Optomechanic interaction in a corrugated phoxonic nanobeam cavity

Mourad Oudich,Yan Pennec,Jordi Gomis-Bresco,Alejandro Martínez,Clivia M. Sotomayor Torres,Daniel Navarro-Urrios,Said El-Jallal,Bahram Djafari-Rouhani,Abdelkader Makhoute

doi:10.1103/physrevb.89.245122

Abstract

The interaction between phonons and photons is investigated theoretically in a phoxonic cavity inside a corrugated nanobeam waveguide presenting band gaps for both electromagnetic and elastic waves. The structure is made by drilling periodic holes on a silicon nanobeam with lateral periodic stubs and the tapered cavity is constructed by changing gradually the geometrical parameters of both the holes and stubs. We show that this kind of cavity displays localized phonons and photons inside the gaps, which can enhance their interaction and also promotes the presence of many optical confined modes with high quality factor. Using the finite-element method, we demonstrate that with appropriate design of the tapering construction, one can control the cavity modes frequency without altering significantly the quality factor of the photonic modes. By changing the tapering rates over the lattice constants, we establish the possibility of shifting the phononic cavity modes frequency to place them inside the desired gap, which enhances their confinement and increases the mechanical quality factor while keeping the strength of the optomechanic coupling high. In our calculations, we take account of both mechanisms that contribute to the acousto-optic interaction, namely photoelastic and interface motion effects. We show that in our case, these two effects can contribute additively to give high coupling strength between phononic and photonic cavity modes. The calculations of the coupling coefficient which gives the phonon-photon coupling strength give values as high as 2 MHz while photonic cavity modes display quality factor of 10${}^{5}$ and even values up to 3.4 MHz but with smaller photonic quality factors.

Highlights

The design of highly dispersive media to control the propagation of both electromagnetic and acoustic waves has received increasing interest during the last few years
We have investigated the AO interaction in a corrugated phoxonic silicon nanobeam presenting band gaps both for photonic and phononic modes
Regarding the AO coupling, particular attention was drawn to the symmetry of the acoustic modes to focus only on the ones that can couple strongly with the trapped photonic modes, namely phononic modes having even symmetry wave fields with respect to the geometry’s symmetries

Summary

INTRODUCTION

The design of highly dispersive media to control the propagation of both electromagnetic and acoustic waves has received increasing interest during the last few years. Eichenfield et al [21,22] fabricated an optomechanical silicon nanobeam with periodic design shape in which localized phonons and photons created inside a cavity defect provide strong AO coupling. Chan et al [23] studied the phonon-photon interaction in a tapered strip nanobeam with holes Most of these works involve photonic cavity modes without necessarily trapping localized phononic modes in a cavity using complete band gap. Based on our recent works [24,25], we have shown that only phononic modes which are of even symmetry with respect to both symmetry planes of the nanobeam (one horizontal and one vertical plane) are suitable to provide nonvanishing optomechanical interaction, allowing the search of confined modes inside gaps of particular even symmetry rather than only in the absolute band gaps. We finish this paper by highlighting the main conclusions over the obtained results

PHOXONIC STRIP WAVEGUIDE

ESTIMATION OF THE OPTOMECHANIC COUPLING

CONCLUSIONS