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Factors Affecting Surface Wave Propagation Janice Hendry Roke Manor Research Limited, Old Salisbury Lane, Romsey, SO51 0ZN Abstract This project has been funded by the SEAS DTC as follow on work to IF012, ADD003 and CC012 PRELIM. The objective of the study is to carry out research to underpin the development of a covert communications system utilising a surface wave launch and receive mechanism in place of conventional antennas. This paper focuses on the factors affecting surface wave propagation; specifically it gives details of a hypothesis for the relation between the skin depth of a medium and the amount of surface wave launched. This demonstrates that the effect of the properties of the medium over which a surface wave propagates is large. This paper also shows the broad nature of applications and potential exploitation routes of a surface wave based technology, in particular it meets a current UK MoD need, namely tactical beyond line of sight operation priority technology for the UK MoD [1]. Keywords: surface waves, electromagnetics, propagation. ground waves, Summary of Work to Date This phase of work focused on gaining a theoretical understanding of the mechanisms affecting surface wave propagation. This will assist with a system design which is proposed to be undertaken in the next phases of this research. The main focus of this work was the factors affecting the propagation of surface waves. It has also been necessary to gain an understanding of the various different types of surface wave that can exist and which of these are most likely to be useful. Once the theory overview was complete, potential system benefits and applications were reviewed, showing the broad nature of applications and potential exploitation routes of a surface wave based technology. Such a technology also assists with the tactical beyond line-of-sight operation priority technology for the UK MoD [1 (p71)] due to the surface wave’s terrain following ability. antenna, communication, monopole, Underhill Research has also been developing a calibration technique. This will enable us to compare the performance of different designs directly by calibrating out the effect of the ground properties. The final part of this work was simulation based, using a simple monopole or dipole as the base design. These simulations were performed to back up the theory discussed in the earlier stages of this work and the techniques developed will be useful for all future simulations. This paper focuses on how the properties of the media over which a wave propagates affects the surface waves and the potential benefits and applications of a surface wave based system. Types of Surface Wave There are many different types of surface wave and each can be defined by the guiding structure required. This year’s work has isolated two potential types of 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 surface wave that may be useful for both civil and military applications, namely the Zenneck surface wave and the trapped surface wave. 1. no variation in Therefore, ∂/∂y=0; 2. variations in the x-direction can be represented by exp(-γox) in the dielectric (air) and by exp(-γ1x) in the lower medium; 3. the permeability, µ is the same in all media considered and equal to the permeability of free space, µo; 4. variations in the z-direction are as yet unknown and must be solved for. Zenneck Surface Wave The Zenneck surface wave is an inhomogeneous plane wave supported by a flat surface and can be represented in both rectangular and cylindrical coordinates. It is a transverse magnetic (TM) mode and requires that the permittivities of the media either side of the interface are different but their permeabilities are the same [2]. It also requires an inductive reactance term in the surface impedance, Zs for the medium it propagates along. In order to excite a TM Zenneck surface wave, two conditions [2] are required: 1. incidence close to the Brewster angle; 2. finite loss in one of the media. A transverse electric (TE) mode is also possible but not discussed in this paper as it is not easily realisable over natural guiding structures. the y-direction. By solving Maxwell’s equations using these boundary conditions, one obtains the ‘resonance condition’. This is defined at z = 0 m and is when the Zenneck surface wave will propagate, u1 σ 1 + jωε1 + uo =0 jωε o (1) where, ω = angular frequency, u = propagation coefficient in the z-direction, ε = permittivity, σ = conductivity. The subscript 1 refers to the property of medium 1 and the 0 to medium 0, in this case free space. Trapped Surface Waves Trapped and quasi-trapped surface waves occur over a dielectric slab or dielectric coated conductors and can support both TE and TM surface waves. They can only exist when the ground is not homogeneous or is ideally stratified [4 (p99)]. A trapped mode occurs when the angle of incidence from the dielectric medium to the air-dielectric interface is greater than the critical angle, θc which is defined by, Figure 1: Boundary conditions for Zenneck wave [3 (p7)] The Zenneck surface wave decays exponentially away from the surface. In order to obtain a solution from Maxwell’s equations, one must first set up the boundary conditions (see Figure 1) and make the following assumptions about the surface wave: sin θ c = 1 ε (2) When the angle of incidence is at or greater than the critical angle total internal reflection will occur, with the field outside the dielectric being evanescent in nature, i.e. it decays exponentially away from the interface [5 (pp712-714)]. 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 conductivity and permittivity (assuming relative permeability is 1). Taking these into account, the equation for skin depth can be derived in full, dS = In effect, when a layer of dielectric is on top of a perfect conductor it acts like an optical fibre or more generically as a dielectric waveguide, as shown in Figure 2 [5 (p 717)]. Effect of Skin Depth A material can be classified as a good conductor or a good dielectric by using the relations: (3) (4) The reason for defining if a material is either a good conductor or good dielectric is to help determine the dominant loss mechanism. In general, real ground has dielectric properties with the only exception being sea water which acts more like a conductor due to its salt content. The skin depth is defined to be the point below the surface of a material when the electric field drops to 1/e of its surface value [6]. Generally this is quoted to be, ds = 2 ωµσ (6) π f tan δ where vp is the phase velocity and tan δ is the dielectric loss tangent, which are defined by, Figure 2: Trapped surface wave σ 〉〉 1 ⇒ good conductor ωε σ 〈〈 1 ⇒ good dielectric ωε υp (5) However, this relation is only true for good conductors as defined by Equation (3). In most cases, this work considers materials that are neither good conductors nor good dielectrics and so the skin depth calculated using Equation (5) is inaccurate. The skin depth of a material is dependent on the material properties, namely υp = 1 µε and tan δ = σ ωε PEC is generally the optimum material for a space wave to propagate over; therefore it may not be immediately obvious that as conductivity increases the magnitude of the surface wave electric field decreases. Bound surface waves cannot exist in or over a perfect conductor (PEC) as it has zero skin depth. A surface wave requires an interface between two media as it exists partially in both. Therefore if the electric field is unable to penetrate into one of the media, a surface wave cannot propagate. This implies that the skin depth is proportional to the magnitude of surface wave produced and indirectly proportional to the magnitude of space wave produced with an exponential dependence. This can be explained mathematically by applying boundary conditions to Maxwell’s equations, but a novel way of thinking is to use the concept of probabilities and the photon transmission path to explain this relationship. Consider the electric field propagation as photons travelling away from the source with time. Assume the source is constantly transmitting and there is zero loss. Now take a transmitter in a vacuum over a perfect conductor; the skin depth will be 0m. A bound surface wave requires the electric field to be able to penetrate through 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 the boundary, forming an interface between the two media. When a skin depth, ds exists, for a real ground a potentially bound surface wave can exist. The higher the surface reactance, Xs the more tightly bound the surface wave is to the interface and the more of the field that is distributed within the surface wave region. The surface wave region can be defined as the region in which the surface wave is able to exist (see Figure 3). Why is this the case? Consider the distribution from a statistical or probability point of view. The larger the surface wave region the higher the probability that a photon will enter this region. In reality, the material properties will vary. These changes of properties can cause the photon to change its direction such that it leaves the surface wave region. This is considered a loss mechanism as the space wave is an unwanted field component in this study. Once again, a simple probability can be considered, the larger the surface wave region the higher the probability that the photon will remain within it. If the skin depth were infinite, a wave in the surface wave region should be greater as the ratio of space to surface wave region would approximate unity. However, there will be a depth beyond which the propagating wave is no longer a surface wave as it is not bound to the interface. Therefore one can define a useful surface wave region or optimal skin depth for surface wave propagation, d s , optimum = d s ,useful + ∆d s (7) The ∆ds term in Equation 7 is due to the fact that if the photon did leave the useful surface wave region, there is still the probability that it will re-enter this region before being received. ds,useful includes some of the area just above the interface as some of the surface wave will be present there also. Figure 3: Figure detailing the surface wave region In summary, to maximise the initial magnitude of surface wave electric field, a larger skin depth is desirable, but for reception, there will be an optimum skin depth as described by Equation (7). It is the author’s recommendation that this explanation is further investigated, but not necessarily as part of this contract; however it should be kept in mind when designing a system. Surface Impedance The properties, and thus surface impedance, of the ground over which a surface wave propagates has a large impact on the ratio of surface wave to space wave launched and how much loss the wave is affected by, and the possible range of, the signal. The surface impedance also defines how tightly bound the surface wave is to the interface and how quickly the space wave will be attenuated in the z-direction away from the interface. The surface impedance is defined in terms of the surface reactance, Xs and resistance, Rs, Z s = Rs + jX s (8) which are found from 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 Rs = Xs = ωµ1 ( ω 2ε12 + σ 12 + ωε1 ( 2 ω 2ε12 + σ 12 ωµ1 ( ) ω 2ε12 + σ 12 − ωε1 ( 2 ω 2 ε12 + σ 12 ) ) ) (9) (10) where the same notation is used as before. Theory predicts that the higher the surface reactance, the faster the decay of the space wave away from the interface, whilst the more tightly bound the surface wave becomes. Therefore, a medium with a high reactance should exhibit better terrain following abilities. A high reactance also results in a decreased surface wave spread outside of the surface increasing the energy within the surface wave region. This can be further enhanced by the fact that a high surface resistance increases the tilt of the wave. However, increasing the resistance also increases the attenuation of the surface wave. This implies that there is a trade-off with regards to the optimum surface impedance for production and propagation of a surface wave whilst minimising the space wave. It can be seen that a high reactance is desirable. However, depending on the application, the desired resistance may vary. One can artificially increase the reactance of a structure by increasing the surface roughness. By increasing the reactance, one can increase how well bound the surface wave is to the interface and reduce the loss of the signal Assuming the application of an antenna propagating over a long distance, one would require that the medium which it propagates over has a high reactance to reduce the space wave component and low resistance to reduce the attenuation of the surface wave. One can then determine the optimum medium properties by differentiating Xs and Rs with respect to ω then equating them to zero [3 (p 18)]. This shows that when Xs is a maximum and Rs is a minimum, the required medium properties are, σ = 3ωε (11) For short range applications, a high resistance may be preferable as more energy is directed into the surface wave region and attenuation occurs with distance. Over larger distances a low resistance would be preferred to reduce this attenuation. Figure 4: Electric field penetration: fresh water and key used for all simulations Electric Field Penetration Simulations Simulations were performed using the frequency-domain software HFSS. The total length simulated was 2.4 km, which is equivalent to 8λ and just under 3λ in height, where λ is the free-space wavelength at 1 MHz. All simulations used a 1 MHz quarter-wave monopole and the colour representation is interpreted using the key in Figure 4 used for all simulations. 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 Six sets of medium properties were simulated, however only the most relevant are detailed in this paper. Figure 4 clearly shows the electric field penetrating into the lower medium, in this case fresh water. The penetration can be seen to be consistent for the full 2.4 km and the electric field has a high magnitude at the interface. This is indicative of the presence of a surface wave but not proof that this is the cause of this increased magnitude. Figure 5 shows the electric field penetration into salt water, which has a high conductivity. Figure 7: Electric field penetration: dry ground Dry ground is perhaps the most interesting of the media simulated. The electric field decays more slowly close to the interface than further above it. Additionally, there is more penetration of the electric field into the dry ground, as predicted by the skin depth equation. Wave Tilt Figure 5: Electric field penetration: salt water The electric field does not penetrate very deeply into salt water due to its high conductivity. It is therefore thought unlikely that much surface wave will be present. One can clearly see that the strength of the electric field in the upper medium is higher than that for fresh water, and shows some similarities to the expected field over PEC. The electric field, magnetic field and direction of propagation should all be perpendicular to each other under ideal circumstances; however a surface wave produces a forward tilt in the electric field. The magnitude of this tilt depends on both the conductivity and permittivity of the medium over which it propagates. This tilt can be calculated from the ratio of horizontal electric field to vertical electric field [7 (p654)], EH 1 = EV ηo 1 σ ∠ tan −1 2 ωε σ +ω ε ωµ 2 2 (12) 2 Note: ∠ denotes that the relation following it represents the phase and ηo is the characteristic impedance of free space. Figure 6: Electric field penetration: wet ground Wet ground has a lower conductivity and permittivity than salt water and therefore has a larger skin depth, as can be seen by comparing the penetration depth of Figure 5 and Figure 6. Figure 8: Diagram to show angle descried in Equation 12 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 The arctangent of the magnitude part of Equation (12) (θ) represents the angle by which the electric field component is tilted from the vertical in the direction of propagation as shown in Figure 8. This implies that there will be a small but finite value of EH for a medium with finite conductivity which is given by the first part of Equation (12). This result could be used to help identify the surface wave in both simulations and measurements. If it is known how much the electric field vector will tilt, and that the electric field is not perpendicular to the direction of travel, the vertical component of the Poynting vector should also be nonzero. It also indicates that the surface wave is highly dependent on frequency and the properties of the ground over which it propagates. Figure 9 shows the tilt angle θ over grounds with different properties. Effect of Frequency and Medium Properties on Wave Tilt 25.00 Wave Tilt (degrees) 20.00 15.00 ` 10.00 5.00 0.00 0.1 1 10 100 Frequency (MHz) Wet Ground Avg Ground Fresh Water Salt Water Dry Ground Copper Figure 9: Effect of frequency on wave tilt for different ground properties Another implication of the phase part of Equation (12) is that the resulting radiation will have elliptical polarisation as opposed to linear polarisation. Local Electric Ground Perhaps the main output regarding potential future designs from the past year’s research is the concept of a local electrical ground. It has been found that the ground properties have the largest effect on the propagation of surface waves. If one were able to control the ground properties over which the surface wave propagates, one should therefore be able to efficiently launch a surface wave. The Goubau horn does exactly this by using a wire between the transmitter and receiver; however for this application, it is unlikely that this design type would be feasible. It is also impossible to control all the ground over which a surface wave propagates over. However, one is able to control the ground surrounding the launch and receive mechanisms. This is common practice for many antenna designs, utilising a local ground plane; however this is usually metallic in nature. In order to launch an efficient surface wave, one requires an optimised dielectric local ground plane. In this work, it will be termed a ‘local electric ground’ such that it is not confused with a metallic ground plane. Developing this idea, and assuming short range covert communication is preferable, a local electric ground with high impedance and high resistance would be preferable. This would maximise the transmission of the energy into the surface wave region and attenuate away quickly the space wave. The exact size of the local electric ground would need to be optimised and there is 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 also the consideration of the preferred shape, i.e. could this local electric ground plane be used to direct the surface wave in a particular direction as opposed to omnidirectional obtained using a standard single line element launch mechanism. In addition to considering a dielectric based local electric ground, one could also consider designs using a corrugated or dielectric coated metallic local electric ground. The latter would be advantageous for the launch of trapped surface waves and the former for the Zenneck surface wave. Dielectric Filled Horn The frequency is expected to be a key issue for this design as at HF the horn will be large. Potential Benefits This section briefly outlines some of the potential system benefits if a surface wave was used as opposed to a space or sky wave based system. As these are system level issues, they have not been fully investigated in this document; however some background research has been performed to back up the following statements. Increased Range This section combines the use of a dielectric slab wave guide for trapped surface waves and the Goubau horn. • Consider a half-horn on a medium with finite conductivity. According to Barlow and Brown [3 (p151)], theoretically, in order to launch a pure surface wave, an infinite aperture is required. However it is known that a dielectric slab waveguide can launch a trapped surface wave and a horn can launch a Sommerfeld-Goubau surface wave. Consider the medium 0 – medium 1 interface as the ‘wire’ (i.e. guiding structure) required for the SommerfeldGoubau. Next combine a horn waveguide and a dielectric waveguide by filling part of the horn with a tapered dielectric slab (see Figure 10). This should ensure that the surface wave produced is tightly bound as it exits the horn and enters free space, or in this case a medium with finite conductivity. This dielectric slab should then act as a dielectric waveguide and ideally direct the wave such that it becomes bound at the interface for its continued propagation. Surface waves are already utilised in some applications indirectly. For example, marine communication and terrestrial radio broadcast can both be received over the horizon. This is partly due to the sky wave but also due to the surface wave. If one could instead transmit all the power into the surface wave, it is expected that much greater ranges could be achieved. In Zenneck’s 1915 book [8 (p249)], he states Potential Capability: Increased range for same power consumption, reduced power consumption for same range. the range could be extended from 1 r2 to 1 r for a signal of the same power utilising surface waves. This relationship can be derived from Maxwell’s equations, but does not necessarily take into account conductive losses in the medium. Covert Signal • Potential Capability: Covert communications, covert sensors In addition to the increased range, surface waves are, by definition, non-radiating and therefore could be considered for covert systems. This assumes that a pure surface wave can be launched or that the space wave can be attenuated away rapidly close to the transmitter. Various design Figure 10: Dielectric filled horn 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 considerations may be able to achieve the latter methodology as some texts state that it is impossible to launch a pure surface wave. However, for real applications, simply ensuring that the majority of the power is transmitted into the surface wave should be sufficient. The main problem that may be encountered is that when the signal travels over certain topologies it may be re-radiated (considered a loss mechanism) and some energy transferred back to the space wave. It is however, expected that the energy reradiated will be small in each incidence that occurs. MoD as stated in the Defence Technology Strategy, published in 2008 [1 (p71)]. A surface wave based technology could provide the UK MoD with this capability in a covert manner and with increased range. The main limitation of terrain following will be the ‘sharpness’ of angle around which a surface wave can still remain bound to the interface. It is expected that some loss through radiation will occur when passing over different topologies and this loss will increase with its ‘sharpness’. However, it is expected that this should not cause excessive loss as most natural topologies are relatively gradual or small compared to the wavelength. Terrain Following • Potential Capability: Non-line-of-sight communication, over-the-horizon communication Terrain following is the ability for the signal, or in this case an electromagnetic wave, to follow the topology of the Earth. Figure 11: Antennas without line-of-sight communication Due to the surface wave being bound to the interface, it should follow the terrain. Space waves on the other hand are diffracted around objects. By utilising a surface wave based system, one could ensure more signal power is transmitted to the desired location, following the terrain rather than being omni-directionally radiated when the space wave is diffracted. This results in the capability of non-line-of-sight communication. This could be useful over short distances due to local topology or over longer ranges, such as over-thehorizon communication. Tactical beyond line-of-sight operation is currently a priority technology for the UK It is unknown what the limits are for the surface wave to remain bound. This knowledge could be used to assist with proving that the field seen over a specific topology is purely the surface wave as opposed to the diffracted or refracted space wave. Two situations were modelled in HFSS, both of which had a smooth, shallow gradient of 108.5 degrees measured clockwise from the z-axis. In the first model (a) an imperfect ground plane with Zs=10+j50 ohms was used,. The second simulation (b) used a PEC ground plane and no surface wave should be present. Figure 12: Terrain following showing total magnitude of electric field over (a) imperfect ground plane; (b) PEC ground plane Figure 12 shows the magnitude of the total electric field and in both cases the wave front appears to follow the terrain; however there is more field present along the surface in Figure 12(a), which has an imperfect ground plane. This could be due to the bound nature of the surface wave. To conclusively prove this, additional 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 investigation needs to be completed. Nonetheless, these simulations are highly indicative that a surface wave is present and that terrain following is occurring. Potential Applications This section details the broad variety of applications of a surface wave based technology, as shown in Table 1. From the table, one can see that a surface wave technology has diverse applications, from land-based to marine, military to civil. Each of these potential applications will have different requirements and will therefore require the design to focus on a different area, e.g. for ground water detection in agriculture, loss through radiation will not be a major problem as covertness is not a concern, whereas with a covert military link, this could pose serious problems. It will therefore be important to focus future research on a few similar applications to maximise the benefit of this work. Table 1: Potential applications of a surface wave based technology Potential Capability Surface Wave Characteristics Assisting with Capability Short range communications (e.g. between sensor nodes) Signal covertness Long range communications / marine communications (e.g. over-the-horizon communications) Increased range Buried object detection Ground would be main region of propagation Terrain following over local topology (e.g. small craters / holes) Terrain following Potential increased range compared to space wave Seabed (buried) object detection Seabed would be main region of propagation Covert communications Signal covertness Surface wave radar (e.g. over-thehorizon radar) Terrain following Communication and sensing through pipes, tunnels, etc. Terrain following Ground water detection (e.g. agriculture) Wave tilt depends on the ground properties Increased range Increased range .Conclusions It has been found that the ground properties have a large effect on surface wave propagation and it may be possible to manipulate the properties surrounding the launch mechanism by the use of a ‘local electric ground’. This should increase the power directed into the surface and may be a very useful technique to rapidly attenuate the space wave component, making the technology more covert. This paper postulates that the skin depth can be related to the efficiency of surface wave propagation by the notion of a ‘surface wave region’. This gives a qualitative view of why dry ground is perhaps better for launching a surface wave as opposed to wet ground. This was then demonstrated in simulations. Initial work was undertaken to examine the surface wave’s terrain following ability. 4th SEAS DTC Technical Conference - Edinburgh 2009 A2 This has been investigated briefly in this phase as tactical beyond line-of-sight operation is currently a priority technology for the UK MoD as stated in the 2008 Defence Technology Strategy [1 (p71)]. A surface wave based technology could provide the UK MoD with this capability in a covert manner and potentially with increased range. This work will form part of an Engineering Doctorate (EngD) at UCL, with fees funded by the EPSRC. Overall, this phase of work has laid good foundations to proceed with the next stage, which will be more practically based. References [1] UK MoD, Defence Technology Strategy: for the demands of the 21st century, UK MoD (2008) [2] Overfelt, P., Review of Electromagnetic Surface Waves: 1960 Through 1987, Naval Weapons Center CA, NWC TP 6880 (Jan 1988) [3] Barlow, H., Brown, J., Radio Surface Waves, Oxford University Press, London (1962) [4] Maclean, T., Wu, Z., Radiowave Propagation Over Ground, Chapman & Hall, 1st Ed., London UK (1993) [5] Collin, R., Field Theory of Guided Waves, IEEE Press, 2nd Ed., USA (1991) [6] Sander, K., Reed, G., Transmission & propagation of Electromagnetic Waves, Cambridge University Press, 2nd Ed. (1986) [7] Jordan, E., Balmain, K., Electromagnetic Waves and Radiating Systems, Prentice-Hall India, 2nd Ed. (2006) [8] Zenneck, J., Wireless Telegraphy, McGrawHill Book Company, 5th printing (1918) Acknowledgements The work reported in this paper was funded by the Systems Engineering for Autonomous Systems (SEAS) Defence Technology Centre (DTC) established by the UK Ministry of Defence. The author would also like to acknowledge the technical assistance provided by Mike Jessup and Steve Simpson of Roke Manor Research Limited and Mike Underhill of Underhill Research. 4th SEAS DTC Technical Conference - Edinburgh 2009 A2