Experimental Realization of Zenneck Type 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 impracticable. However, conventional “coupling-based” approaches face performance issues 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 non-radiative waves over metal surfaces to multiple loads. Our modeling and simulation using Maxwell’s 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 class of power transfer system, based on a wave, whose existence has been fiercely debated for over a century.


Experimental setup
The Fig. S 1 shows the experimental setup used in this study.

Electrical Length: Half Wave Helical Transformer
Throughout 2015-18, authors conducted the experiments to study the voltage oscillation across the GBI resonator system. One such experiment carrying out power transfer across 80 mm metal wall can be seen in fig. S 2. This experiment uses the ground plate and wire arrangement to sustain a meaningful voltage oscillation across the terminals of the load (40 watts halogen).
Based on the experimental findings shown in fig. S 2, the authors tried to replace the equivalent RLC lumped elements(unsuccessfully so). The reasons behind the failure of RLC lumped elements based counterpoise were carefully and qualitatively investigated, through a series of experiments. It was observed that the planar structure of the receiver was unable to sustain a significant value of voltage and current. The gap between the mesh and ground layer is g=1.5 mm. At a target frequency of 27M Hz, g << λ/4. The largest dimension of the transceiver system is A x = 150 mm, which is << λ/2π = 1767mm at target frequency of 27M Hz. Thus, the proposed receiver in its present form is electrically  [1,2]. It has been observed that the dimensions of the lumped RLC elements become the part of the over all electrical length of the antenna beyond 900M Hz [3,4]. However, in the HF regime, the dimensions of the RLC elements can not provide the appropriate electrical length. Electrically small antenna's have poor radiation efficiency, which in turn also hinders the receiving capabilities of high frequency antennas [1,2]. However, the radiation efficiency of the receiving antennas can be improved. As per the standard definition the GBI structure is an electrically small antenna ka << 1 [1,2]. Based on the analysis presented in [2] the quarter wavelength counterpoise is like a mono pole. One such reading of current and voltage values along the length of the quarter wavelength wire counterpoise is listed in table 1. However, this is not a practical dimension for the purpose of power transmission. A multi turn helical alternative would be a better choice. The radiation resistance in this case is related to the area, A loop of a helical loop of N turns by [1,2]: Attaching a multi-turn helical electrical conductor to one of the copper elements of the GBI resonator would simply change the resonance conditions [5,6]. In order to prevent the change of resonant conditions and to drive the reference voltage of the GBI structure to a high level, the half wave helical coil was incorporated in the tesla transformer fashion. Let us first review Sommerfeld's analytical formalism. Retaining the notation as suggested by Sommerfeld [14]; let ω be the frequency in radians, k = 2π/λ = ω/c be the wavenumber and c be the speed of light. Their corresponding relation with the Hertzian potential: From the electrodynamics point of view, Hertzian potential is a vector and now on shall be denoted by − → . The proposed system is electrically small and hence, the current carried by the antenna has no phase variations on the primary side of the helical coil and the GBI structure. Please note, there will be no current carried by the secondary helical coil, as it is in principle an open-circuit. As shown in Fig. S 4, the interface between metal and free space exists as Z = 0. The tangential E field component would be zero in accordance with Maxwell's equation [8]: This is satisfied by combined effect of the dipoles with their corresponding mirror images formed in the metal as shown in the Fig. S4. Sarkar et al. also used Schelkunoff integrals for images formed in imperfect earth [8,9]. Evidently, there are two kinds of dipoles which need to be considered in the case at hand.
1. Vertical dipole, originating from the primary coil at a distance h above z = 0. Leading to expression for the vector potential: In the Fig. S4, the term HU C v denotes the hypothetical unit charge at Z = 0, thus resulting to a force in the Z direction. The E tang = 0.
2. The Horizontal dipole arising from the GBI structure can be expressed by: The horizontal dipole forms a hypothetical unit charge, denoted by HU C h , resulting into a force in the Z direction and thus causing the E tang = 0.
3. If one applies a limit h → 0, then the vertical dipole results in a = 2.e ikR /R, while horizontal dipole's vector potential vanishes. In the present case, we have placed the resonator system at a distance of h = 0.001mm. Its, contribution to the directional characteristic is considered for the final evaluation.
4. Therefore, the generalized forms of the equations S4 and S5, with amplitudes A and B can be expressed as: The horizontal dipole can be expressed as a quadrupole as: The complex refractive index n for the metal is related as: where σ is the conductivity and 0 and are the free-space permittivity and relative permittivity, respectively. The wavenumber in the free-space (k) and the metal (k M ) can be related as:

Three regions in the interface
The height of the location of the Hertzian dipole is denoted by h as mentioned earlier.
There are three distinct regions to be considered for the analysis.

Region-I: z > h (Conducting Earth-Air interface)
In the analysis by Sommerfeld on the problem of dipole over arbitrary ground with finite conductivity, it was assumed that in addition to a primary stimulus originating from the antenna at r = 0 and Z = h, there exists a secondary stimulus, due to localized charge oscillations in the earth. Dealing with the problem in the cylindrical polar coordinates (r, φ, z), we shall use the eigenfunctions u and eigen values Λ.
Where, F (Λ) is the undetermined spectral distributions in the Λ-continuum of the eigenfunctions. The quantity, j 0 is the Bessel's function. The quantities u = j 0 (Λr) cos M z and k 2 = Λ 2 + M 2 .

Region-II: h > z > 0 (Air)
The primary and secondary stimulus exists in this case as well, represented by the analytical relations similar to S10: The equations S10 and S11 follow continuity behaviour of the field at the boundary for an arbitrary F (Λ).

Region-III: 0 > z > −∞ (Earth)
There would be no primary stimulation in this case; the field denoted by M must be continuous throughout.
The equations S11 and S12 satisfy the Maxwells boundary conditions of continuity, their resulting relation would be(region II and region III): (S13) The first term on the LHS of the equation S13 is the prim and the second term is sec from the equation S11. The RHS is the S12 multiplied by n 2 which comes from equation S8. Solving the above equations in the complex plane as shown in Fig. 5, results in the four Riemann sheets(Λ = k and Λ = k M ) and simplifying in their bessel function form, we get the Hankel function of type 1 and 2: Substituting = Λr the equation S14 becomes: Notice, only the Hankel function of the first type remains. Integration through the path w 1 and w 2 , we obtain the following integral: is an arbitrary function of Λ 2 . Thus, the real integral has been converted into a complex integral closing at infinity. Thus the solution for the primary stimulation: It is evident from the fig. 5,in the positive imaginary half plane, the Hankel function of the first order H 1 (Λr) vanishes at infinity. The path of integration avoids the loops Q We have three components Q,Q M and p, the contribution of Q M can be safely ignore for the large values of |k M | because the Hankel function decays exponentially at large distances from the real axis. By applying method of residues and setting up the relationship one arrives at the following new relations for the vector potential: Finally the above equations can be written in a modified form for a wave: Non-resonant field Partial Radiation Guided mode propagation Where, A is a slowly varying amplitude factor, the equation S21 and S22 describe the Zenneck waves, which were originally proposed by Jonathan Zenneck in 1907.

Controversy
There are several controversies pertaining to the above analysis. Especially, the placement of the pole "p". Evident from Jangal et al. "...the location of the pole "p" with respect to the integration path determines the kind of the excited Surface Wave." [13] Where,Z s is the complex surface impedance of the dielectric. Furthermore, the following equation obtained by Jangal et al. points to the center-stage of exact controversy [13]: Take a note that the first term in the equation S24 is the ZW term (negative term), whereas the second term is the an equally contributing term with a positive term [13].

Analysis for Metals
Re-writing the Original Sommerfeld integral in the form suggested in ??, the Hertzian integral for reflected wave from the homogeneous media from the filled half space. For convenience, let us also rewrite k and k M as k 1 and k 2 : Here, R(Λ) is the coefficient of reflection, also represented by Γ(λ) in several published text and is defined as: The roots to the equation S26 would give rise to 4 Riemann sheets in the complex plane, namely As per equation S27; only permissible Riemann sheet is the sheet 1. On this sheet the numerator of equation S26 or the zeros are known as the Brewster zeros.
The permittivity of metal be represented as a complex quantity of the form: = − j ; as per [15].

ICNIRP field compliance
One of the critical questions is the occupational hazard exposure from the proposed system, if used on board marine vessels, smart shipping containers and home IOT device   charging. Therefore, it was necessary to test the international commission for non ionizing radiation protocol compliance of the proposed system. The state-of-the-art Narda field measurement analyzer was used to record the E and H-field values across the spectrum of 1M Hz to 30M Hz. The power fed into the transmitter was 65 watts. The fig.S 10 shows one of the several chosen position of the probe, which recorded maximum field intensities at the receiver and the edge of the metal. Fig.S 11, shows the recorded values of the Narda field test analyzer measurements. As per the ICNIRP regulation, between 10 M Hz and 400 M Hz the maximum permissible value of E -field is 61 V /m [21]. The maximum permissible regulatory value for H-field 0.16 A/m. The measured values of E and H-field in the proposed system is 40.3 V /m and 0.018 A/m, respectively, at 13.3M Hz. Implying, that the proposed system generates a maximum E-field of 33.9 % and H-field of 88.7 % lower than the regulation. Hence, the proposed system is safe for operation for human operators [21]. Table ST 3

Multiple Receiver Capability
Power was transmitted along a 8 m metal sheet, the receivers were placed in various arbitrary configurations. The power reception was uniform despite of the configuration. However, beyond 8 m, a marginal degradation in power reception of the farthest receiver with respect to transmitter was observed. The table ST 4 lists the power transfer metrics for multiple receivers. Both the receivers show approximately the same power reception capabilities. However, as compared to single transmitter-receiver power transfer efficiency, the 1 transmitter to 2 receiver efficiency sees an increment from 51.4 % to 66 %. The table ST 5 shows the multi receiver capability at 15 m, the overall efficiency is 22%. Beyond this range, the power transfer drops below 10%. With proper optimization of thickness of coils and spacing, one can obtain higher values of power transfer range.

Effect on other devices in vicinity
In the previous sections it has been pointed out that, other devices in vicinity have to be of electrically comparable lengths, apart from being resonant. A Samsung Galaxy Note 5 mobile phone was used as a test device (with an inbuilt wireless charging receiver unit, tuned at 13.3M Hz). The mobile phone was kept on the metal sheet, 25 W atts of power was fed into the transmitter side at 13.3M Hz and 27 M Hz. The wireless receiver unit of the phone was unable to pick the power. It was found that the phone's functioning was normal, with normal touch screen response times and internet access. See the video in the supporting information. Two more test subjects were chosen, which included a table lamp with an LED bulb and a 13 inch laptop (laptop was kept in ON status). Both the test devices were subjected to 50 watts of transmitter power. None of the test devices showed any abnormal behavior.  the helical coil counterpoise plays no role in the power transmission through radiation. As claimed earlier, the helical coil counterpoise drives the receiver terminals to a high voltage. Therefore, the proposed system is non-radiative [16,17,18,19,20].

Background of Wave Based Approaches
We will briefly take a note of other µ-wave approaches, which are either under development or have been commercialized. The wave based approaches can be broadly classified according to their applicationsenergy harvesting and transmission-reception. The former case lead to the development of the concept of rectenna(rectifier-antenna). The later case saw the usage of magnetron, as most of the said systems were developed in the frequency regime of 2.45 to 5.8 GHz.
The antenna of a rectenna system receives the electromagnetic energy emanating from the surrounding systems, e.g. stray WIFI or mobile phone communication signals. The high frequency rectifier circuit converts the incoming wave and directs the rectified current to charge the batteries or load [23,24,25].  [23] 60 mW 39 mW 65 % efficiency achieved in milliwatts Not useful for high power applications [24] 10 KW 5 kW 50 % efficiency 1.2 meters range No comment on misalignment issue [25] 35 dBm or 3.16W 3 dBm or 2mW 0.063 % efficiency in any case the maximum power received by Rx is very less [26] 27 dBm or 0.5W -10 dBm or 1µW Threshold limit was set to 1µW as per regulations In any case efficiency 0.00027% [27] 39 dBm or 7.94W 22.02 dBm or 0.16 W Efficiency 2% received current of 40 mA, not suitable for fast charging [28] 220 W DC-RF max 75 % No information on received RF power under question is 2.45 and 5.8 GHz. Besides the efficiency and power handling capability is far below the presented ZW system. However, one does find an exception in the form of [24], where the power handling capability is 10 kW . The presented ZW system has thick copper components and litz wire. The ZW system in its present form can easily handle upto 3kW . The dielectric materials can be replaced by air to increase the power handling capabilities to 20 kW and beyond. As listed in table ST 8, the same issue of extremely low power handling continues. These kind of systems can not handle anything beyond 5 watts of power. There is one similarity between Noda & Shinoda's work and the presented ZW wave concept. Both these systems are capable of handling multi receivers. This is essentially due to the fact that the said systems do not exhibit strong coupling.
As listed in table ST 9, MPT has been utilized for robots inside metallic pipelines. The initial attempts seemed to have failed due to losses arising due to multipath issues created due to the network of pipelines. This is an understandable problem. Its important to have  [32] 2 W 80mW 4 % efficiency, a preceding article of [29,30,31].  [33], [34] --Initial attempts to charge a robot system ran into problems due to uncertainties arising in multi-pipe transmission of radiowaves [35]- [37] --100 mW range, very low power a loosely guided wave in these scenarios and hence, the ZW system can easily resolve this issue. The key is to go beyond 6 GHz for the ZW system.
As per the articles [35]- [37] the issue is the low power handling capabilities. The article does not mention, how they are going to charge a 10 kW electric vehicle using 100 mW received power.
The published articles [38,39] pertain to use of ventilator ducts as waveguides. The ZW system does not need such a closed boundary conditions. Besides, the power handling capabilities of ZW are comparable to the listed systems in table ST 10, the efficiency of the concept prototype of the ZW system performs at par with the listed systems.
By this time, this is absolutely clear that the proposed ZW system can not be com-  Moreover, this is a far-field system [40] 5 W -Max received power 65mW far-field system Listed in table ST 12 is the MPT using beam forming techniques. This is a totally different concept and in its published form, can not be applied to dynamic vehicle charging. However, in far-field region, this technique would be useful [41,42]. In the published articles listed in the table, the vehicles are being charged when they are stationary. Once again, ZW system has distinct advantages over this kind of a system, since ZW is a propagating wave at the interface. Therefore, a single metal line can run across the highway and the mobile vehicle can extract power from the metal line. Other dynamic charging systems employ copper coils embedded in the roads, e.g. OLEV system from KAIST, Korea.
In conclusion, the proposed ZW system is based on a completely different concept, frequency regime and application. It would not be appropriate to draw a comparison among the various wave based systems. Also, we would be indulging in a great disservice to the research community and technologies by claiming that ZW system is "superior". In a fair unbiased light, ZW system has a unique set of properties and have a unique set of applications. Same is the case for MPT based systems.

On Iso-Phases and Iso-Amplitudes
Zenneck in his 1907 paper mentions about relationship of vertical electric field and horizontal electric field and the angle of tilt of the Iso-Amplitudes. The relationship for E-fields in the Air,(the Y and Z axis is defines as per the Fig S13): where, q 0 = ν 0 /σ and q = ν /σ. Where, ν is the wave number, 0 is free space permitivitty , is relative permitivitty and σ is conductivity. For conductors the relationships were given as: Zenneck showed the angle relationship using the elliptical diagram as shown in Fig. S 13a as: As per Zenneck, drawing only half the ellipse diagram each in air and conductive surface the

Material properties and Tilt?
As evident, for a Lossy dielectric the tilt of modes is forward or in the direction of the propagation. For the case of dielectric with higher conductivity the tilt angle is lower as compared to lossy dielectric at a carefully selected conductivity and dielectric constant the tilt would be zero as is the case shown in Fig. 13 b, this also is the case for Surface waves. Therefore, a pure or efficient surface wave mode is excited at inductive impedance structures or corrugated metal surfaces of comparable wavelengths.
But, when the conductive surface is a noble metal such as aluminium, then the conductive σ = 3.8 × 10 −7 S/m. As per the drude's model the real part of complex permitivitty is negative. However, the imaginary part which is controlled by the σ becomes dominant in the M Hz regime [43].
Therefore, in equation S29; by substituting with − j we get: