Traditional sound diffusers are quasi-random phase gratings attached to reflecting surfaces to introduce spatiotemporal incoherence into the backscattered acoustic field. Early designs consisted of periodically tiled diffuser grating unit cells to cover large surfaces. However, spatial periodicity leads to coherent constructive and destructive interference, which is undesirable for achieving acoustic diffusivity. This problem was partially addressed by using aperiodic tiling of unit cells based on pseudorandom sequences. While an aperiodic diffuser spacing can overcome the problems introduced by spatial periodicity, the improvements in performance come at the expense of increased thickness. In this work, we investigate spatiotemporal modulation of the surface acoustic admittance of a metasurface diffuser to improve sound diffusion. Using semi-analytical and finite element models, we demonstrate that the effects of the spatial periodicity can be mitigated without introducing an aperiodic spatial spacing, thus simultaneously minimizing diffuser thickness and improving diffusivity of the backscattered field. We develop a semi-analytical model that employs Fourier series expansion to determine the scattered sound field from a surface admittance consisting of a quadratic residue diffuser whose individual well admittances are modulated in a traveling wave fashion with modulation frequency, ωm, amplitude, Ym, and a wavenumber that matches the unit cell length, Λ. We observe significant improvement in diffusion due to the fact that the spatiotemporal modulation scatters sound into additional frequency-wavenumber pairs associated with harmonics of ωm and their diffraction orders. The semi-analytical model results are verified using a time-domain finite element model and compared with periodic and aperiodic diffuser designs.

1.
M. R.
Schroeder
,
J. Acoust. Soc. Am.
57
,
149
(
1975
).
2.
M. R.
Schroeder
,
J. Acoust. Soc. Am.
65
,
958
(
1979
).
3.
P.
D'Antonio
and
J. H.
Konnert
,
J. Audio Eng. Soc.
32
,
228
(
1984
).
4.
T. J.
Cox
and
Y. W.
Lam
,
J. Acoust. Soc. Am.
95
,
297
(
1994
).
5.
E.
Ballestero
,
N.
Jiménez
,
J.-P.
Groby
,
S.
Dance
,
H.
Aygun
, and
V.
Romero-García
,
Appl. Phys. Lett.
115
,
081901
(
2019
).
6.
T.
Cox
and
P.
d'Antonio
,
Acoustic Absorbers and Diffusers: Theory, Design and Application
(
CRC Press
,
2016
).
7.
J. A.
Angus
and
C. I.
McManmon
,
J. Audio Eng. Soc.
46
,
1109
(
1998
).
8.
J. A.
Angus
,
Appl. Acoust.
60
,
143
(
2000
).
9.
T.
Cox
and
P.
D'Antonio
,
Build. Acoust.
10
,
1–32
(
2003
).
10.
T. J.
Cox
,
J. A.
Angus
, and
P.
D'Antonio
,
J. Acoust. Soc. Am.
119
,
310
(
2006
).
11.
H.
Nassar
,
B.
Yousefzadeh
,
R.
Fleury
,
M.
Ruzzene
,
A.
Alù
,
C.
Daraio
,
A. N.
Norris
,
G.
Huang
, and
M. R.
Haberman
,
Nat. Rev. Mater.
5
,
667
(
2020
).
12.
E. S.
Cassedy
and
A. A.
Oliner
,
Proc. IEEE
51
,
1342
(
1963
).
13.
G.
Trainiti
and
M.
Ruzzene
,
New J. Phys.
18
,
083047
(
2016
).
14.
H.
Nassar
,
H.
Chen
,
A.
Norris
,
M.
Haberman
, and
G.
Huang
,
Proc. R. Soc. A
473
,
20170188
(
2017
).
15.
H.
Nassar
,
X.
Xu
,
A.
Norris
, and
G.
Huang
,
J. Mech. Phys. Solids
101
,
10
(
2017
).
16.
J.
Vila
,
R. K.
Pal
,
M.
Ruzzene
, and
G.
Trainiti
,
J. Sound Vib.
406
,
363
(
2017
).
17.
E.
Riva
,
J.
Marconi
,
G.
Cazzulani
, and
F.
Braghin
,
J. Sound Vib.
449
,
172
(
2019
).
18.
G.
Trainiti
,
Y.
Xia
,
J.
Marconi
,
G.
Cazzulani
,
A.
Erturk
, and
M.
Ruzzene
,
Phys. Rev. Lett.
122
,
124301
(
2019
).
19.
B. M.
Goldsberry
,
S. P.
Wallen
, and
M. R.
Haberman
,
Phys. Rev. B
102
,
014312
(
2020
).
20.
C.
Sugino
,
M.
Ruzzene
, and
A.
Erturk
,
Phys. Rev. B
102
,
014304
(
2020
).
21.
C.
Shen
,
X.
Zhu
,
J.
Li
, and
S. A.
Cummer
,
Phys. Rev. B
100
,
054302
(
2019
).
22.
J.
Li
,
C.
Shen
,
X.
Zhu
,
Y.
Xie
, and
S. A.
Cummer
,
Phys. Rev. B
99
,
144311
(
2019
).
23.
X.
Zhu
,
J.
Li
,
C.
Shen
,
X.
Peng
,
A.
Song
,
L.
Li
, and
S. A.
Cummer
,
Appl. Phys. Lett.
116
,
034101
(
2020
).
24.
R.
Fleury
,
D. L.
Sounas
,
C. F.
Sieck
,
M. R.
Haberman
, and
A.
Alù
,
Science
343
,
516
(
2014
).
25.
Z.
Wang
and
S.
Fan
,
Appl. Phys. B
81
,
369
(
2005
).
26.
R.
Fleury
,
D. L.
Sounas
, and
A.
Alù
,
Phys. Rev. B
91
,
174306
(
2015
).
27.
B. M.
Goldsberry
,
S. P.
Wallen
, and
M. R.
Haberman
,
Phys. Rev. Appl.
17
,
034050
(
2022
).
28.
R.
Adlakha
,
M.
Moghaddaszadeh
,
M. A.
Attarzadeh
,
A.
Aref
, and
M.
Nouh
,
Sci. Rep.
10
,
21339
(
2020
).
29.
X.
Wang
,
A.
Diaz-Rubio
,
H.
Li
,
S. A.
Tretyakov
, and
A.
Alu
,
Phys. Rev. Appl.
13
,
044040
(
2020
).
30.
X.
Wang
,
V. S.
Asadchy
,
S.
Fan
, and
S. A.
Tretyakov
,
ACS Photonics
8
,
3034
(
2021
).
31.
X.
Guo
,
Y.
Ding
,
Y.
Duan
, and
X.
Ni
,
Light: Sci. Appl.
8
,
123
(
2019
).
32.
A.
Shaltout
,
A.
Kildishev
, and
V.
Shalaev
,
Opt. Mater. Express
5
,
2459
(
2015
).
33.
A. M.
Shaltout
,
V. M.
Shalaev
, and
M. L.
Brongersma
,
Science
364
,
eaat3100
(
2019
).
34.
S. P.
Wallen
and
M. R.
Haberman
,
Phys. Rev. E
99
,
013001
(
2019
).
35.
B. M.
Goldsberry
,
S. P.
Wallen
, and
M. R.
Haberman
,
J. Acoust. Soc. Am.
146
,
782
(
2019
).
36.
S. G.
Konarski
,
M. R.
Haberman
, and
M. F.
Hamilton
,
Phys. Rev. E
101
,
022215
(
2020
).
37.
E.
Motato
,
A.
Haris
,
S.
Theodossiades
,
M.
Mohammadpour
,
H.
Rahnejat
,
P.
Kelly
,
A.
Vakakis
,
D.
McFarland
, and
L.
Bergman
,
Nonlinear Dyn.
87
,
169
(
2017
).
38.
A.
Berkhout
,
D.
van Wulfften Palthe
, and
D.
De Vries
,
J. Acoust. Soc. Am.
65
,
1334
(
1979
).
39.
F.
Mechel
,
Acta Acust. Acustica
81
,
379
(
1995
).
40.
T.
Wu
,
T.
Cox
, and
Y.
Lam
,
J. Acoust. Soc. Am.
108
,
643
(
2000
).
41.
E. G.
Williams
,
Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
(
Academic Press
,
1999
).

Supplementary Material

You do not currently have access to this content.