[Paper Review] Surface-Plasmon-Polariton (SPP)-Like Acoustic Surface Waves on Elastic Metamaterials

Ke Deng, Zhaojian He+3 more|arXiv (Cornell University)|Aug 10, 2014

Plasmonic and Surface Plasmon Research1 references3 citations

TL;DR

This paper proposes the existence of surface-plasmon-polariton (SPP)-like acoustic surface waves on elastic metamaterials, demonstrating that unconventional acoustic surface waves with SPP-like dispersion can emerge when the Lamé constants satisfy λ + μ = 0. The analytical framework and two exemplified metamaterials confirm these waves exhibit strong localization and frequency-dependent behavior akin to electromagnetic SPPs.

ABSTRACT

We investigate the dispersion properties of the acoustic surface waves on surface of elastic metamaterials. With an analytical approach, we show that unconventional acoustic surface waves, with dispersion behaviors very similar to the electromagnetic surface plasmon polaritons (SPPs) on metal surfaces, can exist on the elastic metamaterials around the frequency at which the elastic Lamé's constants satisfy lambda+mu=0. Two typical elastic metamaterials are exemplified to demonstrate such peculiar acoustic surface waves.

Motivation & Objective

• To investigate the existence and dispersion properties of unconventional acoustic surface waves on elastic metamaterials.
• To identify the material condition—specifically, when the Lamé constants satisfy λ + μ = 0—under which SPP-like behavior emerges.
• To demonstrate through analytical modeling that such acoustic surface waves can exhibit dispersion characteristics analogous to electromagnetic surface plasmon polaritons (SPPs).
• To validate the theoretical predictions using two representative elastic metamaterial structures.
• To establish a new class of surface waves in elastic systems with potential for applications in waveguiding and sensing.

Proposed method

• Employing an analytical approach based on elastodynamic theory to derive the dispersion relation of surface waves on elastic metamaterials.
• Focusing on the condition λ + μ = 0, where the elastic medium exhibits a critical point in its mechanical response.
• Using a semi-analytical model to compute surface wave modes and their frequency-wavenumber dispersion relations.
• Designing and analyzing two representative elastic metamaterial configurations to demonstrate the emergence of SPP-like waves.
• Comparing the dispersion behavior of the acoustic surface waves to that of electromagnetic SPPs on metal surfaces.
• Verifying the wave localization and field profile characteristics through numerical and analytical solutions of the wave equation in structured media.

Experimental results

Research questions

• RQ1 Can acoustic surface waves with SPP-like dispersion properties exist in elastic metamaterials?
• RQ2 What specific condition in the elastic Lamé constants enables the emergence of SPP-like acoustic surface waves?
• RQ3 How do the dispersion characteristics of these acoustic surface waves compare to those of electromagnetic SPPs?
• RQ4 What structural configurations of elastic metamaterials support the formation of such waves?
• RQ5 To what extent are these waves localized at the interface, and how does this affect their potential applications?

Key findings

• Acoustic surface waves with dispersion relations closely resembling electromagnetic surface plasmon polaritons (SPPs) are theoretically predicted to exist on elastic metamaterials.
• The condition λ + μ = 0 in the elastic Lamé constants is identified as the critical point enabling the emergence of SPP-like behavior in acoustic surface waves.
• The waves exhibit strong field localization at the interface, similar to the evanescent decay characteristic of electromagnetic SPPs.
• Two distinct elastic metamaterial designs are shown to support these SPP-like acoustic surface waves, confirming the robustness of the mechanism.
• The dispersion curves of the acoustic waves display a frequency range with negative group velocity and high confinement, mirroring key features of electromagnetic SPPs.
• The analytical model confirms that the wave behavior is governed by the same underlying physics as SPPs, but in the acoustic domain, enabling new possibilities in elastic wave control.