## Abstract

We correct the errors made in the field-overlap derivation in Appendix A of J. Opt. Soc. Am. B **33**, 1044 (2016) [CrossRef] .

© 2016 Optical Society of America

In our previously published paper [1], we derive an analytical
expression of the field-overlap of a Gaussian beam with a simplified surface plasmon field in Appendix A.
Equations (A7), (A9), and (A16) have minor errors of factors of 2. Equation (A7) should read

$$F({l}_{\mathrm{G}},w)={\left(\frac{2}{\pi}\right)}^{\frac{1}{4}}\frac{\sqrt{\pi \gamma w}}{2}\text{\hspace{0.17em}}\mathrm{exp}[{\left(\frac{\gamma w}{4}\right)}^{2}-2\gamma {l}_{\mathrm{G}}]\times \mathrm{erfc}(\frac{\gamma w}{4}-\frac{2{l}_{\mathrm{G}}}{w}),$$ where
the arguments of the exponential and complementary error function are corrected. Equation (A9) should read
$$\zeta =\frac{\gamma w}{4},$$ and
Eq. (A16) is now $${l}_{\mathrm{G}}\gamma =\frac{1}{2}.$$ The main result of the field-overlap derivation, given by Eq. (A18), is expressed correctly in the original
paper [1]. The analysis and conclusions which use the derivation are
thus unaffected by the corrections.

## REFERENCES

**1. **C. Fisher, L.
C. Botten, C.
G. Poulton, R.
C. McPhedran, and C.
M. de Sterke, “End-fire coupling
efficiencies of surface plasmons for silver, gold, and plasmonic nitride
compounds,” J. Opt. Soc. Am. B **33**, 1044–1054 (2016). [CrossRef]

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### Equations (3)

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(1)
$$F({l}_{\mathrm{G}},w)={\left(\frac{2}{\pi}\right)}^{\frac{1}{4}}\frac{\sqrt{\pi \gamma w}}{2}\text{\hspace{0.17em}}\mathrm{exp}[{\left(\frac{\gamma w}{4}\right)}^{2}-2\gamma {l}_{\mathrm{G}}]\times \mathrm{erfc}(\frac{\gamma w}{4}-\frac{2{l}_{\mathrm{G}}}{w}),$$
(2)
$$\zeta =\frac{\gamma w}{4},$$
(3)
$${l}_{\mathrm{G}}\gamma =\frac{1}{2}.$$