The N-beam approach to describe arbitrary shaped acoustical fields

Abstract

Laser scattering using analytical or semi-analytical theories may rely on the use of beam shape coefficients (BSCs) to encode the description of the incident illuminating electromagnetic fields. Similarly, acoustical BSCs may be introduced to describe an acoustical field incident on a scattering object. An approach called the $N$-neam approach has been used to justify a localization method to evaluate electromagnetic BSCs. In the electromagnetic framework, this $N$-beam approach has been introduced in a very concise way, due to difficulties associated with the use of Maxwell’s equations. The present paper presents the $N$-beam approach for acoustical fields which satisfy Helmholtz equation. Due to the fact that the Helmholtz equation is significantly more tractable analytically and numerically compared to the full set of Maxwell’s equations, the presentation of the $N$-beam method in an acoustical framework can be introduced in a more complete way than in the electromagnetic framework. Furthermore, this approach yields an expression for acoustic fields using expansions that serve as alternatives to the classical spherical wave function expansions – alternatives that have proven invaluable in the electromagnetic context and are, therefore, expected to be similarly beneficial in acoustics.