In sections 5.2 and 5.4 of our original manuscript [1
1. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]
], there are missing factors of 2 in the equations for coherent combining efficiency of one-dimensional Gaussian beams with mismatched spot size W
or divergence Θ
. These equations should read, respectively: η
[1 – σW2
)], and η
[1 – σΘ2
)]. Hence, Fig. 4 of the original manuscript should be replaced by Fig. 1
Fig. 1 Co-alignment and uniformity tolerances for spatially and spectrally Gaussian beams with 1% allowance for combining loss for each effect. The BC is assumed to be lossless and uniform (ηsplit = 1 and Dn = N-1/2). RMS parameter variation refers to beam-to-beam mismatch. Fractional parameters and values are relative to the array average FWHM parameter, colored black in each sketch.
. For further clarification, we also remind the reader that these perturbative Gaussian beam results are calculated for one-dimensional variations. If, as is typical for example, the beam size varies symmetrically in both transverse x
axes, then the losses would add in the perturbative limit, increasing by a factor of two and leading to overall efficiency of η
(1 – σW2
). The same consideration also applies to displacement, pointing, and divergence mismatches, so that symmetric mismatches in both x
axes would lead to twice the losses incurred by mismatch along only one axis.
The remainder of the original manuscript is unaffected by these errors. We thank our colleague Stuart McNaught for bringing these errors to our attention.
References and links
G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]