Waveguide hybrid junctions, such as Magic-T and rat-race couplers, have been of great interest in microwave technology not only for their applications in power monitoring, but also for design and synthesis of various non-reciprocal devices including electromagnetic circulators and isolators. Here, an acoustic rat-race coupler is designed and demonstrated for the first time, working on the basis of constructive and destructive interferences between the clockwise and counterclockwise of a ring resonator. It is then shown how the sound isolation provided by such a coupler enables the realization of an acoustic four-port circulator, a device which has not been reported as yet. Many other promising acoustic devices comprising power combiners, power dividers, mixers, and modulators can be envisioned to be implemented based on the proposed rat-race coupler.

1.
H. A.
Bethe
, “
Theory of diffraction by small holes
,”
Phys. Rev.
66
,
163
182
(
1944
).
2.
R.
Levy
, “
Synthesis of symmetrical branch-guide directional couplers
,”
IEEE Trans. Microwave Theory Tech.
16
,
995
1006
(
1968
).
3.
J.
Hirokawa
,
K.
Sakurai
,
M.
Ando
, and
N.
Goto
, “
An analysis of a waveguide T junction with an inductive post
,”
IEEE Trans. Microwave Theory Tech.
39
,
563
566
(
1991
).
4.
E. J.
Wilkinson
, “
An N-way hybrid power divider
,”
IEEE Trans. Microwave Theory Tech.
8
,
118
(
1960
).
5.
W. A.
Tyrrell
, “
Hybrid circuits for microwaves
,”
Proc. IRE
35
,
1294
1306
(
1947
).
6.
M.
Park
and
B.
Lee
, “
A dual-band Wilkinson power divider
,”
IEEE Microwave Wireless Compon. Lett.
18
,
85
87
(
2008
).
7.
Y.
Sun
and
A.
Freundorfer
, “
Broadband folded Wilkinson power combiner/splitter
,”
IEEE Microwave Wireless Compon. Lett.
14
,
295
297
(
2004
).
8.
Y.
Cheng
,
W.
Hong
, and
K.
Wu
, “
Novel substrate integrated waveguide fixed phase shifter for 180-degree directional coupler
,” in
2007 IEEE/MTT-S Int. Microwave Symp.
, pp.
189
192
.
9.
D.
Pozar
,
Microwave Engineering
, 4th ed. (
Wiley
,
New York
,
2005
).
10.
R. B.
Mouw
, “
A broad-band hybrid junction and application to the star modulator
,”
IEEE Trans. Microwave Theory Tech.
16
,
911
918
(
1968
).
11.
A.
Das
and
S. K.
Das
,
Microwave Engineering
, 2nd ed. (
McGraw-Hill
,
New Dehli
,
2009
), p.
465
.
12.
H. J.
Riblet
, “
Balanced duplexer
,” U.S. patent 2,586,993 (February 26,
1952
).
13.
F. F.
He
,
K.
Wu
,
W.
Hong
,
L.
Han
, and
X.
Chen
, “
A planar magic-T structure using substrate integrated circuits concept and its mixer applications
,”
IEEE Trans. Microwave Theory Tech.
59
,
72
79
(
2011
).
14.
E. J.
Reed
,
M.
Soljačić
, and
J. D.
Joannopoulos
, “
Reversed Doppler effect in photonic crystals
,”
Phys. Rev. Lett.
91
,
133901
(
2003
).
15.
F.
Zangeneh Nejad
and
R.
Fleury
, “
Doppler-based acoustic gyrator
,”
Appl. Sci.
8
,
1083
(
2018
).
16.
H.
Hashemi
and
B.
Analui
, “
All-acoustic duplexers using directional couplers
,” U.S. patent 9,866,201 (January 9,
2018
).
17.
M.
Shin
,
F. M.
Fazi
,
P. A.
Nelson
, and
F. C.
Hirono
, “
Mode-matching-based sound field recording and synthesis with circular double-layer arrays
,”
J. Sound Vib.
333
,
3794
3817
(
2014
).
18.
R.
Fleury
,
D. L.
Sounas
,
C. F.
Sieck
,
M. R.
Haberman
, and
A.
Alù
, “
Sound isolation and giant linear nonreciprocity in a compact acoustic circulator
,”
Science
343
,
516
519
(
2014
).
19.
R.
Fleury
,
D.
Sounas
, and
A.
Alù
, “
An invisible acoustic sensor based on parity-time symmetry
,”
Nat. Commun.
6
,
5905
(
2015
).
20.
R.
Fleury
,
D.
Sounas
,
M. R.
Haberman
, and
A.
Alù
, “
Non-reciprocal acoustics
,”
Acoust. Today
11
,
14
21
(
2015
).
21.
S.
Bhuktare
,
A.
Bose
,
H.
Singh
, and
A. A.
Tulapurkar
, “
Gyrator based on magneto-elastic coupling at a ferromagnetic/piezoelectric interface
,”
Sci. Rep.
7
,
840
(
2017
).
22.
A.
Blanchard
,
T. P.
Sapsis
, and
A. F.
Vakakis
, “
Non-reciprocity in nonlinear elastodynamics
,”
J. Sound Vib.
412
,
326
335
(
2018
).
23.
F.
Li
,
P.
Anzel
,
J.
Yang
,
P. G.
Kevrekidis
, and
C.
Daraio
, “
Granular acoustic switches and logic elements
,”
Nat. Commun.
5
,
5311
(
2014
).
24.
Z. M.
Gu
,
J.
Hu
,
B.
Liang
,
X. Y.
Zou
, and
J. C.
Cheng
, “
Broadband non-reciprocal transmission of sound with invariant frequency
,”
Sci. Rep.
6
,
19824
(
2016
).
25.
C.
Fu
,
B.
Wang
,
T.
Zhao
, and
C. Q.
Chen
, “
High efficiency and broadband acoustic diodes
,”
Appl. Phys. Lett.
112
,
051902
(
2018
).
26.
L. M.
Brekhovskikh
,
Y. P.
Lysanov
, and
J. P.
Lysanov
,
Fundamentals of Ocean Acoustics
(
Springer Science & Business Media
,
New York
,
2003
).
27.
J. H.
Oh
,
H. W.
Kim
,
P. S.
Ma
,
H. M.
Seung
, and
Y. Y.
Kim
, “
Inverted bi-prism phononic crystals for one-sided elastic wave transmission applications
,”
Appl. Phys. Lett.
100
,
213503
(
2012
).
28.
Y.
Li
,
B.
Liang
,
Z. M.
Gu
,
X. Y.
Zou
, and
J. C.
Cheng
, “
Unidirectional acoustic transmission through a prism with near-zero refractive index
,”
Appl. Phys. Lett.
103
,
053505
(
2013
).
29.
Y. L.
Huang
,
H. X.
Sun
,
J. P.
Xia
,
S. Q.
Yuan
, and
X. L.
Ding
, “
Multi-band asymmetric acoustic transmission in a bended waveguide with multiple mechanisms
,”
Appl. Phys. Lett.
109
,
013501
(
2016
).
30.
M.
Maldovan
, “
Sound and heat revolutions in phononics
,”
Nature
503
,
209
217
(
2013
).
31.
H.
Jia
,
M.
Ke
,
C.
Li
,
C.
Qiu
, and
Z.
Liu
, “
Unidirectional transmission of acoustic waves based on asymmetric excitation of Lamb waves
,”
Appl. Phys. Lett.
102
,
153508
(
2013
).
32.
M. B.
Zanjani
,
A. R.
Davoyan
,
A. M.
Mahmoud
,
N.
Engheta
, and
J. R.
Lukes
, “
One-way phonon isolation in acoustic waveguides
,”
Appl. Phys. Lett.
104
,
081905
(
2014
).
33.
B. I.
Popa
and
S. A.
Cummer
, “
Nonreciprocal active metamaterials
,”
Phys. Rev. B
85
,
205101
(
2012
).
34.
H. X.
Sun
and
S. Y.
Zhang
, “
Enhancement of asymmetric acoustic transmission
,”
Appl. Phys. Lett.
102
(
11
),
113511
(
2013
).
35.
A.
Cicek
,
O.
Adem Kaya
, and
B.
Ulug
, “
Refraction-type sonic crystal junction diode
,”
Appl. Phys. Lett.
100
,
111905
(
2012
).
36.
M.
Xiao
,
G.
Ma
,
Z.
Yang
,
P.
Sheng
,
Z. Q.
Zhang
, and
C. T.
Chan
, “
Geometric phase and band inversion in periodic acoustic systems
,”
Nat. Phys.
11
,
240
244
(
2015
).
37.
H.
Esfahlani
,
S.
Karkar
,
H.
Lissek
, and
J. R.
Mosig
, “
Acoustic dispersive prism
,”
Sci. Rep.
6
,
18911
(
2016
).
38.
A. A.
Maznev
,
G.
Gu
,
S. Y.
Sun
,
J.
Xu
,
Y.
Shen
,
N.
Fang
, and
S. Y.
Zhang
, “
Extraordinary focusing of sound above a soda can array without time reversal
,”
New J. Phys.
17
,
042001
(
2015
).
39.
J.
Xu
,
X.
Jiang
,
N.
Fang
,
E.
Georget
,
R.
Abdeddaim
,
J. M.
Geffrin
,
M.
Farhat
,
P.
Sabouroux
,
S.
Enoch
, and
S.
Guenneau
, “
Molding acoustic, electromagnetic and water waves with a single cloak
,”
Sci. Rep.
5
,
10678
(
2015
).
40.
X.
Fan
,
C.
Qiu
,
S.
Zhang
,
M.
Ke
, and
Z.
Liu
, “
Highly asymmetric interaction forces induced by acoustic waves in coupled plate structures
,”
J. Appl. Phys.
118
,
244506
(
2015
).
41.
S.
Zhang
,
Y.
Zhang
,
Y.
Guo
,
Y.
Leng
,
W.
Feng
, and
W.
Cao
, “
Realization of subwavelength asymmetric acoustic transmission based on low-frequency forbidden transmission
,”
Phys. Rev. Appl.
5
,
034006
(
2016
).
42.
K.
Song
,
J.
Kim
,
S.
Hur
,
J. H.
Kwak
,
S. H.
Lee
, and
T.
Kim
, “
Directional reflective surface formed via gradient-impeding acoustic meta-surfaces
,”
Sci. Rep.
6
,
32300
(
2016
).
43.
X. P.
Wang
,
L.
Le Wan
,
T. N.
Chen
,
Q. X.
Liang
, and
A. L.
Song
, “
Broadband acoustic diode by using two structured impedance-matched acoustic metasurfaces
,”
Appl. Phys. Lett.
109
,
044102
(
2016
).
44.
S.
Zhai
,
H.
Chen
,
C.
Ding
,
F.
Shen
,
C.
Luo
, and
X.
Zhao
, “
Manipulation of transmitted wave front using ultrathin planar acoustic metasurfaces
,”
Appl. Phys. A: Mater. Sci. Process.
120
,
1283
1289
(
2015
).
45.
F.
Zangeneh-Nejad
and
R.
Fleury
, “
Acoustic birefringence via non-Eulerian metamaterials
,” arXiv:1803.09070 (
2018
).
46.
T.
Devaux
,
V.
Tournat
,
O.
Richoux
, and
V.
Pagneux
, “
Asymmetric acoustic propagation of wave packets via the self-demodulation effect
,”
Phys. Rev. Lett.
115
,
234301
(
2015
).
47.
Y. F.
Zhu
,
X. Y.
Zou
,
B.
Liang
, and
J. C.
Cheng
, “
Acoustic one-way open tunnel by using metasurface
,”
Appl. Phys. Lett.
107
,
113501
(
2015
).
48.
F.
Zangeneh-Nejad
and
R.
Fleury
, “
Acoustic analogues of high-index optical waveguide devices
,”
Sci. Rep.
8
,
10401
(
2018
).
49.
R.
Fleury
,
A. B.
Khanikaev
, and
A.
Alù
, “
Floquet topological insulators for sound
,”
Nat. Commun.
7
,
11744
(
2016
).
50.
Z.
Shen
,
Y. L.
Zhang
,
Y.
Chen
,
C. L.
Zou
,
Y. F.
Xiao
,
X. B.
Zou
,
F. W.
Sun
,
G. C.
Guo
, and
C. H.
Dong
, “
Experimental realization of optomechanically induced non-reciprocity
,”
Nat. Photon.
10
,
657
661
(
2016
).
51.
C.
He
,
X.
Ni
,
H.
Ge
,
X. C.
Sun
,
Y.
Bin Chen
,
M. H.
Lu
,
X. P.
Liu
, and
Y. F.
Chen
, “
Acoustic topological insulator and robust one-way sound transport
,”
Nat. Phys.
12
,
1124
1129
(
2016
).
52.
G.
Trainiti
and
M.
Ruzzene
, “
Non-reciprocal elastic wave propagation in spatiotemporal periodic structures
,”
New J. Phys.
18
,
083047
(
2016
).
53.
C.
Liu
,
Z.
Du
,
Z.
Sun
,
H.
Gao
, and
X.
Guo
, “
Frequency-preserved acoustic diode model with high forward-power-transmission rate
,”
Phys. Rev. Appl.
3
,
064014
(
2015
).
54.
R.
Sasaki
,
Y.
Nii
,
Y.
Iguch
, and
Y.
Onose
, “
Nonreciprocal propagation of surface acoustic wave in Ni/LiNbO 3
,”
Phys. Rev. B
95
,
020407
(
2017
).
55.
H.
Zhu
and
M.
Rais-Zadeh
, “
Non-reciprocal acoustic transmission in a GaN delay line using the acoustoelectric effect
,”
IEEE Electron Dev. Lett.
38
,
802
805
(
2017
).
56.
R.
Fleury
,
D.
Sounas
, and
A.
Alu
, “
Non-reciprocal acoustic devices based on spatio-temporal angular-momentum modulation
,”
J. Acoust. Soc. Am.
136
,
2281
(
2014
).
57.
Y. G.
Peng
,
C. Z.
Qin
,
D. G.
Zhao
,
Y. X.
Shen
,
X. Y.
Xu
,
M.
Bao
,
H.
Jia
, and
X. F.
Zhu
, “
Experimental demonstration of anomalous Floquet topological insulator for sound
,”
Nat. Commun.
7
,
13368
(
2016
).
58.
A. V.
Poshakinskiy
and
A. N.
Poddubny
, “
Phonoritonic crystals with a synthetic magnetic field for an acoustic diode
,”
Phys. Rev. Lett.
118
,
156801
(
2017
).
59.
F.
Zangeneh-Nejad
and
R.
Fleury
, “
Performing mathematical operations using high-index acoustic metamaterials
,”
New J. Phys.
20
,
073001
(
2018
).
60.
H.
Abbaszadeh
,
A.
Souslov
,
J.
Paulose
,
H.
Schomerus
, and
V.
Vitelli
, “
Sonic Landau levels and synthetic gauge fields in mechanical metamaterials
,”
Phys. Rev. Lett.
119
,
195502
(
2017
).
61.
B.
Rostami-Dogolsara
,
M. K.
Moravvej-Farshi
, and
F.
Nazari
, “
Tunable phononic structures using Lamb waves in a piezoceramic plate
,”
Phys. Rev. B
99
,
094302
(
2016
).
62.
X.
Yang
,
J.
Yin
,
G.
Yu
,
L.
Peng
, and
N.
Wang
, “
Acoustic superlens using Helmholtz-resonator-based metamaterials
,”
Appl. Phys. Lett.
107
,
193505
(
2015
).
63.
X.
Jiang
,
B.
Liang
,
X. Y.
Zou
,
J.
Yang
,
L. L.
Yin
,
J.
Yang
, and
J. C.
Cheng
, “
Acoustic one-way metasurfaces: Asymmetric phase modulation of sound by subwavelength layer
,”
Sci. Rep.
6
,
28023
(
2016
).
64.
Q.
Wang
,
Y.
Yang
,
X.
Ni
,
Y. L.
Xu
,
X. C.
Sun
,
Z. G.
Chen
,
L.
Feng
,
X. P.
Liu
,
M. H.
Lu
, and
Y. F.
Chen
, “
Acoustic asymmetric transmission based on time-dependent dynamical scattering
,”
Sci. Rep.
5
,
10880
(
2015
).
65.
F.
Zangeneh-Nejad
and
R.
Fleury
, “
Topological fano resonances
,”
Phys. Rev. Lett
122
,
014301
(
2019
).
66.
B.
Liang
,
X. S.
Guo
,
J.
Tu
,
D.
Zhang
, and
J. C.
Cheng
, “
An acoustic rectifier
,”
Nat. Mater.
9
,
989
992
(
2010
).
67.
Y.
Li
,
B.
Liang
,
Z. M.
Gu
,
X. Y.
Zou
, and
J. C.
Cheng
, “
Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces
,”
Sci. Rep.
3
,
2546
(
2013
).
You do not currently have access to this content.