Abstract
Active materials have been explored in recent years to demonstrate superluminal group velocities over relatively broad bandwidths, implying a potential path towards bold claims such as information transport beyond the speed of light, as well as antennas and metamaterial cloaks operating over very broad bandwidths. However, causality requires that no portion of an impinging pulse can pass its precursor, implying a fundamental trade-off between bandwidth, velocity and propagation distance. Here, we clarify the general nature of superluminal propagation in active structures and derive a bound on these quantities fundamentally rooted into stability considerations. By applying filter theory, we show that this bound is generally applicable to causal structures of arbitrary complexity, as it applies to each zero-pole pair describing their response. As the system complexity grows, we find that only minor improvements in superluminal bandwidth can be practically achieved. Our results provide physical insights into the limitations of superluminal structures based on active media, implying severe constraints in several recently proposed applications.
Highlights
Active materials have been explored in recent years to demonstrate superluminal group velocities over relatively broad bandwidths, implying a potential path towards bold claims such as information transport beyond the speed of light, as well as antennas and metamaterial cloaks operating over very broad bandwidths
The fundamental challenge in these experiments, and in related theoretical works, is that active systems are inherently prone to instabilities, and defining the group velocity based on the propagation of a signal through a finite, typically short, distance does not necessarily ensure that the system remains stable when considering arbitrary excitation schemes, propagation over longer distances, or different loading conditions
We derive bounds dictated by stability in the quest to realize superluminal group velocities in active media, inspecting the complex frequency response of these structures, and we describe their implications on the functionality of broadband devices based on these principles
Summary
The bound (2) poses a clear limit to the velocity that a medium can support before large distortions or instabilities kick in, and it must apply to any type of finite excitation in time. This is in contrast with claims that active superluminal structures are physical as long as causal materials are employed. Eq (2), implies stringent constraints on the propagation velocity that a medium can sustain for arbitrary pulse excitation before distortions and nonlinearities necessarily kick in In agreement with this expectation, active structures become unstable as their length is increased[18]. We investigate the response of an active dielectric slab of finite thickness d supporting a single inverted Lorentzian resonance, with relative permittivity εr 1⁄4
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