###### Abstract  
This paper investigates the characteristics of surface waves propagating on a grounded anisotropic dielectric slab. Distinct from the existing analyses that generally assume that the fields of surface wave uniformly distribute along the transverse direction of the infinitely large grounded slab, our method takes into account the field variations along the transverse direction of a finite-width slab. By solving [PERSON]'s equations in closed-form, it is revealed that no pure transverse magnetic (TM) or transverse electric (TE) mode exists if the fields are non-uniformly distributed along the transverse direction of the grounded slab. Instead, two hybrid modes, namely quasi-TM and quasi-TE modes, are supported. In addition, the propagation characteristics of two hybrid modes supported by the grounded anisotropic slab are analyzed in terms of the slab thickness, slab width, as well as the relative permittivity tensor of the anisotropic slab. Furthermore, different methods are employed to compare the analyses, as well as to validate our derivations. The proposed method is very suitable for practical engineering applications.  
anisotropic metamaterial; grounded dielectric slab; guided waves; surface waves 2018 20  
and assume that there is no field variation along the direction orthogonal to the propagation direction of surface waves. To the best of our knowledge, no detailed analysis has been introduced for the case that the fields are non-uniformly distributed along the direction transverse to the propagation direction, which is a more practical concern for most engineers. In addition, most substrates used in real applications exhibit nonnegligible anisotropic properties due to either the intrinsic anisotropy of the material or the manufacturing process [21]. The effect of the anisotropy of the material on the propagation characteristics of surface waves is another concern for practical engineering.  
This paper investigates the characteristics of surface waves propagating on a grounded anisotropic dielectric slab, especially focuses on the slab with finite width. By assuming that the surface waves are propagating along the longitudinal direction of the slab, the field variations along the transverse direction are considered. Different methods are compared to analyze the propagation characteristics, as well as to validate our derivations. The main contributions of our work are as follows. (i) It is revealed that no pure TM or TE mode exists on the grounded infinitely large slab if the field is non-uniformly distributed along the direction orthogonal to the propagation direction; (ii) Closed-form analytical expressions are derived to theoretically study the characteristics of quasi-TM and quasi-TE surface modes on the finite-width grounded anisotropic grounded slab. It is found that surface waves propagate away from the longitudinal direction of the finite-width slab with some certain angle, and the angle decreases as the slab width increases; (iii) Different from the existing analyses of surface waves whose fields distribute uniformly along the transverse direction of the infinitely large slab, our method takes into account the variations of the fields distributed on the transverse direction of the grounded anisotropic slab, which has a more practical relevance and can provide a more accurate solution for engineering applications such as designing wideband and high gain antennas based on grounded dielectric slabs [9; 18; 19; 20]. It is worth mentioning that our method is also suitable for grounded isotropic dielectric slab.