Acoustic X-wave reflection and transmission at a planar interface: Spectral analysis

Abstract

The spectral structure of a three-dimensional X-wave pulse incident on a planar surface of discontinuity is examined. Introducing a novel superposition of azimuthally dependent pulsed plane waves, it is shown for oblique incidence that the reflected pulse has a localized wave structure. On the other hand, the transmitted field maintains its localization up to a certain distance from the interface, beyond which it starts disintegrating. An estimate of the localization range of the transmitted pulse is established; also, the parameters affecting the localization range are identified. The reflected and transmitted fields are deduced for X-waves incident from either a slower medium or a faster one. For the former case the evanescent fields in the second medium are calculated and their explicit time dependence is deduced for a normally incident X-wave. Furthermore, at near-critical incidence the transmitted pulse exhibits significant pulse compression and focusing.

Reflection and Transmission of an Electromagnetic X-Wave Incident on a Planar Air-Dielectric Interface: Spectral Analysis

“…In the third paper, the authors investigated the case of a three-dimensional acoustical X-wave. They demonstrated that the transmitted field loses its LW structure; however, it stays localized for a certain distance before it starts disintegrating [16]. Furthermore, they were able to deduce an expression for the dispersion-free range and confirm numerically that such an estimate is consistent with the decay pattern of the transmitted field.…”

“…17] must be rotated by an angle equal to the angle of incidence. Following a procedure introduced for acoustical X-waves incident on a discontinuity surface [16], we transform the Fourier spectral superposition of the electromagnetic X-wave into an azimuthally dependent angular representation [cf. Eq.…”

“…17]. Such an azimuthal angular superposition has proved to be very effective in calculating the amplitudes of the reflected and transmitted acoustical fields [16].…”

“…A scalar-valued version of the azimuthal angular superposition given in Eq. (6) has been used previously to determine the properties of the reflected and transmitted fields due to an acoustic X-wave incident on a surface of discontinuity separating two media [16].…”

“…It is, therefore, important to study the details of a canonical problem involving the reflection and transmission of a localized wave obliquely incident on a planar interface separating two electrically different materials. This problem has been investigated previously in three different papers [14][15][16]. In the first two studies, the authors used a two-dimensional variation of Brittingham's FWM solution.…”