Conformal transformation of Dyakonov surface waves into bound states of cylindrical metamaterials

Abstract

We put forward the use of transformation optics to map surface waves that exist as one-dimensional modes supported by anisotropic structures into bound states in twodimensional geometries. Specifically, we show the conformal mapping of Dyakonov waves existing in infinite planar surfaces separating birefringent media into bound modes supported by a cylindrical structure made of suitable metamaterials. In contrast with the original Dyakonov waves, the resulting fiber-like modes are highly dispersive, may exist as fundamental as well as higher-order states, feature helical wavefronts, and exhibit a lower and upper frequency cut-off. The program we put forward can be applied to all wave phenomena currently known to occur only in planar geometries in different types of anisotropic media.Transformation optics (TO) is a powerful mathematical method based on the form invariance of Maxwell's equations upon coordinate transformation [1,2]. The transformation relies on the physical equivalence between wave propagation in a curved space and in media with general inhomogeneous and anisotropic properties. It provides an approach to control the flow of light in a material with spatially varying constitutive parameters closely related to a coordinate transformation, enabling the exploration of spectacular effects, such as partial invisibility cloaks [3-7], optical illusion [8,9], the optical analogue of gravitational lensing [10,11] and event horizons around black holes [12], as well as the design of a variety of photonic devices [13]. For example, TO has been applied to the design of optical waveguides and cavities in order to achieve multimode waveguide bends with minimal intermode coupling [14] and highly directional emission of whispering gallery modes [15], respectively, as well as omni-directional optical concentrators for solar applications [16,17], metallic nanostructures for ultra-sensitive spectroscopy [18][19][20], and nonlocal effects and van der Waals interactions in plasmonic systems [18][19][20], among other optical phenomena and applications.

Поверхностные Электромагнитные Волны Дьяконова На Границе Раздела Анизотропных Двуосных Кристаллов

“…При этом анализировались лишь некоторые частные случаи границ раздела двуосных кристаллов при относительно простых пространственных ориентациях их оптических осей. Кроме того, в литературе изучались и другие разновидности волн Дьяконова, существование которых возможно на границах раздела других типов веществ, таких, как гиперболические, хиральные и бианизотропные материалы [16][17][18][19], а также возникающих в ограниченных средах [20][21][22][23].…”

Dyakonov surface waves in dielectric crystals with negative anisotropy

“…Very recently, a practically important case of Dyakonov-like surface waves in finite-size resonator structures has been studied for cylindrical waveguides [34,35] as well as for flat interfacial strip waveguides [36,37]. It has been demonstrated that due to a non-zero curvature of cylindrical waveguides, Dyakonov surface waveguide modes (DSWMs) in them inevitably have radiative losses.…”

Dimensional confinement and waveguide effect of Dyakonov surface waves in twisted confined media

“…In Ref. [ 29] it has been shown that the Dyakonov surface waves can be conformally transformed into the bound states of cylindrical metamaterials. Dyakonov-like surface waves have been also theoretically predicted in anisotropic cylindrical waveguides.…”