Waveguide System Achieves Perfect Tunneling Despite Loss and Asymmetry

Researchers are continually seeking to overcome the challenges posed by loss and asymmetry in wave transport, a ubiquitous phenomenon across optics, acoustics, and mechanics. Huayang Cai from the Institute of Estuarine and Coastal Research at Sun Yat-Sen University, working in collaboration with Bishuang Chen from the School of Marine Sciences at the same institution, and colleagues demonstrate coherent perfect tunneling at an exceptional point within a passive one-dimensional waveguide cascade. This study, also involving researchers at the Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), the State and Local Joint Engineering Laboratory of Estuarine Hydraulic Technology, the Guangdong Provincial Engineering Research Center of Coasts, Islands and Reefs, the Guangdong Provincial Key Laboratory of Marine Resources and Coastal Engineering, the Guangdong Provincial Key Laboratory of Information Technology for Deep Water Acoustics, the Key Laboratory of Comprehensive Observation of Polar Environment (Sun Yat-Sen University), Ministry of Education, and the Zhuhai Research Center, Hanjiang National Laboratory, reveals that suppression of a specific output channel arises from directional scattering degeneracy, not resonance or absorption collapse. The findings establish directional degeneracy as a general mechanism for achieving loss-tolerant tunneling via exceptional points, with implications for a wide range of wave-based systems.

The study focused on understanding this universal phenomenon across various wave systems. The approach involved theoretical modelling and analysis of wave propagation through asymmetric and lossy media, detailing a novel framework for predicting and enhancing coherent perfect tunneling in complex systems, thus advancing the understanding of wave behaviour in non-ideal environments. Scientists are investigating a long-standing problem across optics, acoustics, and quantum mechanics, demonstrating coherent perfect tunneling at an exceptional point in a passive one-dimensional waveguide cascade with three coupled interfaces. Using a waveguide-invariant scattering framework, they show that the suppression of a selected output channel originates from a directional scattering degeneracy, rather than from resonance or absorption collapse. This exceptional-point condition emerges when interference between boundary-induced feedback loops promotes a simple zero of the scattering response to a second-order degeneracy, resulting in fixed coherent excitation producing a robust quartic leakage law within a transparency-dominated tunneling window. These results establish directional degeneracy as a general mechanism for loss-tolerant tunneling enabled by exceptional points across a broad class of wave systems. Wave tunneling through finite, lossy structures underpins energy and information transport across optics, acoustics, quantum systems, and electrochemical interfaces. Conventional descriptions of tunneling and transmission rely on resonance conditions, impedance matching, or modal hybridization, concepts rooted in classical wave and mode theories. While successful in idealized settings, these approaches are intrinsically sensitive to loss, asymmetry, and boundary detuning, making perfect transmission fragile in realistic non-Hermitian systems. Beyond photonics, the same boundary-controlled transport challenge recurs in acoustic cloaking, metasonics, microwave networks, and quantum-dot or waveguide-quantum electrodynamics junctions, where loss and fabrication asymmetry are unavoidable. Existing exceptional-point concepts have largely been deployed for absorption control and sensing; however, this work demonstrates how an exceptional point can instead protect useful power delivery, enabling near-unitary tunneling while suppressing a selected outgoing channel. Recent advances in exceptional-point physics have demonstrated that non-Hermitian degeneracies can qualitatively reshape wave transport and interference, with coherent perfect absorption at exceptional points exhibiting anomalous quartic spectral flattening and enhanced robustness. These developments establish exceptional points as a powerful mechanism for controlling dissipation and transport, although existing formulations of tunneling and absorption are predominantly expressed in terms of scattering-matrix eigenmodes or coupled-mode models, obscuring the energetic distinction between total dissipation and useful transmitted power, and offering limited insight into how directionality and asymmetry fundamentally constrain perfect tunneling. This research shows that coherent perfect tunneling at exceptional points emerges naturally as a directional degeneracy within a waveguide-invariant scattering framework. Building on a recently established universal mass-energy relation for lossy one-dimensional waveguides, and its kinetic extension to electrochemical polarization, the team demonstrates that CPT conditions correspond to a geometric collapse of the effective standing-wave magnitude along a specific transport direction, rather than to conventional resonance. This invariant description reveals CPT as a boundary-controlled, direction-selective degeneracy in energy and power space, unifying tunneling, exceptional points, and useful power delivery under a common framework that remains valid in the presence of intrinsic asymmetry and distributed loss. The structure considered is a power-normalized two-port scattering system b(Ω) = S(Ω)a, where a= (a1, a2)T and b= (b1, b2)T denote the complex input and output wave amplitudes, and Ω is the dimensionless angular frequency. The system consists of a passive one-dimensional waveguide cascade formed by two identical lossy propagation segments separated by three lossless interfaces characterised by reflection amplitudes ΓS, ΓI, and ΓL, corresponding to the source, internal, and load interfaces. Distributed attenuation and phase accumulation are encoded in the complex propagation constant K(Ω) = √(iΩ + δR)(iΩ + δG), where δR and δG are non-negative loss parameters associated with the two propagation directions. The resulting round-trip feedback factor is z(Ω) = exp[−2K(Ω)]. In this formulation, all frequency dependence enters exclusively through z(Ω), while the interface reflections control the coupling between multiple scattering paths, rendering the description waveguide-invariant; geometric length, loss, and dispersion are absorbed into a single complex scalar z, whereas boundary-induced interference is governed solely by the interface coefficients. For a fixed excitation direction, the complex amplitude of the suppressed output channel can be expressed as b1(Ω) = N[z(Ω)] / D[z(Ω)], where the denominator D(z) originates from the total ABCD transfer matrix of the cascade and remains finite in the tunneling-dominated regime. The numerator explicitly reads N(z) = (A+ B−C−D)a1 + 2(AD−BC)a2, with A, B, C, D denoting the ABCD elements of the full three-interface cascade, each being analytic functions of z. With only two interfaces, the numerator contains at most a single controllable interference loop and generically supports only a simple zero, yielding linear suppression in complex amplitude. The internal interface introduces an additional independent feedback path, which is the minimal degree of freedom needed to promote a simple zero to a double zero under passive constraints, thereby enabling CPT and the exceptional point. In the fixed coherent operation protocol, the incident state a= afix is held constant while sweeping Ω. Consequently, N becomes an analytic scalar function of z(Ω) alone, and the CPT condition is imposed as N[z(Ω0); afix] = 0, dN/dz|z(Ω0),afix = 0, D[z(Ω0)] ≠0. By contrast, in the per-frequency probe protocol, a= apf(Ω) can be chosen such that b1(Ω) = 0 identically, which does not require the derivative constraint. This double-root condition defines a directional scattering degeneracy: a selected outgoing channel is suppressed without inducing resonance or absorption collapse. Analytically, it enforces a geometric-mean balance between the source and load boundary feedback loops, while the minus sign fixes the relative phase required for destructive interference in the selected output channel under the chosen phase gauge. The internal interface must simultaneously satisfy the critical coupling condition |ΓI| = 2√|ΓSΓL| / (1 + |ΓSΓL|). Without the internal interface, the system supports at most a simple zero in N(z), leading only to linear suppression of the complex amplitude; the third interface provides the additional interference degree of freedom required to promote this simple zero to a second-order degeneracy under passive conditions. Figure 1 visualizes the physical consequences of the CPT condition. In Figure 1A, both the reflection coefficient |S11| and the fixed-input throughput ‖Safixed‖ remain close to unity around Ω0, while deviations from unitarity, quantified by 1 −σmin and 1 −σmax, stay below 10−4, confirming that CPT operates in a transparency-dominated tunneling window. Figure 1B shows the coherent input ratio a2/a1 and phase, shown as 20log10 |a2/a1| and Δφ= arg(a2/a1) for per-frequency probing and the fixed operating state. Figure 1C displays power-balance diagnostics in log scale: the total power deficit 1 −Ptot and the transmitted-channel deficit 1 −P2, together with the suppressed-channel power P1 = |b1|2, for both protocols; CPT manifests without absorption collapse, maintaining P2 ≈1 while suppressing P1 near Ω0. Figure 1D shows the quartic leakage law under fixed coherent operation: on the detuning grid ΔΩ = Ω −Ω0 0, the fixed-input leakage follows P1,fixed ∝|ΔΩ|4, whereas the per-frequency probe remains at numerical floor because b1 is nulled by construction. This work establishes CPT as a distinct non-Hermitian transport regime that is fundamentally different from both resonant tunneling and coherent perfect absorption. In CPT, the suppression of a selected output channel arises from a directional scattering degeneracy rather than from resonance-induced field enhancement or absorption collapse, enabling near-unitary transmission to be maintained. A key insight is the essential role of the internal interface. Systems with only source and load boundaries support at most a simple zero of the scattering response, leading to linear suppression of the complex amplitude. Introducing a third interface provides an additional interference pathway that promotes this simple zero to a second-order degeneracy under passive conditions, thereby stabilising the exceptional point against loss and asymmetry. The observable hallmark of this degeneracy is the quartic leakage law under fixed coherent excitation. Waveguide-invariant scattering analysis reveals a complex amplitude of the suppressed output channel expressed in a rational form, b1(Ω) = N[z(Ω)] / D[z(Ω)], where z(Ω) encapsulates frequency dependence through loss and dispersion. The numerator, N(z), explicitly reads N(z) = (A+ B−C−D)a1 + 2(AD−BC)a2, derived from the three-interface cascade’s ABCD elements, each being analytic functions of z. The introduction of a third interface is crucial, as it promotes a simple zero in the numerator to a double zero under passive constraints, thereby enabling coherent perfect tunneling at an exceptional point. This condition, N[z(Ω0); afix] = 0 and dN/dz|z(Ω0),afix = 0, with D[z(Ω0)] ≠0, defines the exceptional point where tunneling occurs. Fixed coherent excitation, maintaining a constant incident state, afix, while sweeping the frequency, Ω, demonstrates a robust quartic leakage law within a transparency-dominated tunneling window. This quartic dependence signifies that leakage power scales with the fourth power of the excitation, indicating a highly efficient tunneling process. The research establishes that this leakage law arises from a geometric collapse of the effective standing-wave magnitude along a specific transport direction, rather than conventional resonance. This collapse is directly linked to the directional degeneracy at the exceptional point, ensuring that energy is selectively suppressed in one output channel. The round-trip feedback factor, z(Ω), is defined as exp[-2K(Ω)], where K(Ω) = √(iΩ + δR)(iΩ + δG), incorporating distributed attenuation parameters, δR and δG. The separation of frequency dependence into z(Ω) and boundary effects into interface coefficients renders the description waveguide-invariant, meaning geometric length, loss, and dispersion are absorbed into a single complex scalar. This simplification allows for a focus on boundary-induced interference as the primary driver of coherent perfect tunneling, independent of specific waveguide dimensions or material properties. Scientists have long sought to control the flow of energy in complex systems, a pursuit hampered by inevitable losses and imperfections. This research demonstrates a pathway to ‘coherent perfect tunneling’, the seemingly paradoxical transmission of energy even through barriers that should, by conventional understanding, block it. The breakthrough isn’t simply achieving this phenomenon, but doing so in a system deliberately engineered to include loss and asymmetry, conditions far more representative of the real world than the idealised scenarios typically explored. For years, the field has grappled with the trade-off between robustness and efficiency in wave transport, be it for acoustic energy, light, or even mechanical vibrations. Maintaining coherence, the wave-like behaviour essential for tunneling, usually demands pristine conditions, a significant obstacle to practical applications. This work sidesteps that limitation by exploiting ‘exceptional points’, specific parameter combinations where standard rules of wave behaviour break down, and where losses can, counterintuitively, enhance transmission. The implications extend beyond fundamental physics. Imagine designing acoustic shielding that perfectly transmits sound at a specific frequency while blocking all others, or creating mechanical systems with unprecedented energy transfer efficiency. However, the current demonstration relies on a carefully constructed one-dimensional waveguide, a far cry from the complex, three-dimensional materials needed for most real-world devices. Scaling this principle up, and maintaining control over the exceptional point in more disordered environments, remains a substantial challenge. Future research will likely focus on exploring different material platforms and investigating how these effects can be harnessed in more complex topologies, potentially paving the way for a new generation of wave-based technologies.