Eigenmode-Guided Amplification via Spatiotemporal Active Acoustic Metamaterials

TL;DR

This paper introduces a novel spatiotemporal gain-loss framework for controlling eigenmodes in acoustic resonators, enabling programmable energy routing and reconfigurable wave control through eigenmode steering and symmetry manipulation.

Contribution

It develops a new theoretical framework for eigenmode steering in acoustic systems using spatiotemporal gain-loss profiles, including symmetry considerations and dynamic control mechanisms.

Findings

Full-wave simulations confirm precise acoustic energy routing.

Spatiotemporal gain-loss profiles enable eigenmode manipulation.

PT symmetry allows switching between collapse and oscillations.

Abstract

We present a spatiotemporal gain-loss framework for eigenmode steering in coupled acoustic resonators. A cross-coupled gain-loss coefficient links the gain of one resonator to the intensity of its partner, creating nonlinear feedback that conserves total energy while driving the system toward the eigenmode associated with the eigenvalue having the largest imaginary part-a deterministic eigenmode collapse. Spatial gain-loss profiles shape the eigenvalue spectrum and attractor landscape, while temporal modulation governs the transition dynamics. When symmetry prevents direct access to a target eigenmode, controlled spatiotemporal perturbations enable otherwise symmetry-forbidden transitions and accelerate convergence. Within this framework, parity-time (PT) symmetry appears as a special case, allowing tunable switching between collapse and Rabi-like oscillations near the exceptional point. Full-wave simulations of coupled Helmholtz resonators confirm precise and programmable acoustic energy routing, establishing spatiotemporal gain-loss engineering as a route to reconfigurable wave control and analog information processing.