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Composite materials with periodic variations of density and/or sound velocities, so-called phononic crystals, can exhibit bandgaps where propagation of acoustic waves is forbidden. Phononic crystals are the elastic analogue of the well-established photonic crystals and show potential for manipulating the flow of elastic energy. So far, the experimental realization of phononic crystals has been restricted to macroscopic systems with sonic or ultrasonic bandgaps in the sub-MHz frequency range. In this work, using high-resolution Brillouin spectroscopy we report the first observation of a hypersonic bandgap in face-centred-cubic colloidal crystals formed by self-assembly of polystyrene nanoparticles with subsequent fluid infiltration. Depending on the particle size and the sound velocity in the infiltrated fluid, the frequency and the width of the gap can be tuned. Promising technological applications of hypersonic crystals, ranging from tunable filters and heat management to acousto-optical devices, are anticipated.

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We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lamé coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lamé coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.

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