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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 11 — Jun. 3, 2013
  • pp: 13184–13186
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Ultra-wideband optical leaky-wave slot antennas: errata

Yan Wang, Amr S. Helmy, and George V. Eleftheriades  »View Author Affiliations


Optics Express, Vol. 21, Issue 11, pp. 13184-13186 (2013)
http://dx.doi.org/10.1364/OE.21.013184


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Abstract

The errata consist of corrections for one typo and one misinterpretation of the results regarding the antenna efficiency in the original article [Opt. Express 19, 12392–12401 (2011)].

© 2013 OSA

1. Correction 1

There is a typo in Eq. (1) in [1

1. Y. Wang, A. S. Helmy, and G. V. Eleftheriades, “Ultra-wideband optical leaky-wave slot antennas,” Opt. Express 19, 12392–12401 (2011) [CrossRef] [PubMed] .

], where a factor of 2 is missing. The correct expression should read as
Hθ=j2k2Im0lη2ejk2r4πrsinθ(ejk2l2(cosθK))sin(k2l2(cosθK))k2l2(cosθK)
(1)
The factor of 2 arises from the application of the field equivalence principle, such that the original structure can be interpreted as a magnetic current backed by an infinite conducting plane (for each medium). Hence the magnetic current Im0 doubles due to the image theory. This typo has no influence on the radiation patterns presented in [1

1. Y. Wang, A. S. Helmy, and G. V. Eleftheriades, “Ultra-wideband optical leaky-wave slot antennas,” Opt. Express 19, 12392–12401 (2011) [CrossRef] [PubMed] .

] since all results are normalized.

2. Correction 2

There is a mis-interpretation of the results regarding the antenna efficiency (Fig. 8) presented in the first paragraph on page 12400. The re-interpretation and derivations of the analytical expression of antenna efficiency are elucidated as the following.

The antenna efficiency, defined as ηeff = Prad(L)/Pin× 100, is calculated based on the attenuation constant extracted (Fig. 6(b) in [1

1. Y. Wang, A. S. Helmy, and G. V. Eleftheriades, “Ultra-wideband optical leaky-wave slot antennas,” Opt. Express 19, 12392–12401 (2011) [CrossRef] [PubMed] .

]). For nominal λ0 = 1550 nm, the total and radiative attenuation constants are αt = −0.370k0 and αr = −0.207k0, respectively, which implies that the dissipative attenuation constant is αd = αtαr = −0.163k0. The power attenuation along the slot due to these loss mechanisms is illustrated in Fig. 1. (Note that Fig. 1 is used to replace Fig. 8 in [1

1. Y. Wang, A. S. Helmy, and G. V. Eleftheriades, “Ultra-wideband optical leaky-wave slot antennas,” Opt. Express 19, 12392–12401 (2011) [CrossRef] [PubMed] .

] for better clarity.)

Fig. 1 Power decay along the PLS antenna due to the total, radiative and dissipative attenuation constants, respectively.

In order to calculate the radiated power Prad(L) for a slot of length L, the total attenuation in Fig. 1 is discretized into L = NΔz, where Δz is assumed infinitesimally small. Therefore, the radiated power can be written as the sum of the radiation from each Δz section as shown in
Prad(L)=limΔz0n=0N1[Ptot(nΔz)(1e2αrΔz)]=limΔz0n=0N1[Pine2αtnΔz(1e2αrΔz)]=limΔz0[Pin(1e2αrΔz)n=0N1(e2αtΔz)n]
(2)
Recognizing the summation in Eq. (2) is a geometric series, the antenna efficiency can then be written as
ηeff=Prad(L)Pin×100=limΔz0[(1e2αrΔz)1(e2αtΔz)N1e2αtΔz]×100
(3)
Applying L’Hôpital’s rule, the analytical expression for the antenna efficiency is obtained
ηeff=(1e2αtL)12αr12αt×100
(4)
Similarly, the dissipated power percentage can be calculated from
Pdis(L)Pin×100=(1e2αtL)12αd12αt×100
(5)
The results for the radiation and dissipation with respect to the input are shown in Fig. 2, where the sum of these two loss mechanisms is shown to yield the expected total loss, hence confirming the validity of the approach in Eqs. (4) and (5).

Fig. 2 The percentage of the total, radiated and dissipated power loss with respect to the input.

In conclusion, the antenna efficiency can be extracted from the percentage of radiation in Fig. 2 (the blue dashed line). It is shown that it takes an antenna length of 0.5λ0 to lose 90% of the input power; out of this total loss, 50.5% is due to radiation and 39.8% due to dissipation. Additionally, in order to lose 99% of the input power, the PLS antenna should be at least one wavelength long. Finally, a PLS with L = 1.5λ0 attenuates 99.9% of the input power, which can be regarded as equivalent to an infinite slot.

References and links

1.

Y. Wang, A. S. Helmy, and G. V. Eleftheriades, “Ultra-wideband optical leaky-wave slot antennas,” Opt. Express 19, 12392–12401 (2011) [CrossRef] [PubMed] .

OCIS Codes
(260.3910) Physical optics : Metal optics
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 16, 2013
Published: May 22, 2013

Citation
Yan Wang, Amr S. Helmy, and George V. Eleftheriades, "Ultra-wideband optical leaky-wave slot antennas: errata," Opt. Express 21, 13184-13186 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-11-13184

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