## Invented by James F. Corum, Kenneth L. Corum, Basil F. Pinzone, Jr., Joseph F. Pinzone, Quantum Wave LLC

## The Quantum Wave LLC invention works as follows

Disclosed are hybrid communications in which a message from guided surface waves probe nodes is embedded into a surface wave and a message from guided surface waves receiving nodes uses a messaging mechanism that is different.### Background for Hybrid Guided Surface Wave Communication

For more than a century, radio waves have been used to transmit signals using radiation fields that are launched by conventional antenna structures. Electrical power distribution systems of the past century used energy that was guided along electrical conductors, in contrast to radio science. Since the early 1900s, there has been a clear understanding of the difference between radio frequency and power transmission.

To begin with, a few terms will be defined to clarify the concepts that follow. As envisaged in this document, the formal distinction between radiated and guided electromagnetic field is made.

As contemplated in this invention, a radiated field electromagnetic energy is electromagnetic energy that has been emitted by a source structure as waves that aren’t bound to a guide. A radiated electromagnetic is a field, for example, that propagates from an electric structure like an antenna through the air or another medium without being bound to a waveguide. After leaving an electric structure, such as an antena, radiated electromagnetic fields continue to propagate through the medium of propagation until they dissipate. The energy contained in electromagnetic waves cannot be recovered once they have been radiated. If the waves are not intercepted or if the waves are not intercepted then the energy is forever lost. The antennas and other electrical structures are designed in a way that maximizes the ratio between the radiation resistance and the structure loss resistance. Radiated energy is spread out in the space and lost, regardless of whether there is a receiver. Due to geometric spreading, the energy density of radiated fields is dependent on distance. In this sense, the word ‘radiate’ is used. The term “radiate” in all of its forms, as used herein, refers to electromagnetic propagation through this type of radiation.

A guided electromagnetic fields is a propagating wave of electromagnetic energy whose power is concentrated near or within boundaries between media with different electromagnetic properties. A guided electromagnetic field can be defined as a propagating wave whose energy is concentrated within or near boundaries between media with different electromagnetic properties. There is no loss of energy if there is no load that can receive or dissipate energy from a guided electromagnetic field. If there is no load to receive a guided electromagnetic field, then energy is not consumed. A generator or source that generates a guided electromagnetic wave does not produce real power until a resistive load has been presented. In order to achieve this, a generator (or other source) that generates a guided electromagnetic field will essentially run idle until there is a load. It is similar to using a generator to create a 60 Hertz wave and transmitting it over power lines when there is no electrical demand. A guided electromagnetic wave or field is equivalent to what’s called a “transmission line mode.” It is important to note that radiated electromagnetic wave technology requires constant power in order to produce radiated waves. Guided electromagnetic energy, unlike radiated electromagnetic energy, does not continue propagating along a finite-length waveguide even after the energy source has been turned off. The term “guide” is used to describe this transmission mode of electromagnetic propagation. The term “guide” in all its forms, as used herein, refers to the transmission mode of electromagnetic propagation.

Referring to FIG. The graph 100 in Figure 1 shows the field strength (in decibels) as a function distance in kilometers above a arbitrary reference voltage per meter on a log-dB chart to illustrate further the difference between radiated electromagnetic fields and guided ones. The graph 100 in FIG. The graph 100 of FIG. This is the same as the transmission line mode. The graph 100 in FIG. The curve 106 of the radiated field intensity in FIG.

The shapes of curves 103 & 106, for guided wave propagation and radiation propagation respectively, are interesting. The radiated-field strength curve 106 is a straight line that falls off geometrically (1/d where d is the distance). On the other hand, the guided field strength curve (103), has a characteristic exponential decline of e??d/?? The log-log scale shows a distinct knee 109, which is square roots over (d). The intersection point of the guided field strength curves 103 and 106, which is at a crossing range, is at 112. The field strength is much greater for a guided electromagnetic at locations that are closer to the intersection point 112. The opposite occurs at distances greater than crossing distance. The guided and the radiated field strengths curves 103 & 106 illustrate the fundamental difference in propagation between guided and the radiated electromagnetic fields. Milligan, T. Modern Antenna Design. McGraw-Hill 1st Edition 1985. For a discussion on the differences between guided and electromagnetic fields. This is the entire text of 8-9.

The distinction made between electromagnetic waves that are guided and those that are radiated is easily expressed in a formal way and on a rigourous basis. Analytically, it follows that two solutions of such diversity could arise from a single linear partial differential equation – the wave equation. The Green function of the wave equation contains the distinction in nature between guided and radiation waves.

In empty space, wave equations are differential operators whose Eigenfunctions have a continuum of Eigenvalues in the complex wave number plane. The transverse electromagnetic (TEM) field and the propagating fields can be called “Hertzian Waves”. In the presence of conducting boundaries, however, the wave equation and boundary conditions lead mathematically to a representation of wave numbers composed of a continuum spectrum plus a total of discrete spectrums. To this end, reference is made to Sommerfeld, A., ?Uber die Ausbreitung der Wellen in der Drahtlosen Telegraphie,? Annalen der Physik, Vol. 28, 1909, pp. 665-736. See also Sommerfeld, A.?Problems of Radio? Published as Chapter 6 in Partial Differential Equations in Physics, Lectures on Theoretical Physics, Volume VI, Academic Press 1949, pages. 236-289, 295-300; Collin, R. E. “Hertzian dipole radiating over a lossy earth or sea: Some early and late 20th century controversy,?” IEEE Antennas and Propagation Magazine Vol. 46, No. 46, No. 2, April 2004 pp. 2, April 2004, pp. “291-293. Each of these references is incorporated by reference herein in its entirety.

The terms “ground wave” and “surface wave” The terms “surface wave” and “ground wave” identify two distinctly different physical propagation phenomena. Two distinct physical propagation phenomena are identified. Analytically, a surface wave is derived from a distinct polarity that yields a discrete component of the plane wave spectrum. The Excitation of Surface Waves in Planes, for example, is a good place to start. Cullen A. L. (Proceedings of the IEE British, Vol. Cullen, A. L., (Proceedings of the IEE (British), Vol. 225-235). In this context, the surface wave is referred to as a guided surface. In terms of both physics and mathematics, the surface wave in the Zenneck-Sommerfeld sense is not the same thing as the ground waves (in Weyl Norton-FCC sense), which we are all familiar with from radio broadcasting. Both propagation mechanisms are a result of the excitation of discrete or continuous eigenvalue spectrums on the complex plane. As shown by curve 103 in FIG., the field strength of a guided surface wave decreases exponentially as distance increases. The field strength of the guided surface wave decays exponentially with distance as shown by curve 103 of FIG. Branch-cut integrals are the result of Figure 1. C. R. Burrows demonstrated this experimentally in ‘The Surface Wave in radio propagation over Plane Earth’. Proceedings of the IRE Vol. 25, No. 2, February, 1937, pp. The Surface Wave in Radio Transmission (pp. 219-229), and “The Surface Wave” (Bell Laboratories Record, Vol. 2, February 1937). Bell Laboratories Record Vol. 15, June 1937, pp. “Vertical antennas emit ground waves, but do not launch guided surfaces waves.

To summarize, first the continuous part, corresponding with branch-cut integrals of the wave number eigenvalue spectrum produces the radiation field. Second, the discrete spectra and corresponding residues sum arising from poles enclosed by contours of integration result in non-TEM travelling surface waves which are exponentially dampened in the direction opposite to propagation. These surface waves are guided modes of transmission lines. Friedman, B. Principles and Techniques of Applied Mathematics Wiley 1956, pp. pp. 214, 283-286, 290, 298-300.

In free space, the antennas are able to excite the continuum Eigenvalues of the Wave Equation, a radiation field where the outwardly spreading RF energy is lost forever. In-phase will never be recovered. Waveguide probes on the other hand excite discrete Eigenvalues which leads to transmission line propagation. See Collin R. E. Field Theory of Guided Waves. McGraw-Hill 1960, pp. 453, 474-477. Although such theoretical analyses suggested the possibility of launching guided open surfaces over planar or cylindrical surfaces of homogeneous, lossy media, no structures have been known to exist in the engineering arts that could do this efficiently for more than 100 years. Since its inception in the early 1900s, this theoretical analysis has largely remained a concept and no structures have been known to be able to launch open surface guided wave over planar or homogeneous surfaces.

According to various embodiments in the present disclosure, guided surface-waveguide probes that are configured to generate electric fields that couple to a guided surface-waveguide mode on the surface of a losing conducting medium are described. These guided electromagnetic fields are matched substantially in magnitude and phase with a guided wave mode on the lossy medium’s surface. This guided surface wave mode is also known as a Zenneck mode. A guided electromagnetic field is launched on the surface the lossy medium by virtue of the fact the fields generated by the guided waveguide probes are substantially mode-matched with a waveguide surface mode. In one embodiment, the terrestrial medium is used as the lossy conductor medium.

Referring to FIG. The second figure shows a propagation surface that allows for the examination of boundary value solutions of Maxwell’s equations as derived by Jonathan Zenneck in 1907 and published in his paper Zenneck J., “On the Propagation Of Plane Electromagnetic waves Along A Flat Conducting Surface And Their Relation To Wireless Telegraphy”,? Annalen der Physik, Serial 4, Vol. 23, Sep. 20, 1907, pp. 846-866. FIG. FIG. For example, Region 1 could be any lossy conductor. As an example, a lossy medium could be a terrestrial medium like the Earth or another medium. The second medium, Region 2, shares an interface with the first and has different parameters compared to Region 1. The atmosphere, or another medium, can be included in Region 2. This boundary interface’s reflection coefficient is zero for incidences at complex Brewster angles. See Stratton, J. See Stratton, J. 516.

The present disclosure, according to different embodiments, sets forth guided surface-waveguide probes which generate electromagnetic fields substantially mode-matched with a guided surface-waveguide mode on the Surface of the lossy conductive medium comprising region 1. According to different embodiments, these electromagnetic fields can substantially synthesize an incident wavefront at a complex angle Brewster of the lossy medium which can result in zero reflectance.

To explain further in Region 2, where the ej?t fields are assumed and where? “To explain further, in Region 2, where an ej?t field variation is assumed and where? Zenneck’s exact closed-form solution of Maxwell equations that satisfy the boundary conditions at the interface is expressed as the following components for the electric and magnetic fields:

H\n2\n?\n?\n=\nAe\n-\nu\n2\n?\nz\n?\nH\n1\n(\n2\n)\n?\n(\n-\nj\n?\n?\n??\n)\n,\n(\n1\n)\nE\n2\n?\n?\n=\nA\n?\n(\nu\n2\nj\n?\n?\n??\no\n)\n?\ne\n-\nu\n2\n?\nz\n?\nH\n1\n(\n2\n)\n?\n(\n-\nj\n?\n?\n??\n)\n,\nand\n(\n2\n)\nE\n2\n?\nz\n=\nA\n?\n(\n-\n?\n??\no\n)\n?\ne\n-\nu\n2\n?\nz\n?\nH\n0\n(\n2\n)\n?\n(\n-\nj\n?\n?\n? ?\n)\n.\n(\n3\n)

In Region 1, where the ej??t field is assumed, and where z?0 and?0 are present, Zenneck’s closed-form exact solution of Maxwell’s equations satisfying the boundary conditions along the interface can be expressed as follows: Zenneck’s exact closed-form solution of Maxwell equations that satisfy the boundary conditions along an interface can be expressed as the following electric and magnetic field components.

H\n1\n?\n?\n=\nAe\nu\n1\n?\nz\n?\nH\n1\n(\n2\n)\n?\n(\n-\nj\n?\n?\n??\n)\n,\n(\n4\n)\nE\n1\n?\n?\n=\nA\n?\n(\n-\nu\n1\n?\n1\n+\nj\n?\n?\n??\n1\n)\n?\ne\nu\n1\n?\nz\n?\nH\n1\n(\n2\n)\n?\n(\n-\nj\n?\n?\n??\n)\n,\nand\n(\n5\n)\nE\n1\n?\nz\n=\nA\n?\n(\n-\nj\n?\n?\n?\n?\n1\n+\nj\n?\n?\n??\n1\n)\n?\ne\nu\n1\n?\nz\n?\nH\n0\n(\n2\n)\n?\n(\n-\nj\n?\n?\n? ?\n)\n.\n(\n6\n)

In these expressions, “z” is the vertical coordinate normalized to the surface of region 1 and “????” is the radial coordinate. “In these expressions, z is the vertical coordinate normal to the surface of Region 1 and? Hn (2)(?j??) is a complex argument Hankel of the second type and order n. u1 represents the propagation coefficient in the vertical direction (z) in Region 1, while u2 represents the propagation in the vertical direction (z). The value of? Source constants are imposed by the source. A is a constant imposed by the source.

u\n2\n=\n-\njk\no\n1\n+\n(\n?\nr\n-\njx\n)\n(\n7\n)\n\nand gives, in Region 1,\nu 1 =?u 2(?r ?jx).?? The radial transmission constant???? is given by” The radial propagation constant?

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