Elastic Purcell Effect

Abstract

In this work, we introduce an elastic analog of the Purcell effect and show theoretically that spherical nanoparticles can serve as tunable and robust antennas for modifying the emission from localized elastic sources. This effect can be qualitatively described by introducing elastic counterparts of the familiar electromagnetic parameters: local density of elastic states, elastic Purcell factor, and effective volume of elastic modes. To illustrate our framework, we consider the example of a submicron gold sphere as a generic elastic GHz antenna and find that shear and mixed modes of low orders in such systems offer considerable elastic Purcell factors. This formalism opens pathways towards extended control over dissipation of vibrations in various optomechanical systems and contributes to closing the gap between classical and quantum-mechanical treatments of phonons localized in elastic nanoresonators.

Control of the emission of elementary quantum systems using metamaterials and nanometaparticles

“…The boundary conditions in the case of the elastic waves are also more complex and include the continuity of the displacement vector and the normal component of the stress tensor, that is, in the general case of the elastic waves, there are 6 boundary conditions instead of 4 in the electromagnetic case. Nevertheless, the problem of radiation of a point elastic source in the presence of a gold microsphere was solved analytically in [216], where the resonant modes of such a system were found and the Purcell factor was calculated, which in the case of elastic waves is described by an expression similar to the electromagnetic case [216]: The results [216] can be very useful for describing both existing MEMS and NEMS based on conventional materials, and radiation in the presence of more complex elastic metamaterials, with the properties very different from common materials and having the effective densities and stiffness coefficients able to take negative values [217,218]. The resulting effects will be very interesting, as it was when the DNG metamaterials were created in the electrodynamic case.…”

Acoustic diamond resonators with ultrasmall mode volumes

“…This is the explicit normalization used in our earlier work on elastic Purcell effect [8] with interaction between an emitter modelled as a local harmonic force and the displacement field of a resonator. In this contribution, it is convenient to express the normalization of the strain tensor by considering the contribution from strain energy, i.e.,…”

“…This strain coupling is predominantly determined by a cavity's ability to spatially confine phonons beyond the diffraction-limited mode volume ∝ λ 3 , and to suppress the dissipation of phonons into radiative and nonradiative channels. These effects, quantified by the effective mode volume of the acoustic mode V eff and acoustic quality factor Q, respectively, provide a measure of cavity performance through the acoustic analog of the Purcell factor P F ∝ Q/V eff [8].…”

Hybridization of resonant modes and Bloch waves in acoustoelastic phononic crystals

“…Because the physical domain of radiation is infinite, the practical problem of obtaining the eigenmodes is generally non trivial. Different approaches have been proposed in the literature, for instance based on coupling the acoustic Green's function of the infinite radiation medium to the elastic solution in the rod [24,25]. Analytical solutions for the scattering of plane waves by circular cylinders and spheres are also available [26].…”