Study On Acousto-Optic Coupling And Size Effect In Phoxonic Crystal Cavity

Phoxonic crystals（Px Cs）have broad application prospects in ultra-precision measurement,laser cooling,quantum information processing and phonon lasing.Px Cs are artificial crystals formed by periodic arrangement of materials or structures,which have the characteristics of both phononic crystals（Pn Cs）and photonic crystals（Pt Cs）.By introducing defects into nanoscale Px C supercell to form Px C cavity,GHz phonons and hundreds of THz photons can be simultaneously confined in the defect cavity.Thus,strong interactions between phonons and photons are boosted in the nanoscale cavity,which are called as acousto-optic（AO）couplings,or optomechanical interactions.At present,the mechanisms of AO coupling are unclear,the AO coupling is weak and the size effect is not considered.This dissertation aims to achieve strong AO couplings,especially strong nonlinear AO couplings.Firstly,the AO couplings in one-dimensional and two dimensional Px C cavities are studied.Then,the influences of the size effects on phononic crystals and AO couplings are both investigated.Finally,a gigahertz mechanical nanoresonator with high Q-factor is proposed based on AO coupling.The main research contents and results are as follows:（1）The AO couplings in one-dimensional Px C cavity are studied.Four methods are applied to calculate the AO couplings in one-dimensional Px C cavity.The AO couplings between different phononic modes and photonic modes are studied,the mechanisms of the linear AO couplings and quadratic AO couplings are revealed.The symmetries of the Pn C modes are found to be adjuctable.The quadratic coupling are increased for one magnitude by adjusting the thickness of the defect cavity.The enhancement mechanisms of the quadratic AO couplings are revealed.（2）The AO couplings in two-dimensional Px C cavity are studied.A novel model of Px C cavity with combined convex and concave holes is established.The cavity can produce many phonon defect modes and photon defect modes,and it supports AO couplings of many different pairs of phonon modes and photon modes.The optical frequency modulations induced by acoustic wave in an acoustic period are studied.The AO couplings of the degenerate modes are taken into consideration.Both large linear and quadratic AO couplings are obtained in the proposed Px C cavity.The influences of the vibrations of phonon modes on the linear and nonlinear AO coupling are both analyzed.The enhancement mechanism of AO coupling is revealed.（3）The size effects of two-dimensional Pn C are studied.Based on nonlocal strain gradient theory（NSGT）,the size-dependent wave equations of a two-dimensional Pn C are derived.A FEM model is established to solve the nonclassic 4^th partial differential wave equations.The nonclassic model is verified.By simltaneously considering the stiffness-hardening and stiffness-softening effect,both the size effects on the band structures of different polarizations and the first band gap are investigated.The influences of the Pn C unit cells,lattice types and structural parameters on the strength of the size effect are studied.The key structural parameter determining the strength of the size effect is found.（4）The size effects of Px C slab are studied.Based on NSGT,the size-dependent wave equations of nano silicon Pn C slab are derived.The method of solving the nonclassic wave equations is established.The influences of in-plane size effect and the thickness size effect on the band structure of the Pn C slab are investigated.The polarizations acting on of in-plane size effect and the thickness effect are clarified.The influences of different nonlocal parameters on the first gap are further studied.Furthermore,by introducing a point defect into the Pn C slab supercell,the influences of stiffness-hardening and stiffness-softening effects on the defect modes of are investigated.The relationships between the frequency shifts induced by size effects and the nonlocal parameters are revealed.Finally,the size effects on the AO coupling in the Px C slab with defect cavity are investigated.（5）The mechanical resonator with high frequency and high Q-factor is designed.Based on the AO coupling effect,a model of tapered cross-shaped mechanical nanoresonator is established.By designing unit cell in the structure,the phonon and photon cavity modes highly localized in the Px C cavity are realized.By considering all kinds of mechanical losses in room temperature,the Q-factor of the resonator is studied comprehensively.The mechanical resonator of 5.69 GHz with high Q-factor（1.19×10⁴）and strong AO coupling rate（775 k Hz）is obtained.The mechanisms of high Q-factor are revealed.The influences of the size effects on the performance of the mechanical resonator are analyzed.The results of the dissertation are of great theoretical significance and application value for designing devices with strong AO coupling and high-performance,studying high frequency Pn Cs,manupulating phonon with high frequency and promoting the application of resonators with high frequency and high Q-factor.