On the radiation from a Hertzian dipole of a finite length in the uniaxial dielectric medium: erratum

Aamir Hayat; Muhammad Faryad

doi:10.1364/OSAC.2.002855

Abstract

Equations (47) and (49) in [OSA Continuum 2, 1411 (2019) [CrossRef] ] contain an error and the equations are corrected in this erratum.

In our paper [1], Eqs. (47) and (49) had erroneous unit vectors. The correct equations are

(47)$${} \mathbf{E}(\mathbf{r})=\frac{k_{o}\mu_{b}p_{o}\varepsilon_{d}}{2\pi\varepsilon_{o}n_{o}r}\frac{\exp(ik_{o}n_{o}r\Theta)}{\Theta^{2}}\Bigg[\frac{\sin^{2}\theta}{\cos\theta}\mathbf{\hat{z}}-\sin\theta\cos\phi\mathbf{\hat{x}}-\sin\theta\sin\phi\mathbf{\hat{y}}\Bigg]\sin\Bigg(\frac{k_{o}L n_{o}\cos\theta}{\Theta}\Bigg),$$

(49)$${} \mathbf{H}(\mathbf{r})=\frac{k_{o}p_{o}c\varepsilon_{d}}{2\pi r}\frac{\exp(ik_{o}n_{o}r\Theta)}{\Theta\cos\theta}\Big(-\sin\theta\cos\phi\mathbf{\hat{y}}+\sin\theta\sin\phi\mathbf{\hat{x}}\Big)\sin\Bigg(\frac{k_{o}L n_{o}\cos\theta}{\Theta}\Bigg)\,. $$

No other results and conclusions are affected by this inadvertent error. The authors regret this error.

References

1. A. Hayat and M. Faryad, “On the radiation from a Hertzian dipole of a finite length in the uniaxial dielectric medium,” OSA Continuum 2(4), 1411–1429 (2019). [CrossRef]

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Equations (2)

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E (r) = \frac{k_{o} μ_{b} p_{o} ε_{d}}{2 π ε_{o} n_{o} r} \frac{\exp (i k_{o} n_{o} r Θ)}{Θ^{2}} [\frac{\sin^{2} θ}{\cos θ} \hat{z} - \sin θ \cos ϕ \hat{x} - \sin θ \sin ϕ \hat{y}] \sin (\frac{k_{o} L n_{o} \cos θ}{Θ}),

H (r) = \frac{k_{o} p_{o} c ε_{d}}{2 π r} \frac{\exp (i k_{o} n_{o} r Θ)}{Θ \cos θ} (- \sin θ \cos ϕ \hat{y} + \sin θ \sin ϕ \hat{x}) \sin (\frac{k_{o} L n_{o} \cos θ}{Θ}) .