Modulation of complex Bessel modes by generalized impedance metasurfaces for potential acoustic channels

Abstract

Waves described by Bessel functions of different orders have recently attracted widespread attention. Owing to their potential to provide additional available channels in acoustic communications. Their orthogonality in the azimuthal plane enables spatial multiplexing at a given frequency. The number of available channels is thereby increased, facilitating the development of faster and more reliable communication systems. In this paper, traveling waves with different radial wavenumbers as well as azimuthal indices are employed, leading to a significant increase in potential spatial channels. These waves are termed complex Bessel modes (CBMs) and are rigorously orthogonal when confined within a waveguide. Compared with multiplexing based on orthogonality in the azimuthal plane only, CBMs offer additional spatial degrees of freedom for channel multiplexing. However, a sophisticated requirement on modulation arises naturally, owing to the resulting inhomogeneous amplitude and phase distribution. Generalized impedance metasurfaces are therefore introduced to address this challenge. They convert efficiently between different CBMs, achieving 100% power flow conversion efficiency in numerical simulations. Two demonstration generators for CBMs with zero azimuthal index are fabricated with practical structures obtained through optimization. The input waveguide of the generators can be designed to have one-quarter the cross-sectional area of the output waveguide, owing to the flexibility of the generalized impedance theory. Generation of CBMs can therefore be achieved using a single speaker, eliminating the requirement for a large array of speakers and thereby leading to substantial cost reduction and improved stability. High-purity CBMs are demonstrated in both numerical simulations and experiments. This work reveals the potential of CBMs to serve as additional orthogonal spatial channels for acoustic multiplexing. This extension of generalized impedance theory paves the way for more reliable acoustic communications.