Finite elements computational modeling of coupled elastic waveguides

The theoretical study of one-dimensional-infinite systems of elastically coupled parallel waveguides has established the existence of band structures with pseudo-spin characteristics. Those systems, which are named ϕ-bits, have been shown to exhibit a spinor character associated with directional degrees of freedom, which makes them potential quantum mechanical analogs. The realization of such systems is challenged by the three-dimensional and finite nature of physical elastic waveguides. We address this problem, and with it the design of ϕ-bits in general, by developing finite elements models based on COMSOL Multiphysics®. We model systems of one or more coupled finite length Al rods. The analysis of their dispersion relations, transmission spectra, and amplitudes establishes their ϕ-bit character. For three coupled finite length Al rods, the elastic field is associated with wavefunctions, tensor products of a spinor part related to the directional degrees of freedom, and an orbital angular momentum part representing the phase of the coupled waveguides. We demonstrate the possibility of creating non-separable states between these degrees of freedom.