Robust transport and topological valley refraction of fundamental symmetric lamb waves in perforated phononic crystal plates

Phononic crystals represent an interesting class of metamaterials that can be utilized to regulate or manipulate vibration, sound propagation, and thermal transport. Their useful features mainly arise from the bandgaps in their dispersion curves, preventing the passage of waves within specific frequency ranges. However, it is often costly and time-consuming to obtain the dispersion curves, and the reverse engineering of phononic crystals to have pre-defined bandgaps possesses even greater challenges. In this research, we address this issue by employing a deep artificial neural network to predict the bandgap ratio and the characteristics of plausible bandgaps, focusing on the localized resonance in columnar phononic crystals. We utilized two geometric parameters, i. e. the ratio of diameter and height of the cylindrical resonators relative to the lattice constant, achieving a determination coefficient of 0.9993 for predicting the characteristics of the bandgaps and 0.9827 for predicting the bandgap ratio. To verify the model and better understand its behavior, we introduce Shapley values. These values provide a comprehensive insight into how each geometric parameter influences the predicted bandgap ratios.

Section: Introductionmentioning

confidence: 99%

Deep learning of plausible bandgaps in dispersion curves of phononic crystals

Farajollahi,

Seyyed Fakhrabadi

2024

Coupled topological edge and corner states in two-dimensional phononic heterostructures with nonsymmorphic symmetries

Huang,

Chen,

Mao

2024

The exciting discovery of topological phononic states has aroused great interest in the field of acoustic wave control. However, conventional topological edge states and corner states localized at the interface and corner of the two-phase domain wall structures are limited by single channel transmission characteristics, which decreases the flexibility of designing multi-channel acoustic wave devices. Here, we propose a two-dimensional (2D) topological phononic heterostructure with nonsymmorphic symmetries to realize the multiple interface topological multimode interference effect based on the coupling of topological edge and corner states. Topological phase transitions are achieved by altering the rotation angle of the split-ring scatterers in a square lattice. The coupled edge states are generated by the coupling between the edge states of ordinary-topological-ordinary (OTO) interfaces. Moreover, the higher-order topology of the square phononic crystals (PCs) is characterized by nontrivial bulk polarization, the topological and coupled corner states splitting into two pairs appear in the square OTO bend structure owing to the nonsymmorphic PC lack of mirror symmetries. Finally, the topological robustness of the multimode interference effect of coupled edge and corner states against defects is demonstrated. Our results pave the way for guiding and trapping acoustic waves in topological nonsymmorphic heterostructures, whose multi-channel transmission capability can be employed for designing topological phononic filters, couplers and multiplexers.

Wave patterns of the coupled nonlinear Schrödinger equations in photonic crystal fibers with four-wave mixing

Houwe,

Abbagari,

Akinyemi

et al. 2024

In this paper, we examine the behavior of modulation instability within photonic crystals. The model employed is the coherent coupled nonlinear Schrödinger equation, incorporating weak birefringence and four-wave mixing, which arises at the edge of the optical mode. The linear analysis is used to derive the modulation instability spectrum. Throughout the modulation instability spectrum, we identify both stable and unstable modes, thereby confirming the breakdown of the plane wave. For certain four-wave mixing parameters, the amplitude of the modulation instability spectrum and its bandwidths expand, creating an opening for localized structures to emerge. Another aspect of this study has been demonstrated in normal and anomalous dispersion regimes where an increasing initial amplitude of the plane wave is fulfilled. Specifically, numerical simulations highlight the occurrence of Benjamin-Feir instability, where wave patterns emerge under the influence of four-wave mixing. Additionally, solitonic waves are generated, demonstrating the presence of Akhmediev breathers and other modulated structures, confirming that photonic crystals with four-wave mixing are conducive to these formations. The findings from this study could inform future research in the development of nonlinear photonic waveguides.