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• A Systematic design approach of elastic metagratings for retroreflection of flexural waves was proposed. • Near-perfect efficiency were accomplished for single- and multiple-angle retroreflection. • Simply configured, easily manufacturable hole-type scatterers compose the unit cells of the retroreflecting metagratings. • An optimization-based design formulation is posed for effective suppression of unwanted diffraction modes. The potential of elastic wave retroreflection is substantial for various applications such as structural identification and detection. However, realizing accurate retroreflection presents significant challenges owing to the need for high-efficiency anomalous reflection from boundaries. This study delves into the relatively less-explored field of flexural wave retroreflection in thin plates and proposes the use of metagratings for its realization. The present metagratings, which are built from unit cells created by possibly-overlapping circular holes, offer a simple fabrication process owing to their straightforward geometry. They hold an advantage over metasurfaces, which often struggle with wave steering because of their unmanageable higher-order diffraction modes. However, no systematic approach has been proposed so far to design metagratings for flexural wave retroreflection. To address this gap, we have established an optimization problem that identifies the optimal geometries and locations of the circular holes built into the proposed retroreflecting metagratings using a gradient-based optimizer. The design process involves diffraction grating theory and spatial fast Fourier transform. Both single and multiple retroreflections at various angles were considered and the numerical findings were substantiated by experimental results. The findings of this study imply that the investigated metagratings and design approaches have promising potential for more sophisticated wave manipulations. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel metagrating for simultaneous realization of mode-converting and anomalous steering of elastic wave reflection is proposed. • Near-perfect mode-conversion efficiencies are achieved for in-plane waves in thin elastic plate. • Metagratings realize longitudinal-to-shear and shear-to-longitudinal wave mode conversions in scattered refection field. • Higher-order scattered diffraction modes are effectively and selectively suppressed in metagratings. Metasurfaces have recently received much attentions for manipulating waves. However, it is difficult to control all high-order or diffracted modes using the popularly employed metasurfaces. Herein, we propose a new way for converting a normally incident elastic longitudinal (or shear) wave mode to an obliquely reflected elastic shear (or longitudinal) one, using metagratings of elaborately designed and arranged strips. For a longitudinal (or shear) wave incidence upon the free end of an elastic plate, it is intrinsically difficult to realize full-power mode conversion and steer the converted mode without generating undesired reflected waves. We show that our elaborately designed and optimized multiple rectangular strip-type metagratings are effective in simultaneously fulfilling the mode conversion and anomalous steering of elastic waves. Unlike metasurfaces, the proposed metagratings operate via the diffraction theory and multiple rectangular strips permit sufficient design freedom to fulfill the two design objectives. Several numerical simulations in this work show that the proposed strip-type metagratings achieve near-perfect mode-conversion efficiencies reaching 96 %, and the performance is supported by experiments. Applications of the designed metagratings in nondestructive evaluation are also demonstrated. [ABSTRACT FROM AUTHOR]

• A novel elastic metagrating model is proposed for efficient realization of anomalous steering of elastic waves. • The first and higher-order scattered longitudinal waves are selectively suppressed or preserved. • An analytic model is established for the proposed beam-type metagratings and coupled with elastic waves in a continuum. • The effective manipulation of anomalous reflections and beam steering of elastic longitudinal waves is demonstrated. • The physics related to the present metagratings is explored and experimental validation is performed. Metagratings have recently received much attention for effective realization of anomalous wave steering. Governed by the diffraction grating theory and the concept of metamaterials, metagratings allow to suppress superfluous propagations of high-order scattering modes in a selective manner such that wavefronts are accurately steered as designated. While numerous metagratings have been reported in electromagnetic wave research field, little has been explored in the elastic wave regime because of difficulties caused by complicatedly coupled motions among various types of elastic waves. In this circumstance, we newly propose a novel elastic metagrating model to realize anomalous steering of longitudinal waves in elastic continuum medium. Modeled by a periodic arrangement of a single or array of so-called beam-type elastic members, the present elastic metagratings resolve the difficulties in steering a specific scattered mode of elastic longitudinal waves by suppressing undesired modes in the scattered wave field. As the metagratings are attached to a boundary of elastic continuum, both longitudinal and flexural motions in the beam-type members are so coupled with elasticity wave solutions in the elastic medium as to thoroughly manipulate the reflected longitudinal waves from the interface. A set of appropriate geometric parameters of the beam-type members are searched for a direct control of the scattered modes quantitatively. As practical applications, the proposed elastic metagratings are applied to realize anomalous reflections and asymmetric splitting of longitudinal elastic waves. As well as experimental verifications, performance of the designed elastic metagratings are physically interpreted in the perspective of phase modulation. [ABSTRACT FROM AUTHOR]