Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures

Abstract

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic bandgap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete bandgap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in a sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete bandgap.PACS numbers: 42.70. Qs, 41.20.Jb, 78.67.Pt Photonic crystals are artificial materials with a periodic modulation in the dielectric constant which can create a range of forbidden frequencies called a photonic bandgap [1]. Photons with frequencies within the bandgap cannot propagate through the medium. This unique feature can alter dramatically the properties of light, enabling control of spontaneous emission in quantum devices and light manipulation for photonic information technology [2]. Photonic bandgap structures can also be found in nature, and they explain the color diversity of some of the living creatures [3].Complete two-dimensional (2D) and three-dimensional (3D) bandgaps can be realized in photonic crystals, where the refractive index is periodically modulated in two or three dimensions, respectively [1]. Such modulation is necessary to satisfy the Bragg condition simultaneously for all propagation directions, requiring that phase accumulation per period is close to a multiple of π, so that the waves reflected at different interfaces between the regions with low and high refractive indexes interfere constructively and wave propagation is prohibited for any incidence angle. Manufacturing of 3D photonic crystals still remains a technological challenge due to the requirements of large index contrast and high fabrication precision.The simplest periodic structure, both in geometry and manufacturing, is a one-dimensional stack of two types of layers which differ in the dielectric constant [4]. However, such structures may only possess partial bandgaps for certain ranges of propagation directions. Here we study the scattering properties of one-dimensional periodic structures containing layers made of the so-called left-handed metamaterials (LHMs)-artificially created composites which are characterized by simultaneously negative dielectric permittivity and magnetic permeability. Such materials are transparent and can bend light in the opposite direction to normal reversing the way in which refraction usually works [10]. We demonstrate that specially designed one-dimensional structures with negative refraction may exhibit a complete three-dimensional bandgap. First, we show that a layered structure made of two alternating layers of left-handed materials and conv...

Physics of the zero- photonic gap: fundamentals and latest developments

“…We emphasize that the omnidirectional refl ectivity does not necessarily imply a complete PBG, since the latter is more strict, requiring that no mode can exist for any k || values including the cases of k || > ω / c . Shadrivov et al studied the problem in detail [73] . By thoroughly examining the Bloch equations for two polarizations [i.e., Eq.…”

Band Structures and Abnormal Behavior of One Dimensional Photonic Crystal Containing Negative Index Materials

“…The dispersion relations, reflection characteristics, group velocities and n eff of the periodic structure contain negative index materials is calculated numerically using transfer matrix method [16,19,26]. The geometry of the structure under study is shown in Fig.…”

“…The complete band gap in one-dimensional left handed periodic structures has been purposed. The modulation of refractive index in all three spatial directions is required to find a complete band gap and prevent the propagation of electromagnetic waves in all directions [19][20][21]. Singh et al [22] have investigated the structural parameters for the formation of omni-directional band gaps in one dimensional photonic crystal.…”

Tamm states in one-dimensional photonic crystals containing left-handed materials

“…One-dimensional photonic crystal consisting of alternate LHM and conventional right-handed material (RHM) layers have already been investigated through calculating the transmittance or the reflectance the structures (7; 15)and demonstrating of complete band gap (16). In this letter we demonstrate another example of unusual properties of LHM and study electromagnetic surface TE waves guided by an interface between RHM and a 1D periodic structure consisting of alternate LHM and RHM layers which we refer to lefthanded photonic crystal.…”