[Paper Review] Control of acoustic absorption in 1D scattering by indirect coupled resonant scatterers

Aurélien Merkel, Georgios Theocharis+3 more|arXiv (Cornell University)|Sep 4, 2015

Ultrasonics and Acoustic Wave Propagation3 citations

TL;DR

This paper demonstrates experimentally that perfect one-sided acoustic absorption can be achieved in a 1D waveguide using two weakly lossy, indirectly coupled Helmholtz resonators. By tuning the resonator geometry to excite an electromagnetically induced transparency (EIT)-like mode with high Q factor, critical coupling to inherent viscothermal losses enables near-perfect absorption (up to 96%) even in deep sub-wavelength structures (λ/28), with unidirectional behavior in asymmetric configurations.

ABSTRACT

We experimentally report perfect acoustic absorption through the interplay of the inherent losses and transparent modes with high $Q$ factor. These modes are generated in a two-port, one-dimensional waveguide which is side-loaded by isolated resonators of moderate $Q$ factor. In symmetric structures, we show that in the presence of small inherent losses, these modes lead to coherent perfect absorption associated with one-sided absorption slightly larger than 0.5. In asymmetric structures, near perfect one-sided absorption is possible (96 \%) with a deep sub-wavelength sample ($λ/28$). The control of strong absorption by the proper tuning of few resonators with weak losses will open new possibilities in various wave-control devices.

Motivation & Objective

• To demonstrate experimentally that coherent perfect absorption (CPA) can be achieved in a two-port 1D acoustic waveguide using weakly lossy resonators.
• To explore how inherent viscothermal losses and high-Q EIT-like modes can be leveraged to achieve strong, one-sided absorption.
• To investigate the role of structural symmetry and geometric tuning in controlling absorption efficiency and directionality.
• To demonstrate near-perfect absorption (up to 96%) in deep sub-wavelength configurations (λ/28) using asymmetric resonator coupling.

Proposed method

• The system uses a two-port 1D waveguide side-loaded by two Helmholtz resonators (HRs) with moderate Q factors, coupled indirectly through the waveguide.
• The scattering matrix S(f) is measured experimentally to extract transmission and reflection coefficients, with eigenvalues used to identify CPA conditions.
• Critical coupling is achieved by tuning the detuning parameters $ k^{HR}_1 l / π $ and $ k^{HR}_2 l / π $, aligning the EIT-like mode with inherent losses.
• Theoretical modeling uses the S-matrix formalism, with eigenvalues $ \xi_{1,2} = t \pm \sqrt{r^L r^R} $, where CPA occurs when $ \xi_1 = 0 $.
• Asymmetric configurations break mirror symmetry, enabling unidirectional absorption by engineering unequal coupling to left and right incident waves.
• Absorption is quantified as $ \alpha = 1 - |r^L|^2 - |t|^2 $, with maximum values identified at specific frequency and geometric tuning.

Experimental results

Research questions

• RQ1 Can coherent perfect absorption (CPA) be achieved in a two-port 1D acoustic system using only inherent losses and EIT-like modes?
• RQ2 How does structural asymmetry between two indirectly coupled resonators affect one-sided absorption efficiency and directionality?
• RQ3 What is the maximum achievable one-sided absorption in a deep sub-wavelength configuration (λ/28) using weakly lossy resonators?
• RQ4 How do the eigenvalues of the scattering matrix evolve at CPA frequencies in symmetric versus asymmetric configurations?

Key findings

• In symmetric configurations, one-sided absorption reaches up to 60% in experiments (55% theoretically), with a maximum at the symmetrical CPA point where $ \xi_1 = 0 $.
• In asymmetric configurations, near-perfect one-sided absorption of 98% is achieved at $ f_{max} = 618 $ Hz with $ k^{HR}_1 l / π = 1.14 $, $ k^{HR}_2 l / π = 1.06 $.
• A deeper sub-wavelength absorber achieves 96% absorption at $ f_{max} = 244 $ Hz with a structure size of only $ l = 5 $ cm ($ \lambda/28 $).
• At the CPA frequency in asymmetric cases, both eigenvalues of the S-matrix approach zero, indicating full absorption from both incident ports, unlike symmetric cases where only one eigenvalue vanishes.
• The absorption peak is linked to critical coupling of an EIT-like mode, where the high-Q mode's leakage rate matches the inherent loss rate due to viscothermal effects.
• The experimental results confirm that higher absorption is achieved with lower-Q resonators, as their weaker intrinsic losses allow better control via geometric tuning.