Non-reciprocal behavior of one-dimensional piezoelectric structures with space-time modulated electrical boundary conditions

Abstract

Propagation of longitudinal acoustic waves in a one-dimensional piezoelectric structure with space-time modulated electrical boundary conditions is investigated. An analytical model allowing the calculation of eigenmodes for spatially continuous shifts of electrical boundary conditions is compared with finite difference time domain (FDTD) simulation results for a discrete set of time-varying spatially fixed conditions. Both models predict that such a structure behaves as a non-reciprocal device exhibiting unidirectional propagation properties in some frequency ranges. The modulus and direction of the modulation speed vector strongly affect this non-reciprocal behavior. Moreover other nonlinear phenomena such as frequency up and down conversions, wave packet distortion and parasitic echoes occurring in such systems are investigated in detail. Importance of these phenomena is discussed in the context of nonlinear acoustic wave-based components for radio-communication systems.

Strong spatial dispersion in time-modulated dielectric media

“…Metamaterials have recently evolved toward more complex structures, and the possibility of design of new materials based on the temporal modulation of the constitutive parameters has also been explored. Then it can be shown that, when a given medium presents time-modulated constitutive parameters, some effects like nonreciprocity, gain, and tunability can be easily achieved [12][13][14][15][16][17][18].…”

Strong Spatial Dispersion in Time-Modulated Dielectric Media

“…Then, it can be shown that, when a given medium presents time-modulated constitutive parameters, some effects like non-reciprocity, gain and tunability can be easily achieved. [12][13][14][15][16][17][18] The concept of effective medium for a time-modulated material is similar to that of a spatially-modulated, 19,20 in the sense that, when the modulation frequency (spatial or temporal) is fast and the operating wavelength and frequency cannot detect that modulation, we detect an effective medium with some averaged constitutive parameters. When the parameters are spatially modulated, we obtain an effective medium which a strong temporal dispersion (frequency-dependence) but a weak spatial dispersion (wavenumber-dependence).…”

An Archimedes' Screw for Light

“…In non-periodic systems, abrupt switching holds the key to new directions such as time-reversal [13], time-refraction Furthermore, drawing from the combination of spatial and temporal degrees of freedom, space-time metamaterials, whose parameters are modulated in a travelling wavetype fashion [21][22][23][24][25], have recently acquired renewed momentum both for fundamental reasons, as they enable the mimicking and generalization of physical motion beyond the common relativistic constraints, leading to optical drag [26], localization [27] and novel amplification mechanisms [28,29], and for practical applications such as harmonic generation [30], beam steering [31] and power combination from multiple sources [32]. Successful experiments with spatiotemporal modulation include works in acoustics [5,7,33] and elasticity [34], microwaves [3,30], in the infrared [35] and even in diffusive systems [36], and they have recently started pushing closer to the optical domain [37] thanks to the introduction of novel highly nonlinear materials such as ITO [38] and AZO [39]. Finally, homogenization schemes have recently been developed for both temporal [40,41] and spatiotemporal [42] metamaterials.…”