Experimental and Theoretical Realization of Zenneck Wave-based Non-Radiative, Non-Coupled Wireless Power Transmission

A decade ago, non-radiative wireless power transmission re-emerged as a promising alternative to deliver electrical power to devices where a physical wiring proved to be unfeasible. However, existing approaches are neither scalable nor efficient when multiple devices are involved, as they are restricted by factors like coupling and external environments. Zenneck waves are excited at interfaces, like surface plasmons and have the potential to deliver electrical power to devices placed on a conducting surface. Here, we demonstrate, efficient and long range delivery of electrical power by exciting nonradiative waves over metal surfaces to multiple loads. Our modeling and simulation using Maxwells equation with proper boundary conditions shows Zenneck type behavior for the excited waves and are in excellent agreement with experimental results. In conclusion, we physically realize a radically different power transfer system, based on a wave, whose existence has been fiercely debated for over a century.

generation of standing waves. One may come to a conclusion that this is the meta-material equivalent of the quarter-wave Tesla transformer.
We wish to draw the attention to Zenneck wave(Sommerfeld-Zenneck wave), which resides at the metal-air interface, akin to surface plasmons (SP) and surface waves(SW) 9,10 .
While SP and surface wave (SW) have been widely researched areas in optical physics and metasurfaces, they are relatively less studied in the microwave regime 11,[13][14][15] . Likewise, much research around ZW is focused on the communications and geophysics applications [16][17][18] . Unfortunately, ZW has been surrounded by the controversies regarding their physical existence [20][21][22] . The bulk of the controversy arose from the alleged sign error committed by Sommerfeld in 1909 21,22 . Some authors have shown feasibility of such waves by recreating the critical Seneca lake experiment to debunk the Sommerfeld sign error myth 23 . Quite literally, one does not find any study on the utilization of ZW for nonradiative power transfer. Recently in 2014 and 2017 Sarkar et al, have taken great pains to clarify the confusions arising due to the definitions of SW, SP and ZW through their mathematically rigorous articles 21,22 . The properties exhibited by ZWs are like SW and SP, with certain differences. All these three physical phenomena are transverse magnetic (TM) modes and exhibit evanescent field decay away from the metal-air or metal-dielectric or conductive-dielectric interface. Unlike SW, the ZW come into existence as a result of zero of the TM reflection coefficient. SP come into existence at the quasi-particle levels.
Whereas, ZW propagate in the form of localized charge oscillations. Just like SW and SP, when ZW are excited on metal surfaces, the net flow of current is zero. The Brewster angle of incidence in case of ZW is frequency independent. Therefore, the attenuation of ZW waves is frequency independent and the attenuation rate is slow in the transverse direction 21,22 . They sink into a lossy dielectric media, as mathematically demonstrated by Barlow and Cullens in their classic article 24 . This sinking phenomenon was later ex-3 perimentally demonstrated by Jangal et al and Ling et al 16,25 . Here we demonstrate the physical realization of a ZW non-radiative power transmission using the arrangement of a planar ground backed impedance (GBI) surface and a half wave helical transformer at radio frequency (RF). The GBI structure establishes a TM wave across the metal surface, whereas, the half wave helical transformer drives the voltage across the GBI terminals.
The helical transformer is like the telsa transformer (supplementary information). However, unlike the tesla transformer it does not generate standing waves. It was earlier theorized that an infinite vertical aperture is needed to excite a Zenneck wave and hence was not physically realizable 12 . In our results we demonstrate that, although it is not possible to excite a pure ZW, however, waves with strong ZW like properties can certainly be excited. Thus bypassing the problem of infinite vertical aperture. We also demonstrate that unlike the coupled non-radiative wireless power transmission systems, the presence of leaky metal shields does not affect the power transmission efficiency 2,26 . Moreover, we demonstrate uniform power delivery to multiple receiving units with meaningful efficiency by theory and experiment, as we eliminate the frequency peak splitting issue altogether 7 .
We also demonstrate by arriving at the equation 1, that equi-phases of ZW waves tilt backwards in the air, at the metal-air interface 9,10 . Thus, reminiscent with the title of the article by Jeon et.al. 17 . This article implies that there is a link between SP and ZW's at metal-air interface.
While efficient transmission of non-radiative, wireless power over long distances using earth as a conductor is far from practical realization, it may be possible to utilize already existing metal structures to send guided mode waves for powering electrical devices 1,27,28 .
There exist many practical scenarios consisting of metallic infrastructures, such as nuclear plants, railway tracks, space ships, steel building structures, pipelines, etc. Practical applications include powering Internet of things (IoT) devices, charging for -marine vessels,       smart manufacturing floors, and secured shipping containers [27][28][29] .

Results
Please note, that the experimental setup is described in the section 1 of the supplementary material.
The key concept of this study is presented in Fig.1, the detailed analytical model and solution is presented in the supplementary material(under section: analytical formalism).
The Fig. 1 a, shows the mechanism of Tesla transformer based wireless power transfer system. The primary coil consists of low number of turns, while the secondary has large number of turns(quarter-wave). One end of the secondary is left freely suspended in the air. Sometimes, a toroid is attached to the free end of the secondary to restrict the electric field buildup to prevent discharges. The primary and the secondary coils on both the transmission and the receiving end share the common ground. The generator, which operates as a high frequency AC source, is also grounded to the grid, which is in-turn grounded to the earth.
Approach followed in this study. The Fig. 1 b shows the schematic diagram of the system to excite zenneck waves at metal-air interface. Apart from exciting TM-waves using the GBI resonators at the metal-air interface, we use two critical concepts of Tesla transformer, namely-half wave helical coil (Tesla transformer uses a quarter wave coil), in the secondary to build high potential differences across the terminals of the resonator and grounding the coils to the grid ground, capacitively via the metal. This pulls the reference potential of the metal to the same level as the grid ground. Thus, metal is transformed into a neutral entity 29 .
Half wave helical coil. It is well known that a quarter-wave open ended helical coil when mounted over a planar metal acts as a radiating antenna, notable application-vehicle mounted antennas, where the metal body provides a natural ground for the helical coil loaded antenna. In order to prevent radiation we used half wave helical coil. It is well known that, in the 3 to 40 M Hz range the reception parameters of an electrically small antenna needs improvement. In the supplementary material, the section "Electrical Length" describes the approach followed to address the above parameters in this study, in details. • SW:Corrugated metal structures are needed to increase the refractive index in order to excite SW's. Or an air-dielectric-metal(three layer) interface is needed. Alternatively, inductive surface impedance is needed to excite SW 11,14,18,19,24 .
• SPP and SP: Can not be excited at flat metal-air interfaces, without total internal reflection. Other methods of SPP excitation is based on grooves and near-field highly focused optical beams 11,14,18,19,24 . Equi-phases. The Fig. 1 c, shows the equi-phases generated due to the localized field oscillations on the metal-air interface. The phase velocity of the wave in the metal is faster than the free space, hence a backward tilt with an angle φ is observed, in accordance with 9 .
The angle of tilt has been derived in this work from the 1907's article of Zenneck, which satisfy the Maxwell's boundary conditions: Where, ν = 2π/λ; σ is conductivity; complex permitivitty − j ; and free-space permitivitty 0 . The corresponding φ 0 = 90 − φ, this was also mentioned in 24 .The derivation of the above equation is listed in the supplementary material(S33-S36). In case of metal-air interfaces the quantityφ 0 becomes negative and hence a backward tilt. On the otherhand for air-lossy dielectric this angle is a positive quantity and hence a forward tilt.
Sinking of Equi-phases. Likewise, in the Fig. 1 d, the equi-phases undergo a forward tilt and subsequent sinking when they encounter a lossy dielectric 16,24,25 . Hallmark of Zenneck waves. The ZW properties of the proposed system have been experimentally observed and are presented in Fig.2. The resonator system is shown in the Fig. 2 a, dimensions and parameters are presented in the supplementary material( Fig   S 10 and table ST 2). a. Frequency independent slow attenuation rate. The Fig. 2  c. Leaky or partial metal shields. The Fig. 2 e, shows the comparison of measured and simulated results of the transmittance parameters under leaky shielded and non-shielded conditions. The transmittance parameters were observed using the state-ofthe-art vector network analyzer. The FEM model is in good agreement with the measured results. It is observed that the proposed system, unlike the coupled WPT systems, has the ability to perform without any significant efficiency degradation 2,26 . 13 d. Evanescent field/exponential decay. An exponential E-field decay is also observed in the normal direction away from the metal-air interface(listed in Fig. 2  The result listed in Fig.4 a is in the M Hz range. At a first glance, the presented ZW system looks like a capacitive power transfer system. But, this is misleading, we need to look at the details of the phase of the reflectance parameters, when the transmitter is placed in the proximity of the metal. Fig. 4

Discussions
We have demonstrated the excitation of waves on metal surfaces that can be used for delivering electrical power to multiple devices. The waves show slow attenuation property similar to ZW's along the metal-air interface and can be used for efficient powering of devices up to 8 meters using this arrangement. We also show that ZW's can be used for transmitting power across partial metal enclosures. Therefore, the resonator system has the ability to overcome electromagnetic shielding and can be used for powering devices under leaky metal enclosures since the excited waves are non-radiative in nature. Power transmission to multiple receiving resonators with uniform efficiency has also been established experimentally and shows excellent agreement with simulation. The simulation result is compared with coupled mode power transfer system in the supplementary (Fig.   S10). Existing coupled mode WPT systems undergo peak splitting when multiple receiving units are involved. Our study shows that using a wave-based mode of transmission, we can solve this issue. The efficiency of power transmission increases when multiple receiving units are present, as the power is uniformly spread across the metal surface.
This kind of increase, due to multiple receiving units was also observed in a widely followed article, where weakly coupled WPT system is used 33 . The maximum value of E and H-field emitted by the system is 34 % and 89 % lower than the permitted values, regulated by the ICNIRP guidelines at this frequency(Supplementary material Fig. S 12, S 13 and Table ST 3). Thus, this system should not pose as an occupational hazard to human operators. The proposed system has no effect on other devices operating in vicinity(supplementary material demo video links).Since ZW, SW, SP and SPP have an evanescent field, the transceivers need to be in proximity to the interface, on the other hand free space wave bases systems do not have this limitation. However, most free-space wave systems have limitations in power handling, efficiency and can not perform in the presence of leaky shielded environments.