Using self-resonant coils in a strongly coupled regime, we experimentally demonstrate efficient non-radiative power transfer over distances of up to eight times the radius of the coils. We demonstrate the ability to transfer 60W with approximately 40% efficiency over distances in excess of two meters. We present a quantitative model describing the power transfer which matches the experimental results to within 5%. We discuss practical applicability and suggest directions for further studies. In the early 20th century, before the electrical-wire grid, Nikola Tesla (1) devoted much effort towards schemes to transport power wirelessly. However, typical embodiments (e.g. Tesla coils) involved undesirably large electric fields. During the past decade, society has witnessed a dramatic surge of use of autonomous electronic devices (laptops, cellphones, robots, PDAs, etc.) As a consequence, interest in wireless power has re-emerged (2-4). Radiative transfer (5), while perfectly suitable for transferring information, poses a number of difficulties for power transfer applications: the efficiency of power transfer is very low if the radiation is omnidirectional, and requires an uninterrupted line of sight and sophisticated tracking mechanisms if radiation is unidirectional. A recent theoretical paper (6) presented a detailed analysis of the feasibility of using resonant objects coupled through the tails of their non-radiative fields for midrange energy transfer (7). Intuitively, two resonant objects of the same resonant frequency tend to exchange energy efficiently, while interacting weakly with extraneous offresonant objects. In systems of coupled resonances (e.g. acoustic, electro-magnetic, magnetic, nuclear, etc.), there is often a general "strongly coupled" regime of operation (8). If one can operate in that regime in a given system, the energy transfer is expected to be very efficient. Mid-range power transfer implemented this way can be nearly omnidirectional and efficient, irrespective of the geometry of the surrounding space, and with low interference and losses into environmental objects (6). Considerations above apply irrespective of the physical nature of the resonances. In the current work, we focus on one particular physical embodiment: magnetic resonances (9). Magnetic resonances are particularly suitable for everyday applications because most of the common materials do not interact with magnetic fields, so interactions with environmental objects are suppressed even further. We were able to identify the strongly coupled regime in the system of two coupled magnetic resonances, by exploring non-radiative (near-field) magnetic resonant induction at MHz frequencies. At first glance, such power transfer is reminiscent of the usual magnetic induction (10); however, note that the usual nonresonant induction is very inefficient for mid-range applications. Overview of the formalism. Efficient mid-range power transfer occurs in particular regions of the parameter space describing resonant objects strongly coupled to one another. Using coupled-mode theory to describe this physical system (11), we obtain the following set of linear equations (1) where the indices denote the different resonant objects. The variables a m (t) are defined so that the energy contained in object m is |a m (t)| 2 , ω m is the resonant frequency of that isolated object, and Γ m is its intrinsic decay rate (e.g. due to absorption and radiated losses), so that in this framework an uncoupled and undriven oscillator with parameters ω 0 and Γ 0 would evolve in time as exp(iω 0 t -Γ 0 t). The κ mn = κ nm are coupling coefficients between the resonant objects indicated by the subscripts, and F m (t) are driving terms. We limit the treatment to the case of two objects, denoted by source and device, such that the source (identified by the subscript S) is driven externally at a constant frequency, and the two objects have a coupling coefficient κ. Work is extracted from the device (subscript D) by means of a load (subscript W) which acts as a circuit resistance connected to the device, and has the effect of contributing an additional term Γ W to the unloaded device object's decay rate Γ D . The overall decay rate at the device is therefore Γ′ D = Γ D + Γ W . The work extracted is determined by the power dissipated in the load, i.e. 2Γ W |a D (t)| 2
Kurs et al. experimentally demonstrated efficient nonradiative power transfer over distance up to 8 times the radius of the coils by using self-resonant coils in a strongly coupled regime after the effort of Nikola Tesla on wireless energy transfer in the early 20th century REF .
Wireless power transfer via strongly coupled magnetic reso- nances
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