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Acoustic Leaky Vilave Antenna
LWAs as sensing instruments have been developed and in Equation 2. In this way, the device behaves analogously
improved in the subsequent decades by using a periodic to a prism, splitting the frequency components into
modulation, such as an array of holes, instead of a continuous different radiated directions. Several review articles provide
slit (see Figure 3, middle; Monticone a.nd Alu, 2015). This comprehensive overviews of this steering behavior for
approach allows the antenna be divided into representative electromagnetic LWAs (see Jackson et al., 2012; Monticone
unit cells (repeating elements in a geometry such as a hole and Alu, 2015). Although the majority of research of LWA
in the waveguide wall) to predict antenna directionality technology has been for use with electromagnetic waves, the
through the study of dispersion in a small section of the idea was first realized in acoustics by Naify et al. (2013).
antenna rather than the entire array (Caloz and Itoh,
2004; Oliner and Iackson, 2007). Integrating metarnaterial Acoustic |v|3tan«.g¢-,3,-ia|5
C°iiCePt5> which aie discussed in m°i'e detail in Awiistic The topic of acoustic metamaterials has seen rapid expansion
Metamaterials, also provides additional degrees of freedom over me 1351 mo decadg5_ in large part due to the Promise
€01 LWA design (599 Figure 3» 170307"; Li“ 9‘ 31-: 2002)‘ of creating synthetic media whose properties surpass those
So, how does the dispersion-bea.m steering relationship in °f hathiahy eeehiiihg °i' Ciiiiehtiy avahahie iiiaii'ihade
LWAS work? curring a 51“ in the waveguide doesrrst just allow materials with exotic capabilities for wave manipulation such
power to leak out of the waveguide. Instead, it also alters the as ddakihgi iehses that exceed tiaditidhai iesohitioh hihitsv
propagation of the wave inside the waveguide because the and exttannnnary absorption (Custer and Guenneau’
interaction of the wave with the slit is frequency dependent 2013)‘ These metaihatetiai ariahgeihehts hehave lhst hke
and, as a resuhi rhe waveguide is new dispersive‘ any other material except that they have effective material
properties (such as mass and stiffness) that are frequency
T0 understand the di5Persi°n'dneen°nanty relationship‘ dependent and can be positive or negative. This behavior is
we dig ihti’ sdiiie hasic Physics “siiig the Cdotdinate system described in detail in recent review articles by Haberman
defined in Figure 2C with a schematic ofa LWA of length and G“-rld (2016) and Haberman and Norris (2016). In its
1" made “P Of" unit can elements’ which is excited by input simplest form, negative inertia (mass) can be thought of as
Piesshte Pa radiating at angle 9' Eqnannn 1* in which an an out-of-phase time harmonic motion of a moving mass
Parameters are frequency dependent‘ dennes the Complex while negative stiffness requires that an increase in applied
wa‘_'en“'hheh kg‘ ef the leaky ih°de ihside the wavegmde pressure yield a positive expansion. These unusual effective
:2:irreliarfiei63:1;eimp:;Iana:yl:afi:yn;)\::::r];e-f1:I]:€;¢::5m::!i::e gmperties are impossible to create without exploiting
ynamic effects at length scales much smaller than the
flz is knew“ as the Phase Cdhstaht iii the waVeg“ide and “z acoustic wavelength, but have been shown to exist in certain
represents the leakage factor due to the slit or holes in the frequency ranges for ma5§_§Pring_mass and srde_bra_rrCh
waveguide. Discussion of these parameters is described in resonator elemems to induce rregarive dyrmrmc density or
greater detail by Caloz et al. (2004) stiffness, respeerivelyr
kz = 52 — W; (1) .. . . _
The ability of metamaterials to enable negative effective
when a Wave at a SiVeh fieiliieiiey Pmliagates iii the mass and stiffness also has a significant impact on the wave
WaVeS“idev the leaked Powei radiates at a fie‘l“ehCY' propagation characteristicswithin the metamaterial.Because
dePeiideiit angle (9)— defi-“Ed in Eiliiatiiih 2 Wheie kn is the the phase speed is equal to the square root of the stiffness
wavehhihhei iii the shiidhhdihg ihediiiih shah as air °i divided by the mass, the signs of the mass and stiffness terms
Wateh Ndte the siiiihaiity °f this e‘l“ati°ii h’ the iefiaeted must be the same (either both positive or both negative) for
ahgle df radiated aeohstie eheigy °f °“i' iee'ah' ihteifaee the phase speed to be real valued and therefore support wave
eXaiiiPie , _1 pl propagation. When the dynamic density and bulk modulus
E = Sm E (2) are simultaneously negative, wave propagation is supported.
We then change the frequency inside the waveguide. When a However, in this case, the energy and phase velocities are
wave atagiven frequency(/) propagates inthe waveguide, the in opposite directions, and we observe a very nonintuitive
leaked power radiates at an angle (9) determined by the ratio phenomenon known as negative refraction, where phase
of the wave speed in the waveguide to the wave speed in the fronts bend in the opposite direction of the standard
surrounding medium, consistent with Snell’s law as shown refractive index (see visualization at This
act 1 Acuulclcl Tbday 1 mi 2013

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