We theoretically predict existence of S poof Zenneck wave s in the terahertz spectral range that are supported by corrugated surfaces with subwavelength patterning made of material s with high positive dielectric permittivities . 1. Introduction The strong spatial confinement of surface wave s led to a revolution in sensing . Profiting from small modal size s of such waves, surface sensing modality offers high sensitivity and precise localization [1, 2] . Particularly, in the visible spectral range, surface p lasmon -polaritons propagating at the interface between a metal and an analyte were used to revolutionize the field of biosensing. Recently, THz spectral range (frequencies of 0.1 -1 THz) emerged as the next frontier for non -destructive imaging, sensing, and ultra -fast wireless communications [3, 4] . Because of the relative transparency of dry dielectrics to THz radiation and existence of spectr al fingerprints for many biologic al molecules, THz sensing became an emerging research direction that could also benefit from surface wave sensing modality. However, generation and support of highly confined THz modes on flat metal surfaces (analogous to plasmons in the visible) proved to be challenging due to material limitations of metals in th e THz spectral range, thus resulting in highly delocalized surface modes . A breakthrough in THz plasmonic came from realization of Spoof Plasmons on corrugated metallic surfaces with subwavelength patterning [5]. In this paper, we propose and theoretically demonstrate the possibility of Spoof Zenneck surface wave s that also propagate along a corrugated surface with subwavelength patterning, but in direct opposition to Spoof Plasmons, they require materials with high positive dielectric permittivity. Under certain assumptions such modes can exist even in the case of purely real dielectric permittivities and in the absence of material losses. This work is of particular importance to the THz spectral range, where there is an abundance of ceramics featurin g high dielect ric permittivity , and practical demonstration s and application s of such modes hold a significant promi se. 2. Dispersion relation of Spoof Zenneck waves Consider a periodic corrugated surface made of material with permittivity εm adjacent to a lossless dielectric with permittivity ε0 as shown in Fig. 1. Th e periodic structure has a period d and contains grooves of width a and height h. Fig 1. Schematic of the corrugated structure. The period is d and the groove width and depth are a and h. The permittivities of the material and the filling dielectric above the surface and in the groove s are εm and ε0, respectively . The structure is infinite and uniform in the y-direction. The dispersion relation of Spoof Zenneck waves can be found by solving Maxwell equations in the upper and lower semi -infinite domains , while matching them along 𝑧𝑧=0, similarly to a standard derivation used for Spoof Plasmons [6]. At the interface s with material εm we use an impedance boundary condition (IBC) [7], which is valid as long as modal field either decays , or suppressed due to destructive interference, or its coherence is destroyed over the propagation distance d -a within the g roove walls . Then , for the waves propagating along the grooves ( along OZ direction ) one can find their propagation constant 𝛽𝛽𝑧𝑧𝐼𝐼: 𝑘𝑘𝑥𝑥𝐼𝐼tan(𝑘𝑘𝑥𝑥𝐼𝐼𝑎𝑎/2)=−𝑖𝑖𝑘𝑘0𝜀𝜀0 �𝜀𝜀𝑚𝑚, (1) where 𝛽𝛽𝑧𝑧𝐼𝐼=±�𝜀𝜀0𝑘𝑘02−(𝑘𝑘𝑥𝑥𝐼𝐼)2.Then, i n the limit of 𝑑𝑑≪𝜆𝜆 (subwavelength corrugation), an analytic expression for the propagation constant 𝛽𝛽𝑥𝑥𝑆𝑆𝑆𝑆 of a Spoof Zenneck wave propagating along OX axis can be found by solving Maxwell equations in zone II and then matching the fields , while r especting IBC along 𝑧𝑧=0: �𝜀𝜀0𝑘𝑘0 �𝜀𝜀𝑚𝑚+𝑘𝑘𝑧𝑧𝑆𝑆𝑆𝑆�sin�𝛽𝛽𝑥𝑥𝑆𝑆𝑆𝑆𝑑𝑑 2� sin�𝛽𝛽𝑥𝑥𝑆𝑆𝑆𝑆𝑎𝑎 2�=𝛽𝛽𝑧𝑧𝐼𝐼𝑖𝑖�𝜀𝜀𝑚𝑚𝛽𝛽𝑧𝑧𝐼𝐼tan�𝛽𝛽𝑧𝑧𝐼𝐼ℎ�−𝜀𝜀0𝑘𝑘0 �𝜀𝜀𝑚𝑚𝛽𝛽𝑧𝑧𝐼𝐼−𝑖𝑖𝜀𝜀0𝑘𝑘0tan�𝛽𝛽𝑧𝑧𝐼𝐼ℎ�+𝜀𝜀0𝑘𝑘0 �𝜀𝜀𝑚𝑚, (2) where 𝑘𝑘𝑧𝑧𝑆𝑆𝑆𝑆=±�𝜀𝜀0𝑘𝑘02−(𝛽𝛽𝑥𝑥𝑆𝑆𝑆𝑆)2 is the z -component of the wave vector of the surface wave . 3. Results Here we present examples of dispersion relation s of Spoof Zenneck waves supported by the corrugated surface made of materials with purely real and positive permittivity. To validate our derivations, dispersion relation given by (2) is compared with numerical results obtained using COMSOL. Particularly , solid lines in th e left panel of Fig. 2 show dispersion relation s (real and imaginary parts) of Spoof Zenneck waves as obtained by solving (1)-(2) using Newton - Raphson iteration method, while dotted lines correspond to COMSOL simulations. The propagation distance 𝐿𝐿 𝑥𝑥= 1Im(𝛽𝛽𝑥𝑥𝑆𝑆𝑆𝑆)⁄ and the penetration depth into air 𝐿𝐿𝑧𝑧=1|Im(𝑘𝑘𝑧𝑧𝑆𝑆𝑆𝑆)| ⁄ of the modes are also presented in the right panel. Here we use 𝑑𝑑=50 µm, 𝑎𝑎=35 µm and ℎ=75 µm, 𝜀𝜀0=1, 𝜀𝜀𝑚𝑚=100 (case of TiO 2 material [8]). From these results, we note that the fundamental modes in Fig. 2 have a superior cut-off frequenc y of 0.95 TH z. Fig 2. Typical dispersion relation s of the spoof Zenneck waves . (a) R eal (blue, cyan) and imaginary (reg, magenta) parts of the Spoof Zenneck wave propagation constant as computed by the Newton -Raphson iteration method and (1) -(2) (solid), as well as COMSOL (dotted). (b) Propagation distance (blue, cyan) and penetration depth into air (red, magenta) in units of lambda . (Inserts) Distribu tion of the electric and magnetic fields above the surface and inside the groove s for 0.40 THz and 0.75 THz. We see good correspondence between the semi -analytical expressions (1) -(2) and numerical COMSOL simulations in the subwavelength regime 𝜆𝜆>5𝑑𝑑, which covers the operation range of the fundamental mode s. In addition, such modes have tight confinement near the interface as the penetration depth into air is mainly subwavelength in the spectral range of interest. Overall, dispersion relation , including the cut -off frequencies of Zenneck waves can be easily engineered by changing the value of the period d , the groove width a and the groove height h, which make this kind of metamaterial a great candidate for engineering of THz sensor s using highly localized surface modes . This work is also of practical importance as in T Hz range there are many ceramics that feature high positive permittivities .