Dual Metamapping Concentrator: A Unified Geometric Framework for Optical–Acoustic Wave Compression

A unified coordinate-transformation framework is developed to concentrate both electromagnetic and acoustic waves within a single geometric metric. This dual metamapping approach generalizes transformation optics (TO) and transformation acoustics (TA) by demonstrating that both systems obey an identical Helmholtz-type equation when subjected to an isotropic radial mapping. The derived scaling functions serve as universal geometric parameters governing spatial compression, independent of wave type. Analytical derivations establish a one-to-one dual correspondence between the transformed constitutive quantities (ε,μ) in electromagnetism and (ρ,B) in acoustics, thereby preserving full geometric invariance of the governing equations. Numerical simulations based on a piecewise-linear mapping verify identical field compression, intensity enhancement, and phase invariance in both domains, achieving the predicted gain expressed through the ratio of outer-to-inner radii. The proposed theory thus reveals a shared geometric foundation for TO and TA, enabling the design of photoacoustic concentrators, dual-mode sensors, and multiphysics metamaterials that unify optical and acoustic energy control within the same spatial framework