Magnetic-acoustic biphysical invisible coats for underwater objects

Invisible cloaking is one of the representative advancements of modern electromagnetics research associated with the development of metamaterials. To date, various techniques have been developed to improve the feasibility of electromagnetic cloaking devices. The same conception has also been broadly extended to other physical systems controlled by different partial differential equations. In practice, implementing cloaking devices for EM or other waves remains challenging due to material fabrication complexity. At low frequencies, where electric and magnetic fields decouple, the difficulty is reduced. In 2012, Gömöry et al. demonstrated a d.c. magnetic cloak using a superconductor–ferromagnetic (SC–FM) bilayer. Subsequent work extended this approach to the quasi-static regime, enabling magnetic cloaks at room temperature without superconductors for both static and dynamic frequencies. For waterborne applications, magnetic fields and acoustic waves are the two fundamental modalities used to deliver signals or perceive objects. Although acoustic cloaks via coordinate transformation have been proposed, practical implementation is difficult due to inhomogeneous anisotropic requirements; engineering of anisotropic mass density or modulus and even pentamode metamaterials has demonstrated advanced functions but with complexity, thickness, and bandwidth limitations. In practice, thin absorbers are highly desired for stealth based on returning loss in far-field measurements, although near-field systems (e.g., magnetic probes) require different considerations. Some dual-physics metasurfaces manipulate electromagnetic and acoustic waves simultaneously; however, magnetic–acoustic biphysical invisible coats for underwater objects have not been explored. In this work, we propose and demonstrate a biphysical metamaterial invisible coat that simultaneously addresses detection by both magnetic fields and acoustic waves underwater. The design compatibly merges a magnetic invisible cloak and an acoustic stealth structure within a compact form factor. Inspired by circuit analog absorbers (CAAs) for EM waves, we design an ultrathin acoustic impedance-matched broadband absorber consisting of a resonant acoustic metasurface (AMS), a sound spacing layer, and a rigid bottom ground, with a detailed discussion of absorption characteristics. A key contribution is the design of a high-permeability elastic ferromagnetic (FM) spacing layer which, combined with an inner rigid metallic ground, achieves a bilayer magnetic cloaking effect. When FM and AMS layers are sufficiently thin (thus mutually transparent in their specific responses), their relative positions can be alternated, offering freedom to build biphysical coats for different bands. The design is confirmed experimentally and may find applications from military stealth to mitigation of magnetic and ultrasonic disturbances from implanted metallic objects in medical scanning.

The paper situates its contribution within multiple prior streams: (1) Electromagnetic cloaking via metamaterials and subsequent efforts to improve feasibility; (2) Extensions of cloaking to other physical systems governed by similar PDEs; (3) Low-frequency magnetic cloaks beginning with SC–FM bilayers for static fields (Gömöry et al., 2012) and later quasi-static, room-temperature implementations without superconductors for static and dynamic frequencies; (4) Acoustic cloaking via coordinate transformation, with practical difficulties due to inhomogeneous anisotropic requirements; experimental advances using engineered anisotropic mass density and anisotropic modulus, and complex pentamode metamaterials for elastic waves; (5) Thin, broadband absorbers (circuit analog absorbers) as practical stealth solutions in far-field measurements; (6) Prior dual-physics metasurfaces that jointly manipulate electromagnetic and acoustic waves. The gap identified is the absence of magnetic–acoustic biphysical invisible coats suitable for underwater objects, prompting the integrated design presented here.

Materials and methods comprise simulation, fabrication, and measurement protocols for both the magnetic cloak and the acoustic absorber. Simulation for the magnetic cloak: COMSOL Multiphysics 5.4 (2D model) was used to optimize and compute magnetic scattering from a bilayer cylindrical cloak: inner brass (C28000) ground shell radius r1 = 11 mm (electrical conductivity 1.62×10^7 S/m) and an outer FM layer of thickness tFM = r2 − r1. The FM anisotropic permeability tensor in cylindrical coordinates was set as (μrr, μθθ, μzz) with μrr = 1 and μθθ = μzz = μ. COMSOL with MATLAB was used to optimize μFM for different thickness ratios (r2/r1 = 1 + d/r1) starting from the analytical expression for an ideal superconducting core: μFM = (r2 + r1)/(r2 − r1). The objective function minimized o(μFM, tFM) = |ηH(μFM, tFM, f = 250 kHz) − (−0.005)|, i.e., targeting a relative change near −0.5% at 250 kHz to broaden the cloak’s bandwidth. Simulation for the acoustic absorber: The absorber was optimized near 100 kHz (actual center ~105 kHz). AMS geometry: air-cylinder holes of diameter D = 0.15 mm, height H = 0.15 mm, period p = 2.3 mm. A thin PDMS sealing layer was added beneath the bubble metasurface to prevent water ingress; the spacing between the air matrix and the upper PDMS boundary was h = 255 μm. Total PDMS thickness t1 = 1.05 mm. The FM layer thickness was fixed at tFM = 0.13 mm and shown to have marginal effect on acoustic response due to its small thickness. COMSOL Acoustic–Solid Interaction and Frequency Domain modules were used, with plane-wave radiation boundaries in water and low-reflecting boundaries in brass; side boundaries were Floquet periodic. Material parameters: PDMS (ρ = 970 kg/m^3, shear modulus μ = 0.6 + 0.7 f MPa with f in MHz, acoustic impedance Z = 1 MRayl), brass (UNS C28000, Poisson’s ratio 0.362), and water from COMSOL’s library. Sample fabrication: Magnetic cloak—A 0.13-mm-thick soft magnetic sheet (PDMS matrix with plate-shaped hydroxyl iron nanoparticles) was rolled around a brass cylinder (diameter 22 mm, length 50 mm). Flat iron nanoparticles were aligned in-plane via a bias magnetic field during PDMS curing to achieve high in-plane permeability; volume fraction tuned μ. Permeability characterization used a cigarette-shaped rolled core (diameter 5 mm, length 34 mm) placed at the center of Helmholtz coils (diameter 33 cm, spacing 11 cm, 30 turns) driven by a lock-in amplifier (Signal Recovery 7270). Induced signals (1–250 kHz) were measured via a 16-turn ring probe (diameter 9 mm) and μ spectrum obtained by comparing induced complex signals with/without the FM core. Acoustic absorber—The AMS was fabricated by casting PDMS onto an SU-8 mold via standard UV lithography (SU-8 2075 on 4-inch wafer; spin 1600 rpm, soft bake 65 °C 5 min and 95 °C 30 min; UV exposure; postbake 65 °C 5 min and 95 °C 12 min; developed in PGMEA with ultrasonic agitation). PDMS (SYLGARD 184, 10:1 base:curing agent) was degassed (2 h), poured on the mold to form ~1 mm film, baked at 85 °C for 20 min, and peeled. A thin top PDMS encapsulation layer (~50 μm, spin 1000 rpm 1 min; bake 85 °C 10 min) was bonded to the thick PDMS; assembly baked 85 °C 1.5 h and peeled. During experiments, water ingress between AMS and FM can occur and reduces boundary acoustic reflection. Measurement for magnetic cloaking: A pair of large Helmholtz coils (diameter 33 cm, height 1.8 cm) in a water tank (50×50×20 cm^3) was driven by a signal generator (Stanford DS345); the local magnetic field was scanned by a small Helmholtz coil connected to a lock-in amplifier and mounted on a step motor. Performance metric: relative change nv = |Vs|/|V0| from voltages with vs. without sample. A commercial handheld metal scanner (Tianxun 1001B, ~25 kHz) and an oscilloscope (Agilent DSO1022A) assessed practical cloaking (alarm response). Measurement for acoustic stealth: Water-immersion reflection-mode setup used a 100 kHz PZT transducer (Panametrics V1011) at 150 mm from the sample to operate in the far field. Excitation: 10-cycle Hann-windowed 100 kHz tone-burst, 300 V, 25 Hz repetition. For broadband response (e.g., Fig. 6c), a different PZT (VA1C11325, 1 MHz center, −6 dB bandwidth 0.4 MHz) was driven at 150 V, 100 Hz. A pulser (RAM-5000) emitted signals; reflections were received by the same transducer and digitized by a LeCroy HDO6054 oscilloscope via an RDX-6 diplexer (0.25–45 MHz). Time traces were sampled at 10 MHz and averaged 500×; reflection spectra obtained via Fourier transform; reflectivity computed as the ratio of signals with/without the metamaterial coat.

- A compact, submillimeter-thick biphysical metamaterial coat integrates an acoustic metasurface absorber with a bilayer magnetic cloak to simultaneously render underwater objects invisible to magnetic fields and strongly absorb acoustic waves. - Magnetic cloaking: Field disturbance ratio |ΔH| < 0.5% achieved over a broad frequency range (approximately 10–250 kHz), limited at the high end by measurement instrumentation. Simulations and design indicate a bilayer brass+FM configuration can cloak all phases of the a.c. magnetic field cycle within the bandwidth. - Example cloak geometry: inner brass radius r1 = 11 mm; FM shell thickness tFM = 0.13 mm (r2 = 1.012 r1 = 11.13 mm); target μFM ≈ 82.5–85.3 (analytical starting point μFM = (r2 + r1)/(r2 − r1)). A simulated sample with total bilayer thickness 0.63 mm at 25 kHz showed negligible external field disturbance and near-zero internal field, with thickness-to-cavity-radius ratio ~0.06. - Bandwidth dependence: The upper bound fu falls sharply when the inner metallic shell is thinner than ~0.5 mm, indicating a practical lower limit on metal thickness for wideband operation; a thicker inner shell does not substantially reduce the lower bound fl due to ohmic loss at very low frequencies. - Acoustic stealth: The AMS (air bubbles in PDMS) exhibits Minnaert resonance and, with the brass ground, produces a π-phase-shifted reflection that cancels the 0-phase reflection from the ground, mimicking circuit analog absorption. Simulations/analysis show near-unity absorptivity around the designed center frequency (~100–105 kHz), with low reflectivity and transmissivity and good angular tolerance. - Decoupling of functions: With a very thin FM layer (tFM ≈ 0.13 mm), its influence on the acoustic response is marginal; conversely, the AMS layer does not compromise magnetic cloaking, enabling flexible stacking order and compatibility with different AMS designs across spectral regimes. - Practical demonstrations: Tank measurements confirmed magnetic cloaking performance and acoustic reflection suppression consistent with simulations; a handheld metal scanner at ~25 kHz did not trigger alarms when the cloak was applied, illustrating practical magnetic stealth.

The study addresses the practical challenge of simultaneous magnetic and acoustic detectability of underwater objects by harmonizing two mechanisms with distinct physics within a compact architecture. A bilayer magnetic cloak (conductive brass ground plus high-permeability elastic FM shell) guides magnetic flux lines around the object, restoring the external field and minimizing disturbance; when tuned appropriately, this works across a broad quasi-static band. The acoustic component, an impedance-matched absorber using a resonant AMS over a rigid ground, cancels reflections via controlled phase and dissipation, yielding near-unity absorption around the target band. By ensuring the FM layer is ultrathin, mutual interference is minimized: the FM shell is effectively transparent acoustically, and the AMS does not perturb the magnetostatic response, permitting flexible layer ordering. The findings demonstrate that multifunctional stealth is feasible without resorting to complex anisotropic transformation media or thick structures, offering a practical route for underwater stealth, noise reduction, and medical device compatibility. The bandwidth trade-offs (e.g., ohmic losses at low frequencies and skin-depth limitations) and absorber tuning constraints are quantified, clarifying design spaces for future optimization.

This work proposes and experimentally demonstrates a thin, conformal biphysical metamaterial coat that simultaneously achieves magnetic cloaking (|ΔH| < 0.5% from ~10 to 250 kHz) and strong acoustic absorption (near-unity around ~100 kHz) underwater. The design integrates a bilayer magnetic cloak (brass ground with high-μ elastic FM shell) and a resonant acoustic metasurface absorber inspired by circuit analog absorbers. The ultrathin FM layer enables minimal cross-coupling and flexible stacking with different AMS designs, broadening applicability across spectral regimes. These results open a pathway to multifunctional stealth and protection for waterborne applications, including potential mitigation of magnetic/ultrasonic disturbances from implanted metallic objects in medical contexts. Future directions include extending to fully 3D geometries, widening the magnetic bandwidth to lower frequencies (e.g., via active boundaries), tailoring AMS designs for other frequency bands, optimizing materials for higher μ at reduced thickness, and system-level integration for practical platforms.

- Magnetic bandwidth constraints: Passive bilayer cloaks exhibit lower and upper cutoff frequencies (fl, fu) due to ohmic loss and skin-depth effects; at f < ~1 kHz, ohmic loss degrades diamagnetism, while very thin inner metal shells (< ~0.5 mm) sharply reduce fu. - Measurement-limited characterization: The upper measured magnetic frequency was capped at 250 kHz by the lock-in amplifier; broader-band performance beyond this was not experimentally verified. - Material tuning requirements: Achieving very high in-plane μ necessitates alignment and sufficient loading of plate-shaped iron nanoparticles in PDMS, which may introduce fabrication variability. - Acoustic tuning narrowband by design: The AMS absorber is centered near 100–105 kHz; while broadband for its thickness class, peak absorption is inherently frequency-targeted and requires redesign for other bands. - Geometric and thickness constraints: Maintaining ultrathin FM and appropriate inner metal shell thickness is critical for performance; departures can reduce magnetic bandwidth or increase acoustic coupling. - Partial decoupling assumption: While thin FM layers are shown to be marginal to acoustic response in simulations and experiments here, different material choices or thicker layers could introduce coupling not addressed in this study.