High-Order Perfect Absorption in the Absence of Exceptional Point

Abstract: High-order perfect absorption of coherent input has recently attracted significant attention due to its broadband absorption capacity. However, the realization of a high-order perfect absorber relies on the exceptional point (EP) to coalesce the scattering zeros. Here, we present a general scattering framework and achieve the high-order perfect absorber in the absence of EP. We consider the asynchronous coherent input, where a spatial delay introduces a momentum-dependent phase factor beyond the amplitude and phase control in synchronous coherent input. This new degree of freedom enables active control of the momentum dependent output, effectively reshaping the absorption line shape necessary for the high-order perfect absorber. Remarkably, despite the absence of EP, the proposed high-order perfect absorber exhibits significant response to the perturbations in the delay length. Our findings provide insights for the delay induced momentum-sensitive interference phenomenon and offer a new route for wave control.

• The paper shows that high-order perfect absorption can be achieved without exceptional points by exploiting asynchronous, delay-driven coherent inputs.
• It employs a generalized scattering formalism with momentum-dependent delay to engineer third-order absorption and broaden the spectral absorption profile.
• The study offers practical insights for designing broadband absorbers and sensitive sensors in photonics and related fields through delay modulation.

High-Order Perfect Absorption without Exceptional Points: Delay-Driven Non-Hermitian Interference

Introduction

The research addresses a foundational challenge in broadband coherent perfect absorption (CPA) of waves in non-Hermitian scattering systems. Conventional high-order CPA, distinguished by broadened spectral absorption, has been tightly associated with the presence of exceptional points (EPs), where scattering zeros coalesce, enabling engineered absorption profiles. The central thesis of this work is the demonstration—both theoretically and with model realization—that high-order perfect absorbers can be constructed in the absence of EPs by exploiting asynchronous (delayed) coherent inputs. This expands the control space for coherent absorption to include not only amplitude and phase but also a tunable, momentum-dependent delay, establishing a comprehensive framework for delay-induced wave interference phenomena.

Generalized Scattering Formalism and Delay

The authors formalize a scattering framework where the input at two ports is allowed to arrive asynchronously, characterized by a spatial delay. This delay introduces a momentum-dependent dynamical phase, $e^{ikl}$, fundamentally altering the effective interference upon scattering. Within this formalism, variation of the delay is shown to provide active modulation over the output momentum dependence, enabling the engineering of the absorption line shape.

For a two-port system with input vector $a = (a_1, a_2)^T$ and momentum $k$, the delay $l$ modifies the input as $n = |n| e^{i\varphi} e^{ikl}$, where $|n|$ and $\varphi$ are amplitude and phase, and $l$ is the delay length. The critical realization is that tuning $l$ allows all derivatives up to order $n-1$ of the output $a = (a_1, a_2)^T$0 to be set to zero at $a = (a_1, a_2)^T$1, thus achieving $a = (a_1, a_2)^T$2-th order perfect absorption with a broadened absorption profile—without relying on the coalescence of scattering zeros at an EP.

Synthetic Frequency Lattice Model and Analytical Construction

To demonstrate the physical implications, the work constructs an explicit model based on a dynamically modulated ring resonator (synthetic frequency dimension) coupled to a dissipative two-level atom. The system's Hamiltonian supports mapping to a tight-binding chain with a localized, lossy impurity, providing a tractable platform for calculating scattering properties. Scattering coefficients $a = (a_1, a_2)^T$3 and $a = (a_1, a_2)^T$4 are derived with closed-form expressions parameterized by the coupling and dissipation rates.

The standard CPA (synchronous input) produces first-order perfect absorption at isolated points in the frequency-momentum spectrum, with a narrow quadratic line shape. By introducing a finite delay between the two input channels, higher-order zeros in the output can be achieved. The authors analytically and numerically demonstrate the realization of third-order absorption, manifested as a sextic ($a = (a_1, a_2)^T$5) vanishing of the output intensity near the absorption center, constrained entirely via delay rather than spectral parameter tuning.

Numerical and Analytical Results

The numerical analysis illustrates several core results:

• Broadband Absorption without EPs: The absorption profile can be reshaped from quadratic (first-order) to sixth-order scaling near resonance, with corresponding significant widening of the absorption bandwidth. The line shape is controlled entirely by the delay parameter.
• Port-Asymmetry: The delay allows for asymmetric absorption orders at different output ports (e.g., third-order at port 1, first-order at port 2), which cannot be achieved in delay-free or EP-limited configurations.
• Strong Delay Sensitivity: The high-order absorption is shown to be highly sensitive to variations in the delay length, enabling large modulation of output in response to small timing shifts. This sensitivity emerges purely from the change in the order of perfect absorption and is not accompanied by the instability or spectral splitting characteristic of EP-based systems.

Strong numerical evidence is provided for the scaling of the residual output intensity with the momentum-space width $a = (a_1, a_2)^T$6 of the input packet: $a = (a_1, a_2)^T$7 for an $a = (a_1, a_2)^T$8th-order perfect absorber.

Theoretical and Practical Implications

This research separates the concept of high-order perfect absorption from the necessity of an EP, revealing that the fundamental criterion is the existence of higher-order zeros in the output as a function of input momentum, which can be synthesized via delay engineering. This insight undermines the previously axiomatic connection between high-order absorption and non-Hermitian degeneracies. Practically, this unlocks new avenues for robust, broadband absorber design in photonic, acoustic, and electronic platforms, especially in settings where system parameter tuning to EPs is technically infeasible.

Furthermore, the strong and tunable sensitivity to delay suggests promising applications in sensing technology, where perturbations of the delay can be transduced into large output changes, potentially with greater robustness and less noise amplification than at EPs. The findings are broadly extensible to temporal delays, multiport systems, and other synthetic dimensional platforms.

Future Directions

The delay-driven absorption engineering concept opens several pathways for future research:

• Multimode and Multiport Extensions: Generalization to systems with more than two ports and higher synthetic dimensionality, including the control of interference patterns in complex networks.
• Temporal Modulation and Quantum Regimes: Application to systems driven by temporal rather than spatial delays, with relevance for time crystals, quantum weak measurement protocols, and quantum information processing.
• Integrated Photonic Devices: Realization of delay-controlled broadband absorbers and sensors in integrated photonic systems leveraging synthetic dimensions or dynamically controlled delay lines.

Conclusion

The work establishes that high-order perfect absorption in non-Hermitian wave systems can be realized independently of exceptional points, provided that delay in coherent input is exploited as a controllable degree of freedom. This reframing of broadband absorption physics catalyzes a new class of interference-driven device concepts and beckons further theoretical and technological exploration of the delay as a resource in coherent control and wave manipulation.