Defect modes and optomechanic interactions in phoxonic crystals
Résumé
Phoxonic crystals are periodic structures that can exhibit simultaneously phononic and photonic band gaps. When creating defects such as cavities or waveguides inside such dual phononic/photonic crystals, it becomes possible to find simultaneously localized phonons and photons in the frequency range of their corresponding band gaps. Then, one can expect an enhancement of the phonon-photon interaction for the purpose of novel optomechanical devices, in particular the modulation of light by acoustic waves In this work, we present the results of our theoretical works on: (i) the design of 2D, slabs and 1D strips phoxonic crystals, (ii) the search of dual phononic/photonic cavity modes as well as slow guided modes in these structures, and (iii) the optomechanic interaction between confined phonons and photons. The most suitable phoxonic slab structures are made of honeycomb and square lattices of holes in Si. The strip waveguides are constituted by a nanobeam periodically drilled with holes along which stubs are grafted on both sides. We have shown that the holes and the stubs are respectively favorable for the opening of the photonic and phononic gaps. We study the optomechanic interaction in different cavities and waveguides in the above crystals, taking account of both mechanisms that contribute to the acousto-optic interaction, namely the photoelastic (PE) and moving boundary (MB) effects. The strength of the phonon-photon coupling is evaluated by calculating the modulation of the cavity photon frequency by the cavity phonon, namely the photonic mode frequency is calculated at several selected instants of an acoustic period under the assumption that the acoustic mode strain profile is being frozen at these instants. This result is compared to the optomechanic coupling coefficient that expresses the photonic frequency shift induced by the zero-point motion of the mechanical field of the phonon and which can be calculated from the knowledge of the acoustic and optical field distributions inside the cavity. The strength of the optomechanic coupling should be calculated for each phononic and each photonic mode. We compare the contributions of the photoelastic and moving boundaries effects from case to case. Indeed, these effects can act differently and, moreover, they contributions can be in phase and add together or be out of phase and partly cancel each other. Finally, we discuss the influence of the material properties as concerns the photoelastic effect since the latter strongly changes when the optical frequency approaches the energy of the direct band gap.