Optical theorem for acoustic non-diffracting beams and application to radiation force and torque: erratum

Likun Zhang; Philip L. Marston

doi:10.1364/BOE.4.002988

Abstract

We correct minor errors in four equations in our recent paper [Biomed. Opt. Express 4(9), 1610–1617 (2013)]. They are equations (11), (14), (15), and (17) therein, where a factorial ratio $\frac{(n - m)!}{(n + m)!}$ was mistakenly omitted. All the other equations and analysis in the paper were correct.

We correct a factor $\frac{(n - m)!}{(n + m)!}$ that was mistakenly omitted in four equations in our recent paper [1]. They are Eqs. (11), (14), (15), and (17) in [1]. The correct versions of these four equations respectively are,

σ_{ext} = \frac{π}{k^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} Re [2 (1 - s_{n})],

Q_{sca} \equiv σ_{sca} / (π a^{2}) = \frac{1}{{(k a)}^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} ({| s_{n} - 1 |}^{2}),

Q_{abs} \equiv σ_{abs} / (π a^{2}) = \frac{1}{{(k a)}^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} (1 - {| s_{n} |}^{2}) .

Q_{ext, sca} = σ_{ext, sca} / (π a^{2}) = \frac{4}{{(k a)}^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} {sin}^{2} (δ_{n}) .

These equations were correctly given in our earlier paper [2]; they are equations (16)–(18) in [2]. Note also that cosβ is sometimes denoted by b. All the other equations and analysis in [1] were correct and are unaffected by this correction.

References and links

1. L. K. Zhang and P. L. Marston, “Optical theorem for acoustic non-diffracting beams and application to radiation force and torque,” Bio. Opt. Express 4(9), 1610–1617 (2013). [CrossRef]

2. L. K. Zhang and P. L. Marston, “Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres,” Phys. Rev. E 84, 035601 (2011). [CrossRef]

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Equations (4)

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σ_{ext} = \frac{π}{k^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} Re [2 (1 - s_{n})],

Q_{sca} \equiv σ_{sca} / (π a^{2}) = \frac{1}{{(k a)}^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} ({| s_{n} - 1 |}^{2}),

Q_{abs} \equiv σ_{abs} / (π a^{2}) = \frac{1}{{(k a)}^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} (1 - {| s_{n} |}^{2}) .

Q_{ext, sca} = σ_{ext, sca} / (π a^{2}) = \frac{4}{{(k a)}^{2}} \sum_{n = | m |}^{\infty} (2 n + 1) \frac{(n - m)!}{(n + m)!} {[P_{n}^{m} (cos β)]}^{2} {sin}^{2} (δ_{n}) .

Abstract

References and links

Cited By

Equations (4)

Biomedical Optics Express