Elsevier

Annals of Physics

Volume 323, Issue 1, January 2008, Pages 34-48
Annals of Physics

Efficient wireless non-radiative mid-range energy transfer

https://doi.org/10.1016/j.aop.2007.04.017Get rights and content

Abstract

We investigate whether, and to what extent, the physical phenomenon of long-lifetime resonant electromagnetic states with localized slowly-evanescent field patterns can be used to transfer energy efficiently over non-negligible distances, even in the presence of extraneous environmental objects. Via detailed theoretical and numerical analyses of typical real-world model-situations and realistic material parameters, we establish that such a non-radiative scheme can lead to “strong coupling” between two medium-range distant such states and thus could indeed be practical for efficient medium-range wireless energy transfer.

Introduction

In the early days of electromagnetism, before the electrical-wire grid was deployed, serious interest and effort was devoted (most notably by Nikola Tesla [1]) towards the development of schemes to transport energy over long distances without any carrier medium (e.g. wirelessly). These efforts appear to have met with little success. Radiative modes of omni-directional antennas (which work very well for information transfer) are not suitable for such energy transfer, because a vast majority of energy is wasted into free space. Directed radiation modes, using lasers or highly-directional antennas, can be efficiently used for energy transfer, even for long distances (transfer distance LTRANS » LDEV, where LDEV is the characteristic size of the device), but require existence of an uninterruptible line-of-sight and a complicated tracking system in the case of mobile objects. Rapid development of autonomous electronics of recent years (e.g. laptops, cell-phones, house-hold robots, that all typically rely on chemical energy storage) justifies revisiting investigation of this issue. Today, we face a different challenge than Tesla: since the existing electrical-wire grid carries energy almost everywhere, even a medium-range (LTRANS  few∗LDEV) wireless energy transfer would be quite useful for many applications. There are several currently used schemes, which rely on non-radiative modes (magnetic induction), but they are restricted to very close-range (LTRANS « LDEV) or very low-power (∼mW) energy transfers [2], [3], [4], [5], [6].

In contrast to all the above schemes, we investigate the feasibility of using long-lived oscillatory resonant electromagnetic modes, with localized slowly-evanescent field patterns, for efficient wireless non-radiative mid-range energy transfer. The proposed method is based on the well known principle of resonant coupling (the fact that two same-frequency resonant objects tend to couple, while interacting weakly with other off-resonant environmental objects) and, in particular, resonant evanescent coupling (where the coupling mechanism is mediated through the overlap of the non-radiative near-fields of the two objects). This well known physics leads trivially to the result that energy can be efficiently coupled between objects in the extremely near field (e.g. in optical waveguide or cavity couplers and in resonant inductive electric transformers). However, it is far from obvious how this same physics performs at mid-range distances and, to our knowledge, there is no work in the literature that demonstrates efficient energy transfer for distances a few times larger that the largest dimension of both objects involved in the transfer. In the present paper, our detailed theoretical and numerical analysis shows that such an efficient mid-range wireless energy-exchange can actually be achieved, while suffering only modest transfer and dissipation of energy into other off-resonant objects, provided the exchange system is carefully designed to operate in a regime of “strong coupling” compared to all intrinsic loss rates. The physics of “strong coupling” is also known but in very different areas, such as those of light-matter interactions [7]. In this favorable operating regime, we quantitatively address the following questions: up to which distances can such a scheme be efficient and how sensitive is it to external perturbations? The omnidirectional but stationary (non-lossy) nature of the near field makes this mechanism suitable for mobile wireless receivers. It could therefore have a variety of possible applications including for example, placing a source (connected to the wired electricity network) on the ceiling of a factory room, while devices (robots, vehicles, computers, or similar) are roaming freely within the room. Other possible applications include electric-engine buses, RFIDs, and perhaps even nano-robots.

Section snippets

Range and rate of coupling

The range and rate of the proposed wireless energy-transfer scheme are the first subjects of examination, without considering yet energy drainage from the system for use into work. An appropriate analytical framework for modeling this resonant energy-exchange is that of the well-known coupled-mode theory (CMT) [8]. In this picture, the field of the system of two resonant objects 1 and 2 is approximated by F(r, t)  a1(t)F1(r) + a2(t)F2(r), where F1,2(r) are the eigenmodes of 1 and 2 alone, and then

Influence of extraneous objects

Clearly, the success of the proposed resonance-based wireless energy-transfer scheme depends strongly on the robustness of the objects’ resonances. Therefore, their sensitivity to the near presence of random non-resonant extraneous objects is another aspect of the proposed scheme that requires analysis. The appropriate analytical model now is that of perturbation theory (PT) [8], which suggests that in the presence of an extraneous object e the field amplitude a1(t) inside the resonant object 1

Efficiency of energy-transfer scheme

Consider again the combined system of a resonant source s and device d in the presence of a set of extraneous objects e, and let us now study the efficiency of this resonance-based energy-transfer scheme, when energy is being drained from the device at rate Γwork for use into operational work. The coupled-mode-theory equation for the device field-amplitude isdaddt=-i(ω-iΓd[e])ad+iκ[e]as-Γworkad,where Γd[e]=Γd[e]rad+Γd[e]abs=Γd[e]rad+(Γdabs+Γd-eabs) is the net perturbed-device loss rate, and

Conclusion

In conclusion, we present a scheme based on “strongly-coupled” resonances for mid-range wireless non-radiative energy transfer. Although our consideration has been for a static geometry (namely κ and Γe were independent of time), all the results can be applied directly for the dynamic geometries of mobile objects, since the energy-transfer time κ−1 (∼1–100 μs for microwave applications) is much shorter than any timescale associated with motions of macroscopic objects. Analyses of very simple

Acknowledgments

We thank Prof. John Pendry and L.J. Radziemski for suggesting magnetic and acoustic resonances respectively, and Prof. Steven G. Johnson, Prof. Peter Fisher, André Kurs and Miloš Popović for useful discussions. This work was supported in part by the Materials Research Science and Engineering Center program of the National Science Foundation under Grant No. DMR 02-13282, by the US Department of Energy under Grant No. DE-FG02-99ER45778, and by the Army Research Office through the Institute for

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