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Focuses on a study which investigated the diffraction of focused truncated Gaussian beams at a circular aperture. Irradiance in planes normal to the axis; Irradiance in various planes normal to the axis; Expression for the encircled energy.

In this paper, we study terahertz generation through optical rectification in reflection at normal incidence in a dielectric nonlinear crystal. We first analyze, with a nonlinear optical model, the sample parameters (thickness, absorption at both laser and terahertz wavelengths, etc.) for which a terahertz optical rectification reflection scheme is preferable to the common transmission scheme. Then, we report our experimental observations of a reflected terahertz signal generated at the surface of a ZnTe crystal. The reflected terahertz signal shares all the characteristics of a signal generated in transmission but is not limited by absorption losses in the crystal, thereby providing a broader bandwidth. At high pump laser power, the signal exhibits saturation, which is caused by the decrease of the nonlinear susceptibility due to photocarriers generated by two-photon absorption. This reflection scheme could be of great importance for terahertz microscopy of opaque materials like, e.g., humid samples or samples exhibiting strong absorption bands or to study samples for which the transmitted signal cannot be recorded. [ABSTRACT FROM AUTHOR]

In two-transducer, fluid-coupled ultrasonic reflection measurements phase matched to guided modes of elastic solid structures, the effects of misalignment (i.e., differences) between the receiver angle and the incident beam angle on the receiver voltage have been studied. The received voltage is typically due to contributions from the specular reflection and any of the several possible guided wave modes excited by the incident wave field. It is found that misalignment leads to changes in the relative amplitudes of the various contributions. Further, the more highly collimated the beam (or the contributor), the more pronounced are the effects. It is shown that the signal maximum is not a reliable indicator of receiver alignment. These conclusions are based on measurements and on calculations that have been performed at incident angles selected both close to, or far from, phase-matching angles to guided wave modes on plates, curved surfaces, and cylindrical shells. Receiver voltage coordinate scans have been performed with receiver angles misaligned from the incident beam axis by 1 to 4 degrees. The receiver voltage versus scan parameter in planar and curved structures is calculated by employing complex transducer points to synthesize two-dimensional, sheet-beam transducer fields with Gaussian apertures, spectral analysis to formulate the beam-structure interaction problem, and asymptotic methods to evaluate the resulting spectral integrals. The model predictions are generally in good agreement with the experiments. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the dynamics and formation mechanisms of bound states (BSs) of light bullets in the output of a laser coupled to a distant saturable absorber. First, we approximate the full three-dimensional set of Haus master equations by a reduced equation governing the dynamics of the transverse profile. This effective theory allows us to perform a detailed multiparameter bifurcation study and to identify the different mechanisms of instability of BSs. In addition, our analysis reveals a non-intuitive dependence of the stability region as a function of the linewidth enhancement factors and the field diffusion. Our results are confirmed by direct numerical simulations of the full system. [ABSTRACT FROM AUTHOR]

We demonstrate how terahertz time-domain spectroscopy (THz-TDS) operating in reflection geometry can be used for quantitative conductivity mapping of large area chemical vapor deposited graphene films through silicon support. We validate the technique against measurements performed using the established transmission based THz-TDS. Our through-substrate approach allows unhindered access to the graphene top surface and thus, as we discuss, opens up pathways to perform in situ and in-operando THz-TDS using environmental cells. [ABSTRACT FROM AUTHOR]

Speech intelligibility depends on the integrity of spectrotemporal patterns in the signal. The current study is concerned with the speech modulation power spectrum (MPS), which is a two-dimensional representation of energy at different combinations of temporal and spectral (i.e., spectrotemporal) modulation rates. A psychophysical procedure was developed to identify the regions of the MPS that contribute to successful reception of auditory sentences. The procedure, based on the two-dimensional image classification technique known as "bubbles" (Gosselin and Schyns (2001). Vision Res. 41, 2261-2271), involves filtering (i.e., degrading) the speech signal by removing parts of the MPS at random, and relating filter patterns to observer performance (keywords identified) over a number of trials. The result is a classification image (CImg) or "perceptual map" that emphasizes regions of the MPS essential for speech intelligibility. This procedure was tested using normal-rate and 2×-time-compressed sentences. The results indicated: (a) CImgs could be reliably estimated in individual listeners in relatively few trials, (b) CImgs tracked changes in spectrotemporal modulation energy induced by time compression, though not completely, indicating that "perceptual maps" deviated from physical stimulus energy, and (c) the bubbles method captured variance in intelligibility not reflected in a common modulation-based intelligibility metric (spectrotemporal modulation index or STMI). [ABSTRACT FROM AUTHOR]

A model that characterizes the effects of beams and waveforms on the measurement of ultrasonic scattering is described and analyzed. The model includes arbitrary emitter beam patterns and detector apertures as angular spectra of plane waves. Arbitrary emitted pulses and detector time gates are incorporated through frequency spectra of temporal harmonics. A transformation of variables is employed to express the spectrum of the measured pressure as a product in wave space of a system function and the Fourier transform of the medium variations. The analysis shows the influence of beam patterns and a finite detector gate, relates the current model to a prior narrowband analysis, provides asymptotic expressions for beam pattern effects produced by radially symmetric Gaussian apertures, and treats the backscattering configuration for arbitrary apertures and correlated scattering. Numerical computations illustrate the effect of Gaussian, exponential, and uniform circularly symmetric spatial aperture functions on the measurement of the power spectrum of medium variations. The results may be used to design scattering experiments in which measurements yield scaled values of intrinsic parameters of scattering. [ABSTRACT FROM AUTHOR]

The close connection between image formation in geometrical optics and beam transformation by a paraxial optical system is examined analytically using mathematical tools accessible to undergraduate students, such as the Fresnel diffraction integral and Fourier transforms, instead of the more complicated Wigner distribution or coherence functions frequently employed in the literature. It is shown that geometrical optics correctly predicts the plane where a beam is refocused and its magnification only for afocal optical systems or in the limit of point sources. We illustrate this theory by simulating the transformation of a flat-top beam by a pair of lenses. [ABSTRACT FROM AUTHOR]

Complex source pulsed beams (CSPB) are exact wave-packet solutions of the time-dependent wave equation that are modeled mathematically in terms of radiation from a pulsed point source located at a complex space-time coordinate. In the present paper, the physical source realization of the CSPB is explored. This is done in the framework of the acoustic field, as a concrete physical example, but a similar analysis can be applied for electromagnetic CSPB. The physical realization of the CSPB is addressed by deriving exact expressions for the acoustic source distribution in the real coordinate space that generates the CSPB, and by exploring the power and energy flux near these sources. The exact source distribution is of finite support. Special emphasis is placed on deriving simplified source functions and parametrization for the special case where the CSPB are well collimated. © 2000 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A procedure for the measurement of intrinsic scattering object properties is presented and used to obtain illustrative results. The procedure is based on the measurement of the scattered acoustic field as a function of scattering angle and frequency. Measurements are normalized using analytically determined expressions for emitter and detector beams resulting from a combination of unfocused linear elements arranged in a circular configuration. The spatial effects of finite emitter pulse length and detector gate length are represented by a convolution formula valid for narrow-band transmitted signals and long receiver gates. The normalization includes correction for target absorption as well as measurement of the directly transmitted acoustic power in the free field and yields the average differential scattering cross section per unit volume. Under the Born approximation, this quantity is directly proportional to the spatial-frequency spectrum of the scattering medium inhomogeneities. Measured results are reported for two phantoms consisting of glass microspheres embedded in a weakly absorbing agar background medium. For the phantoms employed, scattering effects, rather than increased absorption, are shown to account for most of the difference in transmission loss between pure agar and agar with glass spheres. The measured differential scattering cross sections are compared with theoretical cross sections for distributions of glass spheres measured experimentally. The measured values show good relative agreement with theory for varying angle, frequency, and phantom properties. The results are interpreted in terms of wave space resolution and the potential for tissue characterization using similar fixed transducer configurations. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The feasibility of exciting a localized X-wave pulse from a finite aperture is addressed. Also, the possibility of using a finite-time excitation of a dynamic aperture to generate a finite-energy approximation to an X-wave pulse is explored. The analysis is carried out by using a Gaussian time window to time limit the infinite X-wave initial excitation. Huygens' construction is used to calculate the amplitude of the radiated wave field away from the finite-time source. The decay rate of the peak of the X wave is compared to that of a quasi-monochromatic signal. It is shown that the finite-time X-wave propagates to much farther distances without significant decay. Furthermore, the decay pattern of the radiated X-wave pulse is derived for a source consisting of an array of concentric annular sections. The decay behavior of the radiated pulse is similar to that of an X-wave launched from a finite-time aperture. This confirms the fact that time windowing the infinite energy X-wave excitation is a viable scheme for constructing finite apertures. A discussion of the diffraction limit of the X-wave pulse is also provided. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Acoustic transient Bessel beams (TBB) are a new class of waves which maintain their peak amplitude and general shape as they propagate in free space from an infinite planar aperture. The on axis and far field space-time properties of acoustic TBB waves generated by a finite spatial aperture are investigated using impulse response methods. The on-axis transition from the near field to the far field is investigated and several analogies to the acoustic field generated from a circular piston source are observed. In particular, the importance of an edge generated wave in determining the transition for the TBB field is clearly noted. Space-time properties of the far field are also investigated as a function of polar angle using impulse response methods. Numerical results are presented to illustrate the general characteristics of the on-axis and far field impulse response for a finite aperture. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The spatial-frequency spectra of the spatial properties of a scattering medium can be determined from measurements of scattering over a number of angles or frequencies. In such measurements, the spatial localization associated with transducer beam patterns and time gates causes an uncertainty in the measured spatial-frequency domain properties of the scatterer. This uncertainty is analyzed using an analytic and computational model in which system effects are represented by a spatial-frequency domain function. Wave space resolution in a particular direction is shown to be inversely proportional to the spatial-frequency spread of the system function in that direction. In the backscatter case, wave space resolution is limited in the direction of the scattering vector by a convolution of the emitted pulse and the detector time gate, and resolution in the lateral direction depends mainly on the transducer aperture, increasing approximately in proportion to the aperture diameter. In the case of backscatter measurements, smooth aperture apodization improves lateral resolution somewhat but has little effect on resolution in the direction of the scattering vector. For angular scattering measurements, resolution in all directions depends on both the aperture size and (for sufficiently short time gates) on the time gates employed. Illustration of the practical importance of wave space resolution is provided using analysis of two previously published tissue characterization experiments. © 1995 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A model that characterizes the effects of beams and waveforms on the measurement of ultrasonic scattering is analyzed in detail. The analysis obtains a wideband expression for the system function in terms of an integration over spatial- and temporal-frequency variables. The temporal-frequency integration is reduced to a convolution in the direction of the scattering vector when the temporal frequencies are concentrated in a narrow band around a central frequency. The spatial-frequency integration is simplified to a straight line path when the spatial frequencies in the angular spectra of the emitter are concentrated around a point on the axis of the emitter and the spatial frequencies of the detector sensitivity pattern are similarly concentrated around a point on the axis of the detector. Expressions that result from the temporal and spatial approximations are evaluated analytically for circularly symmetric Gaussian spatial apertures and Gaussian temporal waveforms. In addition, numerical results are obtained to compare the effects of circularly symmetric Gaussian, exponential, and uniform spatial aperture functions on the weight that beam patterns have on measurements of scattering. The results may be used to design experiments from which intrinsic parameters of scattering media can be obtained by an appropriate normalization to remove measurement system effects from the data. [ABSTRACT FROM AUTHOR]

A general model is developed to characterize the effect of an ultrasonic measurement system on the experimental determination of ultrasonic scattering as a function of angle and frequency. The model includes arbitrary emitter beams and detector apertures as angular spectra of plane waves. Arbitrary emitted pulses and detector time gates are incorporated through frequency spectra of temporal harmonics. A transformation of variables is employed to express the spectrum of the measured pressure as a product in wave space of a system function and the Fourier transform of the medium variations. The mean-square value of the measured pressure spectrum is similarly expressed as a product of the squared magnitude of the system function and the power spectrum of the medium variations. The measured quantities are shown to become scaled values of intrinsic scattering characteristics when the system function weight is concentrated relative to the medium characteristics in wave space. The assumption of an indefinitely long detector gate is used to represent the system function as a product in which one factor is a beam function dependent on spatial frequency and the other factors are dependent on temporal frequency. Beam-function calculations as well as calculations of second moments and overall beam weight are made for identical Gaussian-shaped emitter and detector apertures to illustrate the blurring and weighting effects of measurement system beam patterns as a function of scattering angle. The moment calculations are shown to identify circumstances when the medium variation function can be factored out from under the integral and the measurement represented as a simple product of the medium properties and a measurement system weight. The results may be used to design scattering experiments in which degradations due to system effects are within acceptable limits. [ABSTRACT FROM AUTHOR]

An electrical waveform generator based on an aperture-coupled stripline is described. The device is a four-port electrical directional coupler consisting of two striplines coupled through an aperture in their common ground plane. Replacing the aperture layer of the device can produce arbitrarily shaped electrical waveforms with 100 ps structure over a pulse envelope of several nanoseconds. A numerical solution of the telegraph equations using the method of characteristics is used to model and design devices. Excellent agreement is obtained between the model and device performance. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]