## 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], where a factor of 2 is missing. The correct expression should read as

*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

*I*

_{m}_{0}doubles due to the

*image theory*. This typo has no influence on the radiation patterns presented in [1] 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 η_{eff} = *P*
_{rad}(*L*)*/P*
_{in}
*×* 100, is calculated based on the attenuation constant extracted (Fig. 6(b) in [1]). For nominal *λ*
_{0} = 1550 nm, the total and radiative attenuation constants are *α _{t}* = −0.370

*k*

_{0}and

*α*= −0.207

_{r}*k*

_{0}, respectively, which implies that the dissipative attenuation constant is

*α*=

_{d}*α*−

_{t}*α*= −0.163

_{r}*k*

_{0}. 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] for better clarity.)

In order to calculate the radiated power *P*
_{rad}(*L*) for
a slot of length *L*, the total attenuation in Fig.
1 is discretized into *L* =
*N*Δ*z*, where Δ*z* is assumed
infinitesimally small. Therefore, the radiated power can be written as the sum of the radiation from
each Δ*z* section as shown in

*geometric series*, the antenna efficiency can then be written as

*L’Hôpital’s*rule, the analytical expression for the antenna efficiency is obtained

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 0.5*λ*
_{0} 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* = 1.5*λ*
_{0} attenuates 99.9% of the input power, which can be regarded as equivalent to an infinite slot.