Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects

Abstract

We show that the difficulty of cloaking is fundamentally limited by delay-loss and delaybandwidth/size limitations that worsen as the size of the object to be cloaked increases relative to the wavelength, using a simple model of ground-plane cloaking. These limitations must be considered when scaling experimental cloaking demonstrations up from wavelength-scale objects.PACS numbers: 78.67. Pt, 42.81.Dp We will argue that the problem of cloaking becomes intrinsically more difficult as the size of the object to be cloaked increases compared to the wavelength, and is ultimately limited by fundamental considerations involving the delay-bandwidth and delay-loss products, even for ground-plane cloaks [1][2][3] where bandwidth is not limited by causality constraints. The difficulty is greatest for cloaking objects many wavelengths in diameter (unlike experiments cloaking wavelength-scale objects [3][4][5][6][7][8][9][10][11]), but unfortunately this is the most useful regime for resolving an object of interest. We illustrate these limitations with an idealized one-dimensional (1d) system in which cloaking is much simpler than in three dimensions (3d)-only one incident wave need be consideredbut in which the same limitations appear. We argue that the results and conclusions from this simplified model apply even more strongly to 2d and 3d, and are consistent with recent numerical calculations for 3d cloaks [12]. We conclude that cloaking of human-scale objects is challenging at radio frequencies (RF), while cloaking such objects at much shorter (e.g. visible) wavelengths is rendered impractical by the delay-loss product. Despite the simplicity of this analysis, we arrive at fundamental criteria that may help guide future research on the frontiers of cloaking phenomena.There has been intensive interest in cloaking, both theoretically and experimentally, since the inspiring original papers describing how coordinate transformations, mapped into inhomogeneous materials ("transformation optics") [13] could theoretically render an object invisible [14,15]. Since then, many authors have proposed variations on the original cloaking designs [1,2,5,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and there have also been attempts at experimental realization [3][4][5][6][7][8][9][10][11]33]. Most theoretical work, however, has considered only lossless materials. In experiments, significant reductions in the scattering cross-section (partial cloaking) have been demonstrated mainly for objects on the scale of the wavelength, with one recent exception [33] discussed below. Two practical concerns about cloaking have been bandwidth limitations and the impact of losses/imperfections, and we argue that these two difficulties become fundamentally more challenging as the size of the object to be cloaked increases.Pendry pointed out that perfect cloaking in air/vacuum is impossible over nonzero bandwidth, because rays traveling around the object must have velocity > c to mimic empty space [14]; this can be interpreted...

General scaling limitations of ground-plane and isolated-object cloaks

“…Although there have been several experimental demonstrations of ground-plane cloaking [6][7][8][9][10][11][12][13][14][15], as well as theoretical investigation of several variations on the underlying idea [16][17][18][19], we previously argued using a simple one-dimensional model system that the difficulty of ground-plane cloaking must increase proportional to the thickness of the object being cloaked [4]. In this paper, we generalize that simple argument to a rigorous proof for arbitrary cloaking transformations in three dimensions.…”

Macroscopic Invisibility Cloak for Visible Light

“…Any object smaller than this steel wedge can be alternatively adopted. Since this design aims at invisibility in a transparent medium with refractive index close to n = 1.57, a value similar to the background refractive index in [9], it is not subject to the limitations of delay-bandwidth and delay-loss for cloaking in air [20].…”

Electrodynamics of transformation-based invisibility cloaking

“…Note that macroscopic cloaking still complies with the delay-bandwidth and delay-loss limitations in Ref. 88, which can serve as guidance for the design and implementation of practical cloaking.…”