Source Illusion Devices for Flexural Lamb Waves Using Elastic Metasurfaces
Yongquan Liu,
1
Zixian Liang,
2
Fu Liu,
1
Owen Diba,
1
Alistair Lamb,
1
and Jensen Li
1,*
1
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
2
College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China
(Received 10 January 2017; published 21 July 2017)
Inspired by recent demonstrations of metasurfaces in achieving reduced versions of electromagnetic
cloaks, we propose and experimentally demonstrate source illusion devices to manipulate flexural waves
using metasurfaces. The approach is particularly useful for elastic waves due to the lack of form invariance
in usual transformation methods. We demonstrate compact and simple-to-implement metasurfaces for
shifting, transforming, and splitting a point source. The effects are measured to be broadband and robust
against a change of source positions, with agreement from numerical simu lations and the Huygens-Fresnel
theory. The proposed method is potentially useful for applications such as nondestructive testing,
high-resolution ultrasonography, and advanced signal modulation.
DOI: 10.1103/PhysRevLett.119.034301
The ability to make objects invisible has captured our
imagination since ancient times and has become reachable
very recently due to the appearance of metamaterials [1]
together with transformation optics [2–5]. A family of more
general illusion effects has also been established based on
the transformation approach. Either scattering [6,7] or
source radiation [8] can be transformed to prescribed target
patterns. Furthermore, the transformation approach has
been extended to control acoustic waves [9–11] and heat
flows [12–14]. Although some elastic cloaks have been
studied and designed with approximations [15,16], the
transformation method, together with elastic metamaterials
[17–22], is nonuniversal to manipulate elastic waves, as the
governing equation in elastodynamics (i.e., the Navier
equation) cannot keep its form under a general coordinate
transformation [23], unless further approximations [24] are
applied or the proposed Willis media [25] can be realized
and employed with a complex cross-coupling response. It
makes the application of the transformation approach on
elastic waves nontrivial and more generic illusion appli-
cations, which may use negative-index metamaterials with
unavoidable loss and fabrication issues, very challenging.
On the other hand, the recently proposed metasurface
[26–33], a kind of artificial sheet material with subwave-
length-scaled patterns and thickness, can modulate wave
fronts on demand through specific boundary conditions.
The metasurface approach shows the simplicity in fabri-
cation with a low-loss, compact form factor but without
losing the extreme functionality of bulk metamaterials. It
has already been demonstrated as an effective way to
manipulate wave fronts in both optics and acoustics,
including generating an anomalous refraction or reflection,
arbitrary surface plasmon profiles, high-efficiency holo-
grams [26–32], and even an ultrathin invisibility cloak
[33,34], which is a simplified version of a carpet cloak
originally using bulk metamaterials in the transformation
approach [35]. Therefore, the extension of metasurfaces to
elastic waves is expected to be very effective to demonstrate
nontrivial wave phenomena, which associate with richer
physics [20–22] due to its more degrees of freedom than
acoustic and electromagnetic counterparts and a wide range
of potential applications in nondestructive testing, medical
ultrasonography, and earthquake resistance in civil engi-
neering [18,36–40]. Until very recently, Zhu and
Semperlotti [41] have presented the first experimental
demonstration of elastic metasurfaces to achieve the
anomalous refraction of guided waves in solids, based
on a “cross-polarization” conversion (from symmetric S
0
to
antisymmetric A
0
mode) with a transmission efficiency
around 18%, comparing to the theoretical maximum
efficiency 25% in the case of electromagnetic waves
[42,43]. A higher transmission efficiency, together with a
suitable design framework, will be an enabling key to a
much wider range of applications of elastic metasurfaces.
In this Letter, we develop a theoretical framework and
experimental realization of source illusion devices using
elastic metasurfaces. Our approach requires neither the
fore-mentioned form invariance of elastodynamics nor bulk
metamaterials with negative indices yet allows us to
demonstrate a series of all-angle elastic illusion effects.
Figure 1(a) shows a schematic diagram illustrating the
design strategy. The target wave profile, living in the virtual
space, is described by its phase profile ϕ
tar
ðx; yÞ [left-hand
side of Fig. 1(a)]. At the moment, we neglect the con-
tribution of the amplitude profile for simplicity. Suppose
that we have an original source, with a wave field
characterized by its phase ϕ
ori
ðx; yÞ, and a ring-type
metasurface with the phase discontinuity of ϕ
tar
− ϕ
ori
,
being evaluated at the location of the metasurface, will turn
this original incident field into an arbitrary target profile
[right-hand side of Fig. 1(a)]. A photograph of a metasur-
face sample is shown in Fig. 2(a) as well. By doing this, an
observer outside the metasurface (the black dashed circle)
finds the same target field pattern in the physical space as
PRL 119, 034301 (2017)
PHYSICAL REVIEW LETTERS
week ending
21 JULY 2017
0031-9007=17=119(3)=034301(6) 034301-1 © 2017 American Physical Society