Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems

In this work, we investigate non-Hermitian elastic waveguides with periodically applied proportional feedback efforts, implemented through piezoelectric sensors and actuators. Using onedimensional spectral models for longitudinal motion, it is shown that dispersion diagrams of this family of structures exhibit non-reciprocal imaginary frequency components, manifesting as wave attenuation or amplification along opposite directions for all pass bands. The effects of positive an...

Breaking reciprocity has recently gained significant attention due to its broad range of applications in engineering systems. Here, we introduce the first experimental demonstration of a broadband mechanical beam waveguide, which can be reconfigured to represent wave nonreciprocity. This is achieved by using spatiotemporal stiffness modulation with piezoelectric patches in a closed-loop controller. Using a combination of analytical methods, numerical simulations, and experime...

We investigate non-Hermitian elastic lattices characterized by non-local feedback control interactions. In one-dimensional lattices, we show that the proportional control interactions produce complex dispersion relations characterized by gain and loss in opposite propagation directions. Depending on the non-local nature of the control interactions, the resulting non-reciprocity occurs in multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersio...

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical si...

In recent years, unconventional metamaterial properties have triggered a revolution of electromagnetic research which has unveiled novel scenarios of wave-matter interaction. A very small dielectric permittivity is a leading example of such unusual features, since it produces an exotic static-like regime where the electromagnetic field is spatially slowly-varying over a physically large region. The so-called epsilon-near-zero metamaterials thus offer an ideal platform where t...

Parametric amplification -- injecting energy into waves via periodic modulation of system parameters -- is typically restricted to specific multiples of the modulation frequency. However, broadband parametric amplification can be achieved in active metamaterials which allow local parameters to be modulated both in space and in time. Inspired by the concept of luminal metamaterials in optics, we describe a mechanism for one-way amplification of sound waves across an entire fre...

This note analytically investigates non-reciprocal wave dispersion in locally resonant acoustic metamaterials. Dispersion relations associated with space-time varying modulations of inertial and stiffness parameters of the base material and the resonant components are derived. It is shown that the resultant dispersion bias onsets intriguing features culminating in a break-up of both acoustic and optic propagation modes and one-way local resonance band gaps. The derived band s...

We put forward a strategy to achieve synthetic nonlinearities where local and nonlocal contributions compete on similar footing, thus yielding intermediate tunable responses ranging from fully local to strongly nonlocal. The physical setting addressed is a semiconductor material with both Kerr and thermal nonlinearities illuminated by a pulse train with suitable single-pulse width and repetition rate. We illustrate the potential of the scheme by showing that it supports solit...

In this paper, we theoretically, numerically and experimentally demonstrate the acoustic isolator effect in a 1D waveguide with direction dependent controlled boundary conditions. A theoretical model is used to explain the principle of non reciprocal propagation in boundary controlled waveguides. Numerical simulations are carried out on a reduced model to show the non-reciprocity as well as the passivity of the system, through the computation of the scattering matrix and the ...

The nonreciprocal propagation of light typically requires use of materials like ferrites or magneto-optical media with a strong magnetic bias or methods based on material nonlinearities which require use of strong electromagnetic fields. A simpler possibility to produce nonreciprocity is to use spatio-temporal modulations to produce magnetic fields in synthetic dimensions. In this paper we show that dissipatively coupled systems can lead to considerable enhancement of nonreci...