Chapter 2 - Phonon monomode circuits
Résumé
In this chapter, we discuss the vibrational properties of phononic circuits that can be described in the framework of discrete or continuous models. In the case of discrete media, we use the phonon discrete model within the Green’s function method described in Chapter 1 and give the surface response operators necessary to study surface and confined phonons in biatomic and triatomic phononic crystals. In particular, we give a general rule about the existence of two types of discrete modes in finite and semiinfinite crystals. Also, we present a simple multiplexing phonon structure made out of two parallel mono-atomic chains of atoms and of a simple coupling device made out of two other atoms interacting together and with the two chains. We show analytically that these simple structures can transfer selectively along a given path, one phonon from one chain to the other leaving neighbor phonons unaffected. In the case of continuous media, we consider simple acoustic devices consisting of attached resonators in the shape of stubs and loops tubes inserted along a slender tube. These structures can be arranged from very simple structures (two resonators) mimicking the classical analog of Fano and electromagnetic induced transparency resonances, to periodic structures showing the possibility of existence of Bragg and non-Bragg gaps, to quasiperiodic (Fibonacci sequence) structures exhibiting some transmission scaling properties of such systems.