Graded negative index lens with designable focal length by phononic crystal

Abstract

We realize a flat lens with graded negative refractive index by a two-dimensional phononic crystal.The index-grade is achieved by gradual modification of the filling fraction along the transverse direction to propagation. We demonstrate that this lens can realize the focusing and amplification of parallel incident acoustic waves. A formula for the refractive index profile is derived by which the lens with desired focal length can be precisely designed and the aberrations of image can be effectively reduced. This designable lens is expected to bear significance in applications such as coupling or integration with various types of acoustic devices.PACS numbers: 43.20.+g, 43.35.+d, 43.40.+s The ability to manipulate waves has been greatly enhanced with the recent advances in metamaterials (MMs) due to the many unusual properties they possess [1]. One of these predominant properties is the negative refraction which has been utilized to image with flat MM lenses [2]. Alternatively, negative refraction can also be realized by photonic/phononic crystals (PCs) which behave like materials with negative refractive index within some frequency regions 3

High transmission acoustic focusing by impedance-matched acoustic meta-surfaces

“…To obtain excellent focusing without any aberration of the focal spot, we employ the following hyperbolic refractive index profile 8,24,34,35 …”

Focusing of Rayleigh waves with gradient-index phononic crystals

“…Among the most promising devices are surely the gradient-index (GRIN) PCs, which are generally formed by gradually modifying certain physical or geometrical parameters along some directions of the structure. [12][13][14] Similarly to the GRIN optical fibers, their optical counterparts, the GRIN PCs can be used in various technological fields such as the non-destructive evaluation of materials, the energy harvesting, etc. For this purpose, the focusing of different types of waves, either in [15][16][17][18][19][20][21][22][23] or out 13,24 the homogenization regime, has been observed.…”

Hybrid phononic crystals for broad-band frequency noise control by sound blocking and localization

“…7,11 Thus, the results in Table 1 are consistent with the well-known facts. 6,7,10,11 Note that the calculated ERI values are suitable since n 1 > n 2 regardless of whether refractive index values are positive or negative.…”

“…For instance, one can use PCs resembling convex optical lens, 6,7 where positive refraction is utilized. Alternatively, negative refraction based on metamaterials [8][9][10][11] may be used. Negative refraction represents a phenomenon that rays are refracted in reverse sense to that normally expected in nature.…”