposures are based on measurements at shorter wavelengths and with pulses of longer duration than those used in terahertz pulsed imaging systems, so the results should be treated with caution.

Precision of quasi-optical null-balanced bridge techniques for transmission and reflection coefficient measurements

The precision of quasioptical null-balanced bridge instruments for transmission and reflection coefficient measurements at millimeter and submillimeter wavelengths is analyzed. A Jones matrix analysis is used to describe the amount of power reaching the detector as a function of grid angle orientation, sample transmittance/reflectance and phase delay. An analysis is performed of the errors involved in determining the complex transmission and reflection coefficient after taking into account the quantization error in the grid angle and micrometer readings, the transmission or reflection coefficient of the sample, the noise equivalent power of the detector, the source power and the post-detection bandwidth. For a system fitted with a rotating grid with resolution of 0.017 rad and a micrometer quantization error of 1 μm, a 1 mW source, and a detector with a noise equivalent power 5×10−9 W Hz−1/2, the maximum errors at an amplitude transmission or reflection coefficient of 0.5 are below ±0.025.

On approximate electromagnetic cloaking by transformation media

We give a comprehensive study on regularized approximate electromagnetic cloaking in the spherical geometry via the transformation optics approach. The following aspects are investigated: (i) near-invisibility cloaking of passive media as well as active/radiating sources; (ii) the existence of cloak-busting inclusions without lossy medium lining; (iii) overcoming the cloaking-busts by employing a lossy layer outside the cloaked region; and (iv) the frequency dependence of the cloaking performances. We address these issues and connect the obtained asymptotic results to singular ideal cloaking. Numerical verifications and demonstrations are provided to show the sharpness of our analytical study.

Electromagnetic atmosphere-plasma coupling: the global atmospheric electric circuit

A description is given of the global atmospheric electric circuit operating between the Earth’s surface and the ionosphere. Attention is drawn to the huge range of horizontal and vertical spatial scales, ranging from 10−9 m to 1012 m, concerned with the many important processes at work. A similarly enormous range of time scales is involved from 10−6 s to 109 s, in the physical effects and different phenomena that need to be considered. The current flowing in the global circuit is generated by disturbed weather such as thunderstorms and electrified rain/shower clouds, mostly occurring over the Earth’s land surface. The profile of electrical conductivity up through the atmosphere, determined mainly by galactic cosmic ray ionization, is a crucial parameter of the circuit. Model simulation results on the variation of the ionospheric potential, ∼250 kV positive with respect to the Earth’s potential, following lightning discharges and sprites are summarized. Experimental results comparing global circuit variations with the neutron rate recorded at Climax, Colorado, are then discussed. Within the return (load) part of the circuit in the fair weather regions remote from the generators, charge layers exist on the upper and lower edges of extensive layer clouds; new experimental evidence for these charge layers is also reviewed. Finally, some directions for future research in the subject are suggested.

Mountain waves in two-layer sheared flows: Critical-level effects, wave reflection, and drag enhancement

Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too different from that predicted for an unbounded shear layer, while if it is small the differences are marked, with the drag being enhanced by a considerable factor at low Richardson numbers (Ri). The drag may be further enhanced by nonlinear processes, but its qualitative variation for relatively low Ri is essentially unchanged. However, nonlinear processes seem to interact constructively with shear, so that the drag for a noninfinite but relatively high Ri is considerably larger than the drag without any shear at all.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.