Dual Phononic and Photonic Band Gaps in a Periodic Array of Pillars
Abstract: Phononic crystals are a class of materials that exhibit periodic variations in their density and elastic properties. Such crystals modify the propagation of acoustic waves and prohibit the propagation of sound for frequencies within the band gap. They have enabled exciting new ways to control sound in particular in the field of wave guiding and filtering, using point and linear defects introduced in the crystal, as well as in the field of sound isolation. In the photonic crystal counterpart, the medium is made up with a periodically modulation of the refractive index between their constituents. Their performance is determined by frequency gaps, forbidden for the propagation of the electromagnetic waves. In this work, we discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of silicon pillars deposited on a homogeneous SiO2 membrane.
Phononic crystals are a class of materials that exhibit periodic variations in their density and elastic properties [1, 2]. Such crystals modify the propagation of acoustic waves and prohibit the propagation of sound for frequencies within the band gap. They have enabled exciting new ways to control sound [3, 4]. Recently, an issue of interest is based on the study of phononic crystal slabs for potential applications as platforms for integrated technological circuits [6-10]. In the photonic counterpart, the medium is made up with a periodically modulation of the refractive index between their constituents also producing band gaps in which the propagation of electromagnetic waves is forbidden . The existence of photonic band gaps for guided modes in periodic crystal slabs offers new possibility to control the light in integrated photonic devices [12-14].
The simultaneous existence of photonic and phononic band gaps and the confined phononphoton interaction have been investigated in 1D multilayer structures . In infinite 2D structures, relatively few works have been devoted to simultaneous control of phonons and photons [16, 17]. Some recent papers are also dealing with the opto-mechanical crystal slabs that sustain both the optical and mechanical excitations . In two very recent papers, we and another group [19, 20] demonstrated the existence of dual phononic and photonic band gaps in 2.5D crystal plates composed of arrays of void cylindrical holes in silicon slabs with a finite thickness.
The main goal of this paper is to demonstrate the existence of dual phononic-photonic band gaps in the new type of structure constituted by a periodic array of pillars deposited on a layer of finite thickness. We concentrate our calculations on a structure where the pillars and the supporting plate are respectively made of silicon and silica (SiO2). We investigate both the phononic and photonic band structures in three types of lattices, namely square, triangular and honeycomb and for a wide range of the geometrical parameters. In general, the phononic and photonic band structures are respectively calculated by finite element (FE) and by plane wave expansion (PWE) methods. However, finite difference time domain (FDTD) method has also been used to check the correctness and convergence of the results.