High-quality partially coherent Bessel beam array generation: erratum

Chunhao Liang; Xinlei Zhu; Chenkun Mi; Xiaofeng Peng; Fei Wang; Yangjian Cai; Sergey A. Ponomarenko

doi:10.1364/OL.43.004939

Abstract

In this erratum, we correct mistakes in Eqs. (6), (8), and (9), typo in Eq. (11), as well as lattice period magnitudes and units in Fig. 1. We also update the funding information in Opt. Lett. 43, 3188 (2018) [CrossRef] .

Equations (6) and (8) in Ref. [1] should read

I (s) \propto \frac{1}{M} \sum_{n = 1}^{M} {| \tilde{τ} (k s_{⊥} + V_{0 n}) |}^{2},

and

I (s) \propto \sum_{n = 1}^{M} J_{l}^{2} (R | k s_{⊥} + V_{0 n} |) .

The error affected lattice period magnitudes and units in Fig. 1 which we corrected. The revised Fig. 1 is reproduced here.

Fig. 1. (a1)–(c1) OCL distributions $p$ with triangle, square, and hexagon patterns, respectively; (a2)–(c2) modulus of the source degree of coherence $| μ |$ of the corresponding OCLs. (a3)–(c3) radiant intensity distributions of the generated quasi-BBAs with different beam orders. The radiant intensity distributions are normalized by the peak intensity.

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Next, as the units of $v$ and $V_{0 n}$ are inverse meters, Eq. (9) should read

p (u) = \frac{1}{M} \sum_{n = 1}^{M} \exp [- {(u - U_{0 n})}^{2} / 2 w_{s}^{2}],

where

u

is a 2D position vector in the rotating ground-glass disk, surface and

U_{0 n}

is an off-axis displacement, both are measured in meters to adequately describe the experimental situation.

In addition, Eq. (11) contains a typo; the correct Eq. (11) should read

\tilde{τ} (r) \propto \int τ (ρ) \exp (- i k r \cdot ρ / f_{2}) d^{2} ρ .

Here

r

is a transverse position vector in the beam profile analyzer plane. We stress that all experimental results and the corresponding simulations were performed using the correct Fourier definition and hence are unaffected by the typo. We also stress that the above mistakes do not invalidate any of the findings of our original work [1].

Funding

National Natural Science Foundation of China (NSFC) (11474213, 11525418, 91750201); Project of the Priority Academic Program Development of Jiangsu Higher Education Institutions; Qing Lan Project of Jiangsu Province; Postgraduate Research Practice Innovation Program of Jiangsu Province (KYCX17_2024); China Scholarship Council (CSC) (201706920085); Natural Sciences and Engineering Research Council of Canada (NSERC).

REFERENCE

1. C. Liang, X. Zhu, C. Mi, X. Peng, F. Wang, Y. Cai, and S. A. Ponomarenko, Opt. Lett. 43, 3188 (2018). [CrossRef]

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Figures (1)

Fig. 1.

Fig. 1. (a1)–(c1) OCL distributions

p

with triangle, square, and hexagon patterns, respectively; (a2)–(c2) modulus of the source degree of coherence

| μ |

of the corresponding OCLs. (a3)–(c3) radiant intensity distributions of the generated quasi-BBAs with different beam orders. The radiant intensity distributions are normalized by the peak intensity.

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Equations (4)

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I (s) \propto \frac{1}{M} \sum_{n = 1}^{M} {| \tilde{τ} (k s_{⊥} + V_{0 n}) |}^{2},

I (s) \propto \sum_{n = 1}^{M} J_{l}^{2} (R | k s_{⊥} + V_{0 n} |) .

p (u) = \frac{1}{M} \sum_{n = 1}^{M} \exp [- {(u - U_{0 n})}^{2} / 2 w_{s}^{2}],

\tilde{τ} (r) \propto \int τ (ρ) \exp (- i k r \cdot ρ / f_{2}) d^{2} ρ .