International Journal of Antennas and Propagation

Volume 2016, Article ID 6184959, 5 pages

http://dx.doi.org/10.1155/2016/6184959

## Observation of Zenneck-Like Waves over a Metasurface Designed for Launching HF Radar Surface Wave

^{1}ONERA-The French Aerospace Lab, 91123 Palaiseau Cedex, France^{2}Sorbonne Universités, UPMC University of Paris 06, UR2, L2E, 75005 Paris, France

Received 4 May 2016; Revised 2 September 2016; Accepted 18 September 2016

Academic Editor: Weimin Huang

Copyright © 2016 Florent Jangal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Since the beginning of the 20th century a controversy has been continuously revived about the existence of the Zenneck Wave. This wave is a theoretical solution of Maxwell’s equations and might be propagated along the interface between the air and a dielectric medium. The expected weak attenuation at large distance explains the constant interest for this wave. Notably in the High Frequency band such a wave had been thought as a key point to reduce the high attenuation observed in High Frequency Surface Wave Radar. Despite many works on that topic and various experiments attempted during one century, there is still an alternation of statements between its existence and its nonexistence. We report here an experiment done during the optimisation of the transmitting antennas for Surface Wave Radars. Using an infrared method, we visualize a wave having the structure described by Zenneck above a metasurface located on a dielectric slab.

#### 1. Introduction

In 1907, Zenneck was aiming to explain Marconi’s experiments on transatlantic propagation [1]. Since ionization of the atmosphere was mainly thought as the result of Earth radioactivity and was limited to ten kilometers or so [2], Zenneck logically stated that the ionization of the atmosphere could not explain Marconi’s results [1]. He assumed that transatlantic propagation was due to the creation of a new kind of electromagnetic wave which was propagated along the interface between the air and the ground. Zenneck claimed that this wave was a valid solution of Maxwell’s equations and had the main features of a confined wave. Moreover it might have low attenuation along the interface. Two years later, Arnold Sommerfeld confirmed, with a more rigorous approach, that the Zenneck Wave (ZW) was a solution of the Maxwell equations [3]. The controversy then started since the mathematical solution proposed by Sommerfeld was questionable [4, 5]. Among several arguments, a sign mistake was pointed out. This mistake led to the conclusion that the ZW was a calculus artefact and could not exist. Moreover, it froze the discussion in the mathematical domain and kept it aside the physical aspects [6, 7]. As time goes by, according to mathematical approaches, an abundant terminology has been built to name the confined waves which can be propagated at the interface between two materials [8–12] and the ZW has remained a theoretical object. In this context, the main criticism is dealing with the excitation of the ZW. Indeed, the generation of a sole ZW requires a source of infinite dimension or a finite, but unphysical, phase lens. Those points could reinforce the idea that the ZW is a nonphysical solution [13, 14].

Thereby, many interpretations and beliefs have arisen about the ZW. Today, it is difficult to discern the way to provide a proof regarding its existence [15, 16] or nonexistence [17, 18]. Nevertheless, the wave excited over an air/ground interface is a main issue for High Frequency (HF) Surface Wave Radars (SWR). The HFSWR can take advantage of low loss propagation along the interface. Hence, understanding the Zenneck Wave issue may allow improving the radar coverage by increasing the energy propagated along the ground.

It is well known that to deal with the complexity of wave excitation at air/ground interface we need to use negative permittivity and permeability materials [19]. This is the reason why we are using such materials.

In the next section we recall some theoretical aspects of the Zenneck approach. In Section 3 the measurement results are described. At last, Section 4 contains concluding remarks.

#### 2. Theoretical Approach

##### 2.1. The Zenneck Wave

More than one century ago, Zenneck himself has suggested some clues to better understand his assumption about the existence of a low loss Surface Wave. Nevertheless, he noticed that the phase speed of this wave exceeded the speed of the light. But, as recalled by Ling et al., the group velocity of the ZW along the interface never exceeds the speed of the light, whatever the phase velocity is [1, 20]. Zenneck also remarked that the propagation vector was tilted toward the dielectric medium. As a result, the equiphase planes and the orthogonal equimagnitude planes are also slanted by comparison with the case of propagation above a perfect electric conductor [21, 22]. The ZW can be represented using notably the formulation of James Wait [5] if a negative permittivity material is chosen for the ground as suggested in [19]. The excited wave is tilted towards the interface. Hence it seems to sink inside the lower dielectric medium (Figure 1). It also differs from the leaky waves by the tilt angle, since leaky waves are growing as they propagate and seem to rise away from the dielectric [19].