Coherent Virtual Absorption in Dielectric Slabs: A Temporal Analysis of Symmetric and Asymmetric Geometries

Coherent virtual absorption refers to time-limited storage of optical energy in lossless configurations due to excitation of a complex zero frequency through proper temporal engineering of the incident wave. Given the dynamics underlying the effect and the storage-release mechanism occurring for finite excitation pulses, studying and understanding the associated time dynamics are crucial for enabling future applications. In this work, we carefully investigate this phenomenon in symmetric and asymmetric geometries, shedding light on practical considerations in situations when a closed-form analytical solution is not readily available. Combinations of time domain analysis and spectral filtering are used to enable systematic analysis of these structures. Our approach can be generalized to more complex structures, including multilayered and inhomogeneous cases, providing new opportunities for optimized energy storage and advanced sensing applications utilizing complex-frequency dynamics in lossless designs.

💡 Research Summary

The paper investigates coherent virtual absorption (CVA) in loss‑free dielectric slabs by exploiting complex‑frequency excitations that align with a zero of the scattering matrix (S‑matrix). Starting from a simple symmetric slab, the authors analytically compute the S‑matrix eigenvalues and eigenvectors in the complex frequency plane, identifying an infinite set of zeros. A zero eigenvalue requires the two incident ports to be driven with equal amplitude and a relative phase of either 0° or 180°, which can be realized by two counter‑propagating pulses that are temporally engineered to contain a complex exponential factor e^{iωt} with ω = ω′ + iω″. Because an infinite exponential growth or decay is unphysical, the authors shape the pulse with a Gaussian envelope and a rapid switch‑off time, ensuring that the complex‑frequency component dominates only for a finite duration.

Using finite‑difference time‑domain (FDTD) simulations, the authors launch such pulses from both sides of the slab. While the pulse is present, the total electric field inside the slab builds up smoothly, and the scattered (reflected and transmitted) fields remain essentially zero, confirming that the system is operating at an S‑matrix zero. When the excitation is abruptly switched off, the stored energy is released, which is observed as a sign reversal in the instantaneous power measured at a point outside the slab. The authors quantify this release in two ways: (1) a direct time‑domain calculation of the scattered power from the difference between total and incident fields, and (2) a spectral‑filtering technique. In the latter, the spatiotemporal field is Fourier‑transformed to the (k, ω) domain, a mask isolates the negative‑k components (corresponding to the reflected wave), and an inverse transform yields the scattered field alone. Both methods agree that the scattered energy is minimal at the exact zero and grows rapidly as the complex frequency moves away from the zero in the upper or lower half‑plane.

The study is extended to asymmetric configurations where the slab consists of two layers with different refractive indices. Here the eigenvector associated with the zero imposes unequal amplitudes and a specific phase offset between the two ports, enabling highly asymmetric coherent control: one side can experience near‑perfect absorption while the opposite side sees little interaction. This demonstrates that CVA can be tailored for directional energy storage.

Beyond the single‑layer case, the authors discuss how their combined time‑domain and spectral‑filtering framework can be generalized to multilayered, inhomogeneous, or metasurface structures, where analytical solutions are unavailable. They argue that complex‑frequency engineering provides a route to emulate virtual gain or loss, access bound states in the continuum, and achieve transient lasing thresholds without actual material gain or loss. Potential applications include ultrafast optical memory, enhanced sensing through transient field enhancement, and dynamic control of nonlinear processes.

In summary, the work provides a thorough temporal analysis of coherent virtual absorption in dielectric slabs, validates the phenomenon with both direct and spectral methods, explores symmetric and asymmetric geometries, and outlines a scalable methodology for more complex loss‑free photonic systems. This advances the understanding of complex‑frequency dynamics and opens pathways for practical energy‑storage and sensing technologies in nanophotonics.