A perfectly matched layer absorbs all incoming waves without reflection — regardless of frequency, polarization, or angle of incidence. It's the ideal absorber, the electromagnetic equivalent of a black body. In computational electromagnetics, perfectly matched layers (PMLs) are mathematical constructions used to terminate simulation domains: they absorb the outgoing waves so the simulation behaves as if the domain extends to infinity. In physics, achieving a PML requires either materials with exotic properties (negative refraction, gain-loss balance) or geometries that convert wave energy to heat through gradual impedance matching.
Iplikçioğlu (arXiv 2602.23347, February 2026) shows that a temporal metamaterial — a medium whose permittivity and permeability are switched simultaneously and passively in time — acts as a one-dimensional perfectly matched layer. The absorption is not spatial (the material doesn't have a gradient profile in space). It's temporal: the material properties change in time, and the time variation generates effective conductivities that dissipate wave energy.
The mechanism works through impedance matching. When both permittivity and permeability are switched simultaneously, the impedance — the ratio of the electric and magnetic fields — can remain matched to free space throughout the transition. A wave entering the temporal metamaterial sees no impedance discontinuity and therefore generates no reflection. But the time-varying material parameters create effective electric and magnetic conductivities that absorb the wave's energy. The wave enters without reflection and is absorbed without transmission. This is what a perfectly matched layer does.
The result exceeds the Rozanov bound — a fundamental limit on how thin a passive absorber can be while absorbing all radiation above a certain frequency. The Rozanov bound applies to spatial absorbers with fixed material properties. A temporal metamaterial circumvents it because the bound's derivation assumes time-invariant materials. Changing the material in time opens a degree of freedom that static absorbers don't have.
An approximate matching condition is derived for the case where permittivity and permeability are not switched exactly simultaneously — asynchronous modulation. Small timing mismatches introduce reflections, but the matching condition specifies the acceptable tolerance. Full-wave simulations validate the analytical predictions.
The concept extends to two dimensions: a temporal PML that absorbs waves propagating in a plane, not just along a single direction. This would provide a physical realization of the computational PML that has been used as a mathematical convenience for three decades.
The absorber has no structure — no gradient, no layers, no resonances. The absorption is in the timing.