Theory of grating-coupled excitation of Dyakonov surface waves Kiran Mujeeb a , Muhammad Faryad b , Akhlesh Lakhtakia c , Julio V. Urbina d a Quaid-i-Azam University, Department of Electronics, Islamabad, 45320, Pakistan b Lahore University of Management Sciences, Department of Physics, Lahore, 54792, Pakistan c The Pennsylvania State University, Department of Engineering Science and Mechanics, University Park, Pennsylvania 16802, United States of America d The Pennsylvania State University, Department of Electrical Engineering, University Park, Pennsylvania 16802, United States of America Abstract. Excitation of Dyakonov surface waves guided by a plane wave incident on a columnar thin film (CTF) deposited on a surface-relief grating decorating a dielectric substrate was studied by using the rigorous coupled-wave approach, when the grating plane, the plane of incidence, and the morphologically significant plane of the CTF are all different. The absorptance for a specific linear polarization state of the incident plane wave was plotted as a function of the polar angle of incidence, at a fixed azimuthal angle, and those absorptance peaks were identified that are inde- pendent of the thicknesses of the CTF and the dielectric substrate. The angular locations of these absorptance peaks were correlated with the solution of the canonical boundary-value problem for surface-wave propagation. Dyakonov surface waves can be excited in a wider range of directions in the interface plane by p-polarized illumination than by s-polarized illumination. When the incidence and the grating planes do not coincide, it is possible to excite Dyakonov surfaces for multiple values of the polar angle of incidence. 1 Introduction A Dyakonov surface wave is guided by the planar interface of two homogeneous dielectric mate- rials of which at least one is anisotropic. Theoretical predictions were made in the 1980s for one partnering material being isotropic and the other a uniaxial dielectric material, 1, 2 both being loss- less. Since then, Dyakonov surface waves have been predicted for the planar interfaces of several combinations of dielectric materials: 3, 4 isotropic/biaxial, 5, 6 uniaxial/uniaxial, 7, 8 biaxial/biaxial, 9 and gyrotropic/gyrotropic. 10 More than twenty years elapsed after the first theoretical prediction for a Dyakonov surface wave to be observed experimentally in 2009, 11 and a confirmatory exper- imental result was reported in 2014. 12 In these experiments the interface of an isotropic dielectric material and a biaxial dielectric material was incorporated in a prism-coupled configuration, 4, 13, 14 with light made to enter a high-refractive-index coupling material to be incident on its interface with the isotropic dielectric material, this second interface being parallel to the guiding interface. When dissipation in both partnering materials is negligibly small, theory predicts and experi- ments have confirmed that Dyakonov surface waves can propagate in very narrow ranges of direc- tions in the interface plane. 3, 11 In other words, the angular existence domain of Dyakonov surface waves in the interface plane is tiny. Enlargement of the angular existence domain is possible when at least one of the partnering dielectric materials is either dissipative or active. 15–17 Theory indicates that the combination of dissipative and active dielectric materials can be used to excite amplifying Dyakonov surface waves in certain directions and attenuating Dyakonov surface waves in other directions. 18 Parenthetically, the use of partnering materials with magnetic properties 19–21 can also deliver larger angular existence domains, but our focus here is on dielectric partnering materials. Whether dissipation in the partnering dielectric materials is significant or negligible, the char- acteristics of a Dyakonov surface wave are always strongly dependent upon the direction of propa- gation in the interface plane. This superdirectivity combined with sharp absorption peaks indicative 1