Metamaterial properties of periodic laminates

In this paper we show that a 1-D phononic crystal (laminate) can exhibit metamaterial wave phenomena which are traditionally associated with 2- and 3-D crystals. Moreover, due to the absence of a length scale in 2 of its dimensions, it can outperform higher dimensional crystals on some measures. This includes allowing only negative refraction over large frequency ranges and serving as a near-omnidirectional high-pass filter up to a large frequency value. First we provide a theoretical discussion on the salient characteristics of the dispersion relation of a laminate and formulate the solution of an interface problem by the application of the normal mode decomposition technique. We present a methodology with which to induce a pure negative refraction in the laminate. As a corollary to our approach of negative refraction, we show how the laminate can be used to steer beams over large angles for small changes in the incident angles (beam steering). Furthermore, we clarify how the transmitted modes in the laminate can be switched on and off by varying the angle of the incident wave by a small amount. Finally, we show that the laminate can be used as a remarkably efficient high-pass frequency filter. An appropriately designed laminate will reflect all plane waves from quasi-static to a large frequency, incident at it from all angles except for a small set of near-normal incidences. This will be true even if the homogeneous medium is impedance matched with the laminate. Due to the similarities between SH waves and electromagnetic (EM) waves it is expected that some or all of these results may also apply to EM waves in a layered periodic dielectric.