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Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear response laws and causality in the time and frequency domains with the aim of pedagogical clarity. We will show that it is easy to violate causality in the frequency domain by making a vanishing absorption approximation. Furthermore, we will show that there can be subtle differences between Fourier transforming Maxwell equations and using a monochromatic source function. We discuss how these concepts can be obscured and offer some suggestions to improve the situation. (Contains 1 table and 1 figures and 4 footnotes.)

Some experiments are conveniently performed in the time domain, some in the frequency domain, and some use a hybrid approach. Does the domain make any difference in the ultimate resolution of the experiment? Or can the details of the experiment always be tweaked so that the different approaches give the same answer? We consider a simple optics experiment and consider both time and frequency measurements and take into account the influence of noise, finite dynamic range, attenuation, and the duration of the measurement. (c) 2005 American Association of Physics Teachers. [DOI: 10.1119/1.1891172]

Non-contacting acoustical methods can be used to extract various material properties of liquid or solid samples without disturbing the sample. These methods are useful even in the lab since they do not involve coupling anything to the sample, which might change its properties. A forteriori, when dealing with potentially dangerous materials, non-contacting methods may be the only safe solutions to mechanical characterization. Here, we show examples of using laser ultrasound to remotely insonify and monitor the elastic properties of several granular explosive simulants. The relatively short near-infrared laser pulse length (a few hundred nanoseconds) provides a broad-band thermoelastic source of ultrasound; we intentionally stay in the thermoelastic regime to avoid damaging the material. Then, we use a scanning laser Doppler vibrometer to measure the ultrasonic response of the sample. LDV technology is well established and very sensitive at ultrasonic frequencies; atomic level motions can be measured with modest averaging. The resulting impulse response of the explosive simulant can be analyzed to determine decay rates and wave speeds, with stiffer samples showing faster wave speeds and lower decay rates. On the other hand, at the low-frequency end of the acoustic spectrum, we use an electronically phased array to couple into a freely suspended sample's normal modes. This allows us to gently heat up the sample (3 °C in just under 5 min, as shown with a thermal IR camera). In addition to the practical interest in making the sample more chemically visible through heat, these two measurements (low-frequency resonant excitation vs high-frequency wave propagation) bracket the frequency range of acoustic non-destructive evaluation methods available. [ABSTRACT FROM AUTHOR]

We have designed and built an ultrasonic parametric array with an emphasis on creating an intense, collimated beam of low frequency sound. With this device, we can insonify a small area of ground or a small target at range and induce vibrations. These vibrations can be synchronously detected with any stand-off device such as a laser-Doppler vibrometer or the millimeter wave vibrometer we describe in Smith et al. [J. Appl. Physics 108, 024902 (2010)]. Despite nonlinear conversion losses, the array produces sound pressure levels in excess of 90 dB at 1 kHz, 1.5 m in front of the array using 25 low-cost 40 KHz transducers. [ABSTRACT FROM AUTHOR]

Remote sensing of ground vibration is a key tool in the detection of shallowly buried objects, such as land mines. Millimeter wave systems show promise for replacing laser Doppler vibrometers as the key sensing technology on the grounds of reduced cost and because they provide a larger (10 cm versus 1 mm), more robust sensor footprint. We have developed a double-conversion interferometer operating at 39 GHz that can be built for about $10 000. The system employs quadrature detection in order to provide reliable sensitivity over wavelength-sized changes in target range. Laboratory tests show that it can estimate sinusoidal ground motion from a 1 s time series with an uncertainty of about 5 μm. [ABSTRACT FROM AUTHOR]

We demonstrate 260 GHz (λ=1.15 mm) near field imaging using a conical Teflon probe whose tip protrudes through an aperture in a tapered aluminum holder. The imaging system is based on a quasioptical millimeter wave vector network analyzer. We present a variety of different imaging examples of dielectrics and metals, in both reflection and transmission modes, as well as an analysis of interesting diffraction and scattering effects observed in some of the images. The probe has an approximate tip diameter of 0.17 mm and an aperture size of about 1 mm. We observe horizontal resolution ranging from 0.2–0.5 mm depending on the sample being imaged. [ABSTRACT FROM AUTHOR]

The presence and nature of fractures can have a profound impact on the elastic and mechanical properties of materials. Whether it is a fracture-induced loss of strength or the creation of a long-wavelength anisotropy, being able to infer the presence and properties of fractures in a material has many applications. Detecting changes in the spectra of mechanical resonances due to the presence of fractures is not difficult. A more interesting issue is which elastic moduli are sensitive to the presence of these fractures and how are these moduli related to the stiffness of the material? Resonant ultrasound spectroscopy was performed on acrylic cylinders with internal cracks. Inversions were performed for both isotropic and anisotropic moduli. Good agreement was obtained between isotropic moduli and projected (optimal isotropic moduli obtained from anisotropic moduli) for nonverlapping cracks. The same projections yielded poorer agreement for the sample with overlapping cracks. The results also show that the degree of anisotropy depends upon the amount of crack overlap, and that the isotropic shear modulus is a reliable measure of decreasing stiffness. [ABSTRACT FROM AUTHOR]

It is difficult to find a definition for a wave. There is a fine line between non-wave-like and wave-like behavior. Waves are chemical, biological and physical phenomena and the core of matter and time. Bearing in mind various examples of waves, the best definition of wave is an organized propagating imbalance.

Quasi-optical (QO) methods of dielectric spectroscopy are well established in the millimeter and submillimeter frequency bands. These methods exploit standing wave structure in the sample produced by a transmitted Gaussian beam to achieve accurate, low-noise measurement of the complex permittivity of the sample [e.g., J. A. Scales and M. Batzle, Appl. Phys. Lett. 88, 062906 (2006); R. N. Clarke and C. B. Rosenberg, J. Phys. E 15, 9 (1982); T. M. Hirovnen, P. Vainikainen, A. Lozowski, and A. V. Raisanen, IEEE Trans. Instrum. Meas. 45, 780 (1996)]. In effect the sample itself becomes a low-Q cavity. On the other hand, for optically thin samples (films of thickness much less than a wavelength) or extremely low loss samples (loss tangents below 10-5) the QO approach tends to break down due to loss of signal. In such a case it is useful to put the sample in a high-Q cavity and measure the perturbation of the cavity modes. Provided that the average mode frequency divided by the shift in mode frequency is less than the Q (quality factor) of the mode, then the perturbation should be resolvable. Cavity perturbation techniques are not new, but there are technological difficulties in working in the millimeter/submillimeter wave region. In this paper we will show applications of cavity perturbation to the dielectric characterization of semi-conductor thin films of the type used in the manufacture of photovoltaics in the 100 and 350 GHz range. We measured the complex optical constants of hot-wire chemical deposition grown 1-μm thick amorphous silicon (a-Si:H) film on borosilicate glass substrate. The real part of the refractive index and dielectric constant of the glass-substrate varies from frequency-independent to linearly frequency-dependent. We also see power-law behavior of the frequency-dependent optical conductivity from 316 GHz (9.48 cm-1) down to 104 GHz (3.12 cm-1). [ABSTRACT FROM AUTHOR]

Phased source arrays are physically-distributed arrays of radiators (source transducers) driven by time-delayed copies of a common signal. The time delays are chosen so that the net antenna pattern of the array is focused on either a particular target or lies in a particular direction. A simple example is an array of broadcast antennae with an individual element's time delay determined by the length of its feed cable. By switching among sets of feed cables the composite antenna may be made to have major lobes in different directions, in terms of both elevation and azimuth, as needed to meet the varying requirements of daytime and nighttime operation. These arrays have either fixed delays or a few, selectable sets of fixed delays. Phased receiver arrays are based on exactly the same principles as their source counterparts-a correspondence that is spelled out in a little more detail in the implementation section of this article. In all other respects, the term phased array will mean phased source array. We are interested here in electronically-steerable phased arrays, that is, phased arrays with electronically-controlled time delays. These systems are capable of rapid shifts over many antenna patterns which make it practical to quickly scan the major lobe of the outgoing signal over a range of azimuths and elevations. One application of this technology is military target-tracking radar systems, which may have to (nearly) simultaneously track many potential threats much more rapidly than would be feasible with a physically steered antenna. Perhaps the most active area of the application of phased-array technology is in bio-medical devices which image the body with ultrasound. This field is driven by the needs of medical diagnosis and treatment; it is fortunate that the human body represents a relatively homogeneous environment of acoustic speeds which rewards the development of sophisticated imaging methods. [ABSTRACT FROM AUTHOR]

Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear response laws and causality in the time and frequency domains with the aim of pedagogical clarity. We will show that it is easy to violate causality in the frequency domain by making a vanishing absorption approximation. Furthermore, we will show that there can be subtle differences between Fourier transformingMaxwell equations and using a monochromatic source function. We discuss how these concepts can be obscured and offer some suggestions to improve the situation. [ABSTRACT FROM AUTHOR]

The electrical conductivity of a CdS thin film controlled by grain structures is essential to enhance its photoconductivity to be able to be fit as a window material in CdS/CdTe heterojunction solar cells. In order to characterize a thin film, electromagnetically, we employed an open cavity resonator with a sub-millimeter Vector Network Analyzer. Our technique is capable of measuring complex dielectric permittivity, ε~, of a photovoltaic film as thin as 0.1 μm. We measured the real part of the complex dielectric permittivity, εre, and electrical conductivity, σre (derived from the imaginary part, εim), of unannealed and annealed CdS films with thicknesses ∼0.15 μm on ∼3 mm thick-borosilicate glass substrates, at room temperature. We obtain the (thermally activated) electrical conductivity between 100 and 312GHz, which is less in annealed samples than in unannealed ones by ∼2 orders of magnitude. Contrary to our expectations, the carrier concentrations extracted from these data by fitting a Drude model are ∼1016 cm-3 (unannealed) and ∼1014 cm-3 (annealed). We investigate the connection between the grain size and carrier concentration. [ABSTRACT FROM AUTHOR]

Exploiting the fine structure of strongly scattered waves could provide a wealth of new information in seismology, ultrasonics, acoustics, and other fields that study wave propagation in heterogeneous media. Therefore, noncontacting laser-based measurements of ultrasonic surface waves propagating in a strongly disordered medium are performed in which the ratio of the dominant surface wavelength to the size of a scatterer is large, and waves that propagate through many scatterers are recorded. This allows analysis of scattering-induced dispersion and attenuation, as well as the transition from ballistic to diffusive propagation. Despite the relatively small size of the scatterers, multiple scattering strikingly amplifies small perturbations, making changes even in a single scatterer visible in the later-arriving waveforms. To understand the complexity of the measured waveforms, elastic spectral-element numerical simulations are performed. The multiple-scattering sensitivity requires precise gridding of the actual model, but once this has been accomplished, we obtain good agreement between the measured and simulated waveforms. In fact, the simulations are invaluable in analyzing subtle effects in the data such as weak precursory body-wave diffractions. The flexibility of the spectral-element method in handling media with sharp boundaries makes it a powerful tool to study surface-wave propagation in the multiple-scattering regime. [ABSTRACT FROM AUTHOR]

Resonant Ultrasound Spectroscopy (RUS) uses normal modes of elastic bodies to infer material properties such as elastic moduli and Q. In principle, the complete elastic tensor can be inferred from a single measurement. For centimeter-sized samples RUS fills an experimental gap between low-frequency stress-strain methods (quasi-static up to a few kHz) and ultrasonic time-delay methods (hundreds of kHz to GHz). We use synchronous detection methods to measure the resonance spectra of homogeneous rock samples. These spectra are then fit interactively with a model to extract the normal-mode frequencies and Q factors. Inversion is performed by fitting the normal-mode frequencies. We have successfully applied this technique to a variety of isotropic and anisotropic samples, both man-made and natural. In this paper we will show in detail the procedure applied to a cylindrical core of Elberton granite. By means of a statistical fit of the measured normal modes and an independent laser ultrasonic measurement, the granite core was inferred to have orthorhombic symmetry. A 10 per cent P-wave anisotropy was measured in the plane perpendicular to the core axis. [ABSTRACT FROM AUTHOR]

Examines the data and model uncertainty estimation for linear inversion. Model-based estimates of the noise characteristics from a single realization data; Use of noise estimates to characterize the set of reasonable models; Examples of vertical seismic profiling and cross-well tomography.

Examines the development of the Bayesian approach on inferences about finite-dimensional subsets of earth models. Computation of posterior marginal distributions; Derivation of the modified Bayesian formulation; Calculation of probability intervals from the marginal posterior distributions.

Presents several letters related to medicine in Great Britain. Risks of total hip replacement; Medical implications of prostaglandins and asthma; Application of the declaration of the President of the General Dental Council on operator and anesthetists.

At the meso and macro-scale, the connection between the elastic and the electromagnetic properties of granular materials such as rocks is complicated and involves, among other things, the chemical, mineralogical, and geometric features of the grains and their host medium. In the previous work, we showed how to perform rapid near-field millimeter wave scanning to obtain high-spatial resolution maps of the spatially varying dielectric permittivity of heterogeneous materials, including rocks. Here, we extend this concept to laser ultrasound and map the spatially varying mechanical properties of materials with similar resolution. [ABSTRACT FROM AUTHOR]

In analogy with optical near-field scanning methods we use tapered dielectric waveguides as probes for a millimeter wave vector network analyzer. By scanning thin samples between two such probes we are able to map the spatially varying dielectric properties of materials with subwavelength resolution. Using a 150 GHz probe in transmission mode we see spatial resolution of better than 500 μm. Here, we apply the technique to rocks map the mineralogy at the submillimeter scale. [ABSTRACT FROM AUTHOR]