Topology Optimization Of Phononic/Photonic Crystals With Exotic Properties

The manipulation of sound and light waves plays important roles in areas of defence,aeronautics and astronautics and medicine.However,traditional materials have some drawbacks on the manipulation of sound and light waves.Phononic crystals(Pn Cs)and photonic crystals(Pt Cs)are artificial composites made of one material periodically embedded in other material with different physical properties.By engineering the microstructures of Pn Cs and Pt Cs,they can exhibit exotic properties,such as band gap,unidirectional tran smission,Dirac-like cones and topological edge states.These properties can be applied for isolating sound waves and electromagnetic wave,thus have important applications in aeronautics and astronautics,defence and daily life.The exotic properties of Pn Cs and Pt Cs are highly dependent on the configuration of the unit cell.Currently,the methods to design Pn Cs and Pt Cs are mainly trial-and-error approach based on experience.In order to overcome the drawback of traditional trial-and-error approach based on experience,topology optimization has been applied into the design of Pn Cs and Pt Cs.Most studies are focused on designing band gaps of Pn Cs and Pt Cs based on classical band diagrams.However,these methods could not design complete band gaps and cont rol the locations of band gaps.In addition,there are no systematic studies on the design on Dirac-like cones and topological insulators.This paper develop a systematic and scientific way to design Pn Cs and Pt Cs with exotic properties by topology optimization.The main content and conclutions include:A topology optimization approach for designing the spatial decay of evanescent waves in Pn Cs is developed.The study is systematically conducted for both out-of-plane and in-plane modes at various frequencies.By maximizing the minimum imaginary part of wave vector at the specific frequency,bands gaps around different specific frequencies are successfully obtained for both in-plane and out-of-plane modes.By simultaneously maximizing the minimum imaginary part of wave vectors of in-plane and out-of-plane modes at the specific frequency,Pn Cs with complete band gaps are successfully designed.By simultaneously maximizing the minimum imaginary part of wave vectors at virious frequencies,Pn Cs with multi band gaps are successfully designed.The proposed optimization algorithm can successfully overcome difficulties in opening band gap at desirable frequencies,especially for the complete band gap and multiple band gaps.A topology optimization approach for designing the Pn Cs to achieve unidirectional acoustic transmission(UAT)is proposed.By maximizing the minimum imaginary part of wave vector along ?X direction and constrainting the minimum imaginary part of wave vector along ?M direction below a minimal value,symmetric and asymmetric Pn Cs with partial band gaps around various frequencies are successfully obtained.Then,UAT devices are constructed by placing the optimized Pn Cs in a bend wave guide.Full wave simulations show that the rectifying efficiency for those UAT devices is very high.A topology optimization approach for designing the Pt Cs with complete band gap is built.The optimization problem is formulated with maximizing the minimum imaginary part of complex wave vectors for transverse magnetic(TM)and transverse electric(TE)modes.In doing so,the complete band gap at the specific frequency is obtained at the desired frequency,and the optimized structures of photonic materials with novel topological patterns are achieved.The proposed optimization algorithm can successfully overcome difficulties in opening complete band gap at desirable frequencies for Pt Cs.A topology optimization approach for designing Dirac-like cones in Pt Cs is developed.By exciting the monopolar and dipolar modes at the same frequency through topology optimization,Dirac-like cones for both TM and TE modes are successfully obtained.The exotic wave manipulation properties associated with Dirac-like cones,such as cloaking,wavefront shaping and tunnelin g through bent channels,are exhibited based on the optimized Pt Cs.The proposed method could be also used to design the third order Dirac-like cones,which have potential applications in nonlinear optics.All topological patterns of the optimized Pt Cs hav e regular and smmoth features,meaning they can be readily fabricated.A topology optimization approach for designing quantum spin hall effect-based topological photonic insulator is built.Pt Cs with double Dirac cones are firstly designed by exciting the dipolar and quadrupolar modes at the same frequency.Trivial and nontrivial Pt Cs are desigined by exciting the dipolar below and up the quadrupolar modes,respectively.By combining the optimized trivial and nontrivial PCs and forming an interface,topological photonic insulators with extra-wide edge band gap are successfully obtained.The proposed method could flexibly modify the location of topological edge states,which has great significance of practical application.