Active Scattering-Cancellation Cloaking: Broadband Invisibility and Stability Constraints

Physical limitations on broadband invisibility based on fast-light media

“…In particular, the resonance frequency ω 0 and the ratio of plasma frequency ω p to ω 0 for this additional resonance should be large with respect to the original two inverted Lorentzian resonances, in order for the refractive index of the cloaking material to remain approximately dispersionless and between zero and unity in the frequency range of interest. This modified, causal, material dispersion, however, typically leads to an unstable scattering response 18 , characterized by the onset of unbounded temporal oscillations (corresponding to unstable scattering poles), as shown in Fig. 2 c, d and the Supplementary video .…”

“…In the context of cloaking, gain media, fast-light media, and so-called non-Foster circuits (active circuits implementing negative resistances, capacitances, inductances) have already been proposed, years before ref. 1 , to realize invisibility cloaks that, while not perfect and still constrained by causality, are indeed more broadband and efficient than their passive counterparts 17 , 18 . Yet, there are several limits and design considerations that must be taken into account and deserve further discussion.…”

“…Indeed, the complex wave interactions inside a cloaking structure containing active media may trigger unstable field oscillations under a generic illumination (or just noise), transforming the invisibility cloak into an emitting (lasing) structure, thereby disrupting the entire cloaking functionality. Stability can be ensured with a proper design, but usually at the cost of limiting the operational bandwidth of the cloak and the maximum scattering suppression, as we discuss in 18 . However, no discussion of stability, or of the transient temporal response of the invisibility cloak, is provided in ref.…”

“…Although stability may be ensured by suitably tuning the parameters, for example by decreasing ω 0 and ω p / ω 0 , the refractive index would then become substantially dispersive within the frequency band of interest, which would compromise the cloaking bandwidth considerably. In addition, stability also typically demands a broad linewidth for the inverted Lorentzian resonances 18 , which implies a larger imaginary part of the refractive index within the operating bandwidth, thereby further deteriorating the cloaking performance. As a result, the cloaking bandwidth and the maximum scattering suppression would be limited if causality and stability are both properly ensured, as was shown in ref.…”

“…As a result, the cloaking bandwidth and the maximum scattering suppression would be limited if causality and stability are both properly ensured, as was shown in ref. 18 with physical material dispersion models. Consequently, one cannot simply conclude that an invisibility cloak based on fast-light media can operate “over any desired frequency band, so long as the superluminality condition is attained,” as claimed in ref.…”