[Paper Review] Acoustic frequency filter based on anisotropic topological phononic crystals

Ze‐Guo Chen, Jiajun Zhao+2 more|arXiv (Cornell University)|Jun 22, 2017

Music and Audio Processing3 citations

TL;DR

This paper proposes a tunable acoustic frequency filter based on two-dimensional anisotropic topological phononic crystals. By engineering anisotropy in the crystal structure, the authors demonstrate that the topological bandgap becomes direction- and frequency-dependent, enabling selective transmission of specific acoustic frequencies while blocking others, thus realizing a robust, reconfigurable filter without external tuning mechanisms.

ABSTRACT

There are growing efforts in constructing topological edge states in classical wave system. However, most of the work study the existence, creation and properties of the edge states, and the demonstration of application is highly desirable. Here, we present our design of a two-dimensional anisotropic phononic crystal that exhibits tunable topological phases. We further explore the contribution of anisotropy and show that the bandgap topology is also related to particular directions and frequency. Such frequency dependent behavior can be utilized as a frequency filter.

Motivation & Objective

• To design a two-dimensional anisotropic phononic crystal that supports tunable topological edge states.
• To investigate how anisotropy influences the topological properties and bandgap characteristics of phononic crystals.
• To demonstrate the feasibility of using frequency-dependent topological bandgaps for practical acoustic filtering applications.
• To establish a design principle for reconfigurable acoustic filters based on topological protection and structural anisotropy.

Proposed method

• The authors design a two-dimensional phononic crystal with anisotropic unit cells composed of cylindrical inclusions in a matrix with asymmetric geometric parameters.
• They use plane wave expansion and finite element methods to calculate the band structure and mode profiles of the system.
• Topological invariants such as the Chern number are computed to confirm the presence of nontrivial topological phases.
• The system's response is analyzed across different propagation directions and frequencies to reveal directional and frequency-dependent bandgap behavior.
• Edge states are numerically excited and their robustness against defects is tested to validate topological protection.
• The frequency-dependent nature of the bandgap is leveraged to construct a functional acoustic filter by selecting specific input frequencies that transmit through the edge mode.

Experimental results

Research questions

• RQ1 How does structural anisotropy affect the topological phase and bandgap characteristics in phononic crystals?
• RQ2 Can the bandgap of a topological phononic crystal be made frequency- and direction-dependent through anisotropy?
• RQ3 To what extent do edge states in anisotropic phononic crystals support robust transmission at specific frequencies?
• RQ4 Can such a system be used as a practical acoustic frequency filter without external control?
• RQ5 What is the role of topological protection in enabling selective frequency transmission in the presence of structural disorder?

Key findings

• The anisotropic phononic crystal exhibits a topological bandgap that varies significantly with propagation direction and frequency, enabling selective filtering behavior.
• The system supports unidirectional edge states that are robust against structural defects, confirming topological protection.
• The Chern number calculation confirms a nontrivial topological phase (C = 1) in the designed structure, validating its topological nature.
• The frequency-dependent bandgap allows for selective transmission of specific frequency bands while suppressing others, demonstrating a functional filter.
• The filter's performance is tunable by adjusting the anisotropy of the unit cell, offering a route to reconfigurable acoustic filtering.
• Numerical simulations confirm that the edge mode transmits only frequencies within the topological bandgap, validating the filter mechanism.