Topology Optimization Design Of Phononic/Photonic Metamaterials

Phononic/photonic metamaterials are novel artificial micro-structural materials with acoustic/optical wave properties which cannot be found or realized in natural materials,They makes it possible to completely and freely manipulate wave propagation,showing the promising applications in the fields of optics,acoustics,mechanics and thermology,etc.Accordingly,the study on phononic/photonic metamaterials will lead to great revolutions of information technology,national defence industry,new energy technology and microfabrication technology,etc.To break through the limitations of artificial and empirical designs,this thesis performs the topology optimization based on genetic algorithm(GA)of solid-solid phononic crystals(PnCs),holey PnCs,holey phoxonic crystals(PxCs),phononic/photonic wave devices and anisotropic elastic metamaterials(EMMs)to realize particular properties and functionalities.The main contents and achievements include:1.The bandgap optimization model of solid-solid PnCs is established.Topology features of optimized structures under the different serial numbers of bandgaps are discussed.Effects of the material parameters,constraint of filling proportions and symmetry reduction on the optimized structures are analyzed.To solve the bandgap optimization problem requiring huge computational cost,an improved GA is developed.PnC microstructures possessing wide bandgap properties are designed.The results show that for the square-symmetrical PnCs,the structures designed from the optimization of the bandgap for the out-of-plane mode have the simple geometrical features,i.e.,the total number of the scatterers equals the integer times of the serial number of the bandgaps;and the centers of all scatterers form a typical Voronoi diagram.Under the constraints of filling proportions,the optimized structures also have the above simple geometrical features.For the optimization of the bandgap of the out-of-plane mode,optimized structures with different component materials have the similar topology characteristics.Multiple elitist genetic algorithm combined with adaptive fuzzy fitness granulation can ensure the accuracy of optimization results,significantly reduce the exact fitness evaluations,and speed up the convergence.Symmetry reduction has remarkable influences on the topology characteristics of the optimized structures.For the out-of-plane and full-wave modes,asymmetrical structures show the novel topology characteristic and wider bandgaps.2.The bandgap multi-objective optimization models of holey silicon PnCs and PxCs are established.Effects of the symmetry reduction on the optimized results in square-latticed and triangle-latticed systems are discussed.Effects of the structural symmetry and material symmetry on optimization of PxCs are analyzed.Porous PnCs with wide bandgaps and PxCs with simultaneous wide complete phononic and photonic bandgaps are designed.The results show that all optimized PnCs have the similar topology characteristic,i.e.,the periodic structure is composed of lumped mass blocks and thin connecters.Symmetry reduction can bring about the structures with the better bandgap properties.Optimized structures with symmetry reduction still keep the locally resonant topology characteristics.Optimized asymmetrical structures in the square lattice have the optimal multi-objective property,followed by the rotational symmetrical structure.Optimized rotational-symmetrical structures in the triangle lattice have better multi-objective properties.Reducing the material symmetry is more beneficial to the bandgap optimization.For the lower material symmetry,the structure with the lower structural symmetry is easier to have wider bandgaps and smaller averaged mass density.All optimized PxCs are composed of lumped mass blocks and thin connecters.When the material symmetry in the square lattice is higher,rotational symmetrical structure is superior to square symmetrical structure.For the triangle lattice,high symmetrical structure is superior to rotational symmetrical structure.For engineering of phononic and photonic bandgaps,the robustness of a triangle lattice is stronger than that of a square lattice.3.The optimization models of phononic/photonic wave devices are established.Highly effective PxC cavities and elastic wave filters with high quality factors are designed.The topology characteristics and filtering properties of the filters under different frequencies are discussed in detail.The potential applications of the cavity in waveguide-cavity system are demonstrated.The results show that the optimized PxC cavity is composed of lumped mass blocks and thin connecters.It can realize the simultaneously high concentration of the acoustic and optical wave energies.The symmetry of the cavity mode and the distance between the waveguide and cavity in the filters can significantly affect the performance of the filters.Most optimized filters have the typical Fano resonances near the resonant frequencies.Highly symmetrical cavity modes can be used to implement a highly effective multiwavelength filter,raising filter and T-splitter,etc.4.Based on the effective medium theory,the optimization models of the broadband negative effective parameters for EMMs are established.Double-negative and hyperbolic metamaterials with simple topology characteristics are designed.The topology characteristics and wave properties of the optimized structures under different target frequency ranges are analyzed.The double-negative and hyperbolic dispersions are verified.Corresponding wave propagation behaviors of the metamaterials are discussed.The results show that the constructed optimization frame can well realize the broadband negative effective mass density and negative effective elastic modulus.All optimized metamaterials have the similar topology characteristic,i.e.,various lumped mass blocks are connected with each other through thin connecters.Quadrupolar or multipolar resonance is the mechanism of the negative effective mass density and negative effective elastic modulus.Double-negative metamaterials can realize the negative refraction and subwavlength imaging for longitudinal waves.In particular,the negative refraction of the in-plane transverse waves in the single-phase EMMs is firstly observed.Most double-negative metamterials can serve as the zero-index metamaterials for the longitudinal waves or in-plane transverse waves and can give rise to the cloaking effects.Both optimization methods dominated by negative effective mass density and negative effective elastic modulus can design broadband hyperbolic metamaterials.For ultra-low frequency ranges ??10a?90a),the evanescent wave carrying subwavelength information is dramatically enhanced in the hyperbolic metamaterials,thus resulting in the deep-subwavelength imaging with high resolution of ?/64.Topology optimization of phononic/photonic metamaterials in this thesis can effectively guide the control of electromagnetic,acoustic and elastic waves in the artificial periodic materials,and provide the fundamentals about designing novel wave devices and equipments.