Loss compensation in time-dependent elastic metamaterials

Abstract

Materials with properties that are modulated in time are known to display wave phenomena showing energy increasing with time, with the rate mediated by the modulation. Until now there has been no accounting for material dissipation, which clearly counteracts energy growth. This paper provides an exact expression for the amplitude of elastic or acoustic waves propagating in lossy materials with properties that are periodically modulated in time. It is found that these materials can support a special propagation regime in which waves travel at constant amplitude, with temporal modulation compensating for the normal energy dissipation. We derive a general condition under which amplification due to time-dependent properties offsets the material dissipation. This identity relates band-gap properties associated with the temporal modulation and the average of the viscosity coefficient, thereby providing a simple recipe for the design of loss-compensated mechanical metamaterials.

Strong spatial dispersion in time-modulated dielectric media

“…What we see is a spatially homogeneous material with some dielectric constant ε b and, at t = t 0 , a periodic modulation is applied until t = t f . This situation is similar to that analyzed for acoustic waves in [14,28]. We can assume that we are far away from the band gap, where the material would be unstable, and that the conditions for the application of the effective medium condition hold.…”

“…We can see how, for t < t 0 , a wave is propagating through the material with some frequency ω b and wavenumber k b . Once the modulation begins, we excite a "transmitted" and "reflected" wave, but the wavenumber of these waves continues being k b , and it is the frequency that the quantity has changed [14,19]. To obtain the new frequency in the effective material we need to solve the dispersion relation…”

“…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].…”

Dynamic Nonreciprocity in Loss-Compensated Piezophononic Media

“…To realize pronounced insulation, high flow rates are required, which inevitably leads to turbulence and shock-wave generation [2,4,5]. Another strategy relies on tailoring space-time modulation of the involved material to generate nonreciprocity [6][7][8][9][10][11]. Carefully designed nonlinear macroscopic structures have been realized to exhibit nonreciprocity without breaking time-reversal symmetry.…”

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

“…It may be used to create topologically nontrivial properties for photons 12 . D. Torrent et al 13 have proven that in a dissipative material with time dependent mechanical characteristics, dissipation can be compensated by the amplification of the fields due to the time-dependent properties. Periodicity of the propagation medium may also depend on both time and spatial coordinates 14 .…”