Negative Refractive Index and Higher-Order Harmonics in Layered Metallodielectric Optical Metamaterials

Abstract

We study the propagation of light in a three-dimensional double-periodic Ag/TiO 2 multilayer metamaterial composed of coupled plasmonic waveguides operating in the visible and UV spectral range. For these frequencies, light propagation in the plane of the waveguides is described by a negative phase velocity, while for the orthogonal direction light propagation is described by a Bloch wave composed of a large number of harmonics. As a result, the material cannot generally be described by a single phase index: decomposing the Bloch wave into different harmonics we show that for the wavelength range of interest the positive index m=1 harmonic dominates the propagation of light in the orthogonal direction. These results are corroborated by numerical simulations and optical refraction experiments on a double-periodic Ag/TiO 2 multilayer metamaterial prism in the 380-600 nm spectral range, which show that positive refraction associated with right-handed harmonics dominates. Studying the isofrequency contours we find that despite the occurrence of multiple harmonics the double-periodic structure can act as a flat lens: for a slab consisting of an integer number of unit cells all harmonics are degenerate and constructively interfere at the image plane. This work identifies important considerations relevant to the design of many three dimensional periodic metamaterials.

Principles of electromagnetic waves in metasurfaces

“…Clearly the parallel component is between ε 1 and ε 2 , the perpendicular component can be much larger than 1, resulting in extremely short wavelength. When 0,      the dispersion curve of this effective medium is hyperbolic, thus enabling the directive transmission and negative refraction [50][51][52]. The short wavelength and hyperbolic dispersion of SPP could be used to achieve far-field imaging of subwavelength objects.…”

Generalized antireflection coatings for complex bulk metamaterials

“…12 r is the reflection coefficient from air to coating, and 23 r is the reflection coefficient from the interface between coating and metamaterial). From Eq.…”

Subwavelength Artificial Structures: Opening a New Era for Engineering Optics

“…As illustrated in Figure , using equivalent material parameters, generalized optical laws and transformational optics, multiscale optical design becomes possible. Many exotic metamaterials have been developed to realize new functionalities, such as super‐resolution imaging enabled by negative index materials and beam collimating and energy tunneling via zero index materials . In addition, as topological photonic crystals, the newly emerging Dirac and Weyl materials have attracted considerable attention in functional optoelectronic devices such as optical isolators and topological lasers.…”