# Two-Wire Power Line Microwave Communication Using Low-Loss Modes
## 1 Background  
The propagation of a low-loss surface wave on an open waveguide consisting of a single lossy conductor in free space was investigated by [PERSON] in 1899 and later, in 1907, extended to the case of dielectric-coated conductors by [PERSON] [1; 2; 3]. In 1950, [PERSON] described the mode as a means of facilitating \"wide-band long-distance communication\" [4; 5]. That work resulted in the identification of discrete propagation modes for lossy conductors, dielectric-coated conductors or other conductors with appropriately modified surfaces, as discussed by [PERSON] [6] (pp. 718-720). Of interest, presented here is the Sommerfeld-Goubau (SG) mode on a bare lossy conductor. In the early 1950s, a significant amount of work was reported by [PERSON] et al. and [PERSON] concerning the development of launchers for exciting this mode as well as investigations of environmental impacts, such as rain, snow and ice and the effects of bends on attenuation [4; 5; 7; 8; 9]. The launcher design work was heuristic and focused on matching the transverse variation of the source field to that of the SG mode. Coated wires were of special interest since the coating results in a more rapid decay of the field around the conductor, and experimental launchers for these modes were reported. At about the same time, [PERSON] studied the transition of quasi-TEM waves on a wire above earth to the SG mode as the frequency increased into the microwave region [10; 11]. Little additional work on this mode was reported until 2004, when [PERSON] and [PERSON] suggested its use in the terahertz frequency range as a lower-loss waveguide than either metallic tubes or optical fibers. Specifically mentioned were spectroscopy, sensing and imaging applications but not communications [12]. In 2006, [PERSON] discussed the possibility of low-loss transmission and the capability for transmitting high power in the millimeter-wave or terahertz frequency ranges [13]. The specific idea of using the SG mode for wide-bandwidth open-waveguide communication on power lines was introduced by [PERSON] in 2009 [14; 15; 16]. This was followed in 2016 by an announcement from AT&T concerning a project to use SG-modepropagation on power lines for broadband communication [17]. Interest in the area of broadband communication using this mode of propagation continues. For example, [PERSON], [PERSON] and [PERSON], reported a model for estimating channel capacity for open waveguides constructed from lossy conductors [18]. In the past, a great deal of work has been conducted concerning the problem of exciting currents on infinite wires with and without loss when using voltage sources [19; 20]. However, voltage sources are not appropriate for communication along energized electric power lines since a high-frequency source cannot be inserted into the line. Hence, field coupling is the only option. While research on designing SG-mode launchers was conducted in the 1950s, its emphasis was on dielectric-coated wires, given their more rapid transverse decay of fields. A complete solution for induced current consists of both SG mode current and a current relating to the continuous spectrum of radiation modes. In 1964, a more rigorous theory for the excitation of the SG mode using a ring source of magnetic current (identical to a voltage source for the ring radius equal to the conductor radius) surrounding an infinite lossy conductor was reported by [PERSON] and [PERSON] [21]. In addition to the SG mode current, they calculated the radiated fields using steepest descent integration (SDI). Unfortunately, calculating these radiated fields is not equivalent to calculating the current due to the continuous spectrum. This is because for field points near the conductor, the simple form of SDI in [21] is not accurate since the SG pole is close to the saddle point [6]. Because this field is needed to calculate the current via Ampere's law, the current cannot be determined accurately. Hence, Ref.