Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs

Y Pennec,V Laude,Y El Hassouani,N Papanikolaou,J O Vasseur,C Li,E H El Boudouti,B Djafari Rouhani,S Benchabane,A Martinez

doi:10.1364/oe.18.014301

Abstract

We discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of holes drilled in a Si membrane. We investigate in detail both the centered square lattice and the boron nitride (BN) lattice with two atoms per unit cell which include the simple square, triangular and honeycomb lattices as particular cases. We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as BN lattices close to honeycomb. Otherwise, all investigated structures present the possibility of a complete phononic gap together with a photonic band gap of a given symmetry, odd or even, depending on the geometrical parameters.

Highlights

Phononic crystals [1,2], constituted by a periodical repetition of inclusions in a matrix background, has received a great deal of attention during the last two decades [3]
We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as boron nitride (BN) lattices close to honeycomb
We have theoretically investigated the possibilities to open phononic and photonic band gaps in silicon slabs drilled with circular air holes

Summary

Introduction

Phononic crystals [1,2], constituted by a periodical repetition of inclusions in a matrix background, has received a great deal of attention during the last two decades [3]. Some of us and other authors have demonstrated [8,9,10,11,12,13,14] that with an appropriate choice of the geometrical and physical parameters, these finite thickness structures can exhibit absolute band gaps This makes them suitable for similar applications as in the case of 2D phononic crystals with the additional property of confinement in the vertical direction. Sadat-Saleh et al [24] have demonstrated the possibility to open phononic and photonic band gaps in complex arrays like multiple cylinders per unit cell in lithium niobate 2D structures. The aim of this paper is to investigate in detail the conditions of existence of simultaneous phononic and photonic band gaps in finite 2D crystals of various structures constituted by a periodic array of holes in a silicon slab.

Geometry and method of calculation

Square lattice

Honeycomb lattice

Boron nitride lattice

Conclusion