Large two-dimensional sonic band gaps

We show that absolute sonic band gaps produced by two-dimensional square and triangular lattices of rigid cylinders in air can be increased by reducing the structure symmetry. In the case of square lattices, symmetry reduction is achieved by a smaller diameter cylinder placed at the center of each unit cell. For triangular lattices the reduction is achieved by decreasing the diameter of the cylinder at the center of the hexagons in the lattice. Theoretical predictions are also demonstrated experimentally: starting from a honeycomb lattice ~using cylinders of 4 cm of diameter size and 6.35 cm nearest-neighbor distance! we have studied the transition to a triangular symmetry by putting rods with increasing diameter ~in the range 0.6‐4 cm! at the center. The greatest enhancement of the attenuation strength observed in transmission experiments has been obtained in the high frequency region for diameter ratios in the range 0.1‐0.3. @S1063-651X~99!51212-9# PACS number~s!: 43.20.1g, 42.25.Bs, 52.35.Dm Since the seminal work of Yablonovitch @1# and John @2#, who open the research in photonic crystals ~PC!, we have witnessed the appearance of new devices based on the existence of photonic band gaps ~PBG! in these dielectric periodic structures. Also, because the underlying theory is applicable to other kind of waves, acoustic and elastic, a search for periodic structures having properties of sonic band gap ~SBG! or elastic band gap ~EBG!, respectively, is currently being performed. Therefore, the design, construction, and technological applications of a completely new type of crystals that could be called classical wave crystals is becoming a very promising project at the beginning of the new century. In the field of acoustics much theoretical work has been done proposing structures having SBG’s properties @3‐6#. The existence of SBG is due to a complex interplay between the sound velocity and density ratios of the composite materials, and their spatial arrangement. Experimentally, a few works have claimed to observe absolute band gaps @7,8#. Therefore, the actual possibility of building up composite material having SBG open a new technological research on environmental protection. One of the goals of PBG and SBG theory is the search of materials and/or topologies producing large gaps at the desired range of frequencies. In PC it has been shown that full PBG can be enlarged by decreasing the crystal symmetry through the introduction of a two-point basis set. Thus, for example, 3D PC based on a face-centered-cubic structure do not possess a full PBG between the first and second bands, but the ones having a diamond structure do because the additional point basis lifts the degeneracy of some bands @9# .I n the same manner, in two-dimensional ~2D! structures, Anderson and Giapis @10# obtained larger gaps when they add a different size rod at the center of each unit cell of square and honeycomb lattices. The latest conclusion awakened our interest about whether this sort of mechanism is effective in creating large SBG and/or enhancing the attenuation measured in some 2D sonic crystals ~SC! previously studied by us @8#. In this Rapid Communication we show that this mechanism is also effective in SC, being the cause for such SBG enlargement a combination of two mechanism: ~i! the achievement of higher filling fractions, and ~ii! the symmetry reduction. Also, here we demonstrate that mechanism ~ii! is much more effective than mechanism ~i!. The wave equation for the propagation of pressure waves p(r), with harmonic frequency, v, in a 2D-space r5(x, y) defined by a composite system having a sound velocity, v(r), and density, r(r), can be written as