After publication, we have discovered an error in [1] relating to the sign convention of the topological charge q. Following the definition of Φ = mϕ in Eq. (8), it should have been noted that m = 2q. Accordingly, the q-plate mentioned in the final paragraph of Section 8 has a topological charge of q = −1/2.

Similarly, it should have been stated in Section 3 that Φ = −ϕ for a stress-engineered optical (SEO) element. This implies that an SEO element by itself corresponds to the m = −1 case analyzed in Sections 4–8, without any need for a half-wave plate. The experimental results presented in Section 9 are still valid because a half-wave plate was not used, since it would have had no effect in the paraxial regime. However, it must be noted that a half-wave plate should not be used when working at higher numerical apertures. (That is, the half-wave plate in Fig. 8 should be omitted.)

The authors deeply regret these oversights in the original manuscript. Nonetheless, we are pleased to report that the experimental configuration for bottle field generation is even simpler than originally thought.