Backward waves with double zero-group-velocity points in a liquid-filled pipe

Abstract

Hollow cylinders often exhibit backward propagation modes whose group and phase velocities have opposite directions, and these exhibit a minimum possible frequency at which the group velocity vanishes at a nonzero wavenumber. These zero-group-velocity (ZGV) points are associated with resonant conditions in the medium. On the basis of ZGV resonances, a non-contact and laser ultrasound technique has been developed to measure elastic constants of hollow pipes. This paper provides a theoretical and numerical investigation of the influence of the contained liquid on backward waves and associated ZGV modes, in order to explore whether this ZGV technique is suitable for in-service non-destructive evaluations of liquid-filled pipes. Dispersion spectra and excitation properties have been analyzed. It is found that the presence of the liquid causes an increased number of backward modes and ZGVs which are highly excitable by a point source. In addition, several guided modes twice undergo a change of sign in the slopes of their dispersion curves, leading to two ZGV points. This phenomenon of double ZGVs in one backward wave, which is caused by strong mode repulsions, has not been found in isotropic hollow cylinders, but it can be observed in a fluid-filled thin-walled pipe.

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

“…We refer to the detailed review of literature provided by Cui et al (2016) in their introduction. They describe studies of elastic waves in bodies of different geometry (plates, rods, etc), both theoretical investigations as well as experimental confirmation.…”

Pulse propagation in the slow and stopped light regime

“…In this case, one would be able to derive coupled mode analysis in the slow and stopped light regime, so far treated only with the full Maxwell equations via FDTD algorithms [6, 11-13, 37, 38, 57-59]. Finally, our results could also be used in many additional contexts such as acoustic waves [43][44][45], spin waves [46], water waves [47], quantum/matter waves [48,49] etc..…”

“…For a Drude metal, when taking into account Eq. (45) and ignoring the details of the waveguide width, we can estimate, R n ∼ 1 ω 0 . For a dispersive dielectric, R n will be smaller, hence, the following analysis can be regarded as an estimate for an upper limit.…”

“…As a result, various potential applications emerged, including in particular optical memory in optical communication systems [6,[11][12][13], nonlinear optics [7,[14][15][16][17][18][19][20][21], Brillouin scattering [22,23], and more recently, quantum computing [10,[24][25][26][27][28][29], e.g., based on electromagnetic induced transparency [2,3,8,9,[30][31][32]; Additional potential applications are tissue imaging [33], sensing [34], low threshold lasing [35][36][37][38][39], photochemistry [40,41] and even tabletop cosmology [42]. Slow and stopped light regimes occur also in other wave systems like acoustic waves [43][44][45], spin waves [46], water waves [47], quantum/matter waves [48,49] etc.. Slow light has been demonstrated in various platforms, including atom...…”