We have investigated band-gap structures of three typical sonic/phononic crystals, namely periodic arrays of methacrylic resin cylinders in air, aluminum cylinders in air, and steel cylinders in water, by two different FDTD methods; one method is a sonic one that deals with only longitudinal waves, and the other is an elastic one that includes also shear waves. We show that both FDTD methods give almost the same band-gap structures for the former two crystals. Namely, the band-gaps by the sonic FDTD method lie at higher frequency only by 0.01 ~ 0.02 in the normalized frequency than those by the elastic one. The theoretical band-gap structures agree well with the experimental ones. In contrast, it is shown that the third crystal should be analyzed by the elastic FDTD method. Resonant-mode wave-guides are made by a periodic repetition of single-defects along a line in a sonic crystal of rigid cylinders in air. The obtained resonant and well-guided transmission band lies inside the full band-gap of the original bulk crystal. A combination of such wave-guides with a line-defect wave-guide is shown to have desirable characteristics for filtered wave-guides and wave-couplers.

1.
J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light, Princeton University Press, Chichester, West Sussex 1995.
2.
Sigalas
M. M.
, “
Defect State of Acoustic Waves in a Two-Dimensional Lattice of Solid Cylinders
,”
J. Appl. Phys.
, vol.
84
, pp.
3026
3030
,
1998
.
3.
Sigalas
M. M.
and
Garcia
N.
, “
Theoretical Study of Three Dimensional Elastic Band Gaps with the Finite-Difference Time-Domain Methods
,”
J. Appl. Phys.
, vol.
87
, pp.
3122
3125
,
2000
.
4.
Miyashita
T.
and
Inoue
C.
, “
Numerical Investigations of Transmission and Waveguides Properties of Sonic Crystals by Finite-Difference Time-Domain Method
,”
Jpn. J. Appl. Phys.
, vol.
40
, Part 1, no.
5B
, pp.
3488
3492
, May
2001
.
5.
S. G. Johnson and J. D. Joannopoulos, Photonic Crystals, The Road from Theory to Practice, Kluwer Academic Publishers, Boston 2002.
6.
Miyashita
T.
, “
Full Band Gaps of Sonic Crystals Made of Acrylic Cylinders in Air - Numerical and Experimental Investigations -
,”
Jpn. J. Appl. Phys.
, vol.
41
, Part 1, no.
5B
, pp.
3170
3175
, May
2002
.
7.
T. Miyashita, “A Study on Transient Behaviors of Wave Propagation in the Waveguides Made of Two-Dimensional Artificial Crystals like Sonic Crystals and Photonic Crystals,” [in Japanese] IEICE, ‘Special Issue with Digital Data,’ vol.J85–A, No. 10, pp. 1138–1145, October 2002.
8.
Khelif
A.
,
Deymier
P. A.
,
Djafari-Rouhani
B.
,
Vasseur
J. O.
, and
Dobrzynski
L.
, “
Two-dimensional phonomic crystal with tunable narrow pass band: Application to a waveguide with selective frequency
,”
J. Appl. Phys.
, vol.
94
, pp.
1308
1311
,
2003
.
9.
Miyashita
T.
, “
Sonic crystals and sonic wave guides
,”
Meas. Sci. Technol.
vol.
16
, No.
5
, pp.
R47–R63
R47–R63
, May
2005
.
This content is only available via PDF.
You do not currently have access to this content.