Perfect Absorption in the Critically Damped Regime

Abstract

We revisit the conditions for perfect electromagnetic absorption in a homogeneous lossy layer on a reflecting substrate. Using phasor diagram analysis, we demonstrate a fundamental physical similarity between the high-refractive-index limit (classic Dallenbach quarter-wavelength absorbers) and the epsilon-near-zero regime (half-wavelength resonances). In both extremes, perfect absorption relies on long cyclic multipath propagation and gradual amplitude decay. Crucially, we uncover that in the intermediate regime near $n = 1$, this picture changes fundamentally: the trapping efficiency drastically increases, and backscattering is eliminated almost instantaneously within a single round-trip. Using temporal coupled-mode theory, we prove that this low-contrast state minimizes the system's quality factor to a global minimum of $Q \approx 0.69$. This critically damped state mirrors universal highly damped stabilization principles found in acoustics and mechanics, driving anomalous spectral broadening and enabling nearly instantaneous dissipation of ultrashort pulses without time-domain ringing.