Abstract
In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal.
Highlights
Left-handed materials (LHMs) or negative refractive-index materials (NIMs), characterized by simultaneously negative permittivity and permeability, were initially proposed and theoretically analyzed by Veselago in the 1960s [1], and have recently attracted renewed interest because of the experimental progresses [2,3,4,5]
The photonic band structure and equifrequency contours (EFCs) are calculated by the plane wave expansion method and plotted in Fig. 1(b) and Fig. 2, respectively. 961 plane waves are employed to assure the convergence of numerical calculations
A Gaussian beam with a normalized frequency ω0= 0.313 is incident to the photonic crystal (PhC) with angles φ = 30ο and φ = 60ο to the normal of the interface, as shown in Fig. 5(a) and Fig. 5(b), respectively. In both of the two circumstances, the incident beams are refracted in the opposite directions of the reflected beams, namely, the effective index of this PhC slab is neff = −1. This kind of negative refraction is a pure left-handed behavior that corresponds to vg ⋅ k < 0, which is different from the quasi-negative refraction caused by anisotropy in the first partial band gap of a squarelattice PhC
Summary
Left-handed materials (LHMs) or negative refractive-index materials (NIMs), characterized by simultaneously negative permittivity and permeability, were initially proposed and theoretically analyzed by Veselago in the 1960s [1], and have recently attracted renewed interest because of the experimental progresses [2,3,4,5]. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by numerical simulations using the finite-difference time-domain method (FDTD) [25]. We compare these left-handed behaviors with the quasi-negative refraction and its resulted focusing effects.
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