R. A. Méndez-Sánchez

Compressional and torsional wave amplitudes in rods with periodic structures

To measure and detect elastic waves in metallic rods a low-frequency electromagnetic-acoustic transducer has been developed. Frequencies range from a few hertz up to hundreds of kilohertz. With appropriate configuration of the transducer, compressional or torsional waves can be selectively excited or detected. Although the transducer can be used in many different situations, it has been tested and applied to a locally periodic rod, which consists of a finite number of unit cells. The measured wave amplitudes are compared with theoretical ones, obtained with the one-dimensional transfer matrix method, and excellent agreement is obtained.

Anderson localization in finite disordered vibrating rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length, measured using these wave amplitudes, decreases as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. From the spectrum, the nearest-neighbor spacing distribution can be obtained. This distribution can be described by a phenomenological expression that depends on a parameter α, related to the level repulsion, which is also a function of the frequency. Therefore, the localization length can be expressed in terms of the parameter α. There exists a range in which the localization length grows linearly with α. However, at low values of this parameter the linear dependence does not hold.

Topological defects in 1D elastic waves

Abstract It has been recently shown theoretically that a topological defect in a 1D periodic potential may give rise to two localized states within the energy gaps. In this work we present an experimental realization of this effect for the case of torsional waves in elastic rods. We also show numerically that three, or even more, localized states can be present if the parameters characterizing the topological defect are suitably varied.

Electromagnetic prompt response in an elastic wave cavity

A. M. Mart́ınez-Argüello, M. Mart́ınez-Mares, M. Cobián-Suárez, G. Báez, and R. A. Méndez-Sánchez Departamento de F́ısica, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México Distrito Federal, Mexico Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Apartado Postal 21-267, 04000 México Distrito Federal, Mexico Instituto de Ciencias F́ısicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62210 Cuernavaca Mor., MexicoIn a wave resonant scattering process the interference of the continuous scattering amplitude with a discrete resonant state, both of the same undulatory nature, gives rise to a Fano resonance profile. We report experimental evidence of a new kind of Fano resonance, in which the continuous amplitude is of a different nature than that of the resonant wave. The continuous amplitude, of a electromagnetic nature, comes from the measurement process and induces a new type of prompt, or rapid, response of the system which we describe theoretically including this response as a direct process.

A new Fano resonance in measurement processes

A. M. Mart́ınez-Argüello, M. Mart́ınez-Mares, M. Cobián-Suárez, G. Báez, and R. A. Méndez-Sánchez Departamento de F́ısica, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México Distrito Federal, Mexico Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Apartado Postal 21-267, 04000 México Distrito Federal, Mexico Instituto de Ciencias F́ısicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62210 Cuernavaca Mor., MexicoIn a wave resonant scattering process the interference of the continuous scattering amplitude with a discrete resonant state, both of the same undulatory nature, gives rise to a Fano resonance profile. We report experimental evidence of a new kind of Fano resonance, in which the continuous amplitude is of a different nature than that of the resonant wave. The continuous amplitude, of a electromagnetic nature, comes from the measurement process and induces a new type of prompt, or rapid, response of the system which we describe theoretically including this response as a direct process.

Mechanical rainbow trapping and Bloch oscillations in chirped metallic beams

The mechanical rainbow trapping effect and the mechanical Bloch oscillations for torsional waves propagating in chirped mechanical structures are here experimentally demonstrated. After extensive simulations, three quasi-one-dimensional chirped structures were designed, constructed and experimentally characterized by Doppler spectroscopy. When the chirp intensity vanishes, a perfect periodic system, with bands and gaps, is obtained. The mechanical rainbow trapping effect is experimentally characterized for small values of the chirp intensity. The wave packet traveling along the structure is progressively slowing down and is reflected back at a certain depth, which depends on its central frequency. For larger values of the chirping parameter the rainbow trapping yields the penetration length where the mechanical Bloch oscillations emerge. Numerical simulations based on the transfer matrix method show an excellent agreement with experimental data.

Doorway states in elastic one dimensional systems

Whenever a state of a “distinct” and simple nature is immersed in a sea of states of a different, more complicated, structure a strength function phenomenon appears: the amplitude of the distinct state is spread over the complicated eigenstates with a Lorentzian-like shape. The distinct state acts as a doorway state whenever this state is coupled to the continuum and to the sea of complicated states, but the latter are coupled to the continuum only through the distinct state. We present numerical and experimental results for an elastic system which presents a doorway state and the temporal evolution of the phenomenon is measured directly for the first time. The delayed and stationary responses of the system are discussed.

Classical Analogs of a Diatomic Chain

Using one dimensional rods with different configurations classical analogs of quantum mechanical systems frequently used in solid state physics can be obtained. Among this analogs we have recently discussed locally periodic rods which lead to band spectra; the effect of a topological defect, and the Wannier Stark ladders. In this paper, we present an elastic analog of the diatomic chain and show how the acoustical and optical bands emerge, as well of the nature of the wave amplitudes.