Abstract

In our previous paper, we incorrectly calculated the total applied force on the metal particle. We have corrected the results and the affected figures. These corrections do not affect the conclusions of the published paper.

© 2014 Optical Society of America

In [1], we calculated the total applied force Fsur on the metal particle by the surface tension of the surrounding glass induced by the temperature distribution. A minus sign is missing in Eq. (10), which should have been written

Fsur=0π2πr02sinθcosθp(T)dθ=4πr00πsinθcosθσ(T(tc,r0,θ))dθ.

The temperature dependences of the surface tension σ(T) N/m was approximated as

σ(T)=5.38×105T+0.333.

These equations are used in the numerical calculations, but errors were found in the associated codes for the above equations. In Eq. (10), cos θ was used instead of sin θ, and in Eq. (12), the initialization value of 0.333 was missed. We have corrected these errors and recalculated the results.

In consequence, the force applied to the metal particle from the surrounding glass Fsur was calculated to be ~2.8 μN at a power of 21.3 W. In [1], the migration speed of the particle was calculated by assuming the force applied from the surrounding glass Fsurto be equal to the viscous resistance force Fres. Fres was calculated by assuming that the viscosity of the surrounding glass was constant using the viscosity at r = 54 μm and θ = 90°. Using this assumption, the migration speed was calculated to be ~1.0 μm/s. The speed was smaller than the experimental particle speed (~72 μm/s). The viscosity was calculated using the viscosity at r = 50 μm and θ = 0° from the temperature (~1720 K). The recalculated speed was 16 μm/s. Figure 1 shows the speed of the moving particle, which was measured for various laser powers. Measured and calculated velocities matched better than in [1].

 figure: Fig. 1

Fig. 1 Speeds of stainless-steel particle migration under laser illumination at various powers. Calculated velocity was corrected.

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The results in Fig. 6 of [1] also differ. Figure 2 shows the speed of the particle calculated by assuming that the stationary particle was accelerated with a constant force of 2.8 μN. The speed of the particle exceeded 90% of its terminal speed in less than 50 ns.

 figure: Fig. 2

Fig. 2 Speed of stainless-steel particle migration under laser illumination. The laser power was 21.3 W.

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The general conclusions of the original article are unaffected. We apologize for these errors.

Acknowledgment

Support from Japan Society for the Promotion of Science through a Grant-in-Aid for Scientific Research (Grant No. 24656096) is gratefully acknowledged.

References and links

1. H. Hidai, M. Matsushita, S. Matsusaka, A. Chiba, and N. Morita, “Moving force of metal particle migration induced by laser irradiation in borosilicate glass,” Opt. Express 21(16), 18955–18962 (2013). [CrossRef]   [PubMed]  

References

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  1. H. Hidai, M. Matsushita, S. Matsusaka, A. Chiba, and N. Morita, “Moving force of metal particle migration induced by laser irradiation in borosilicate glass,” Opt. Express 21(16), 18955–18962 (2013).
    [Crossref] [PubMed]

2013 (1)

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Figures (2)

Fig. 1
Fig. 1 Speeds of stainless-steel particle migration under laser illumination at various powers. Calculated velocity was corrected.
Fig. 2
Fig. 2 Speed of stainless-steel particle migration under laser illumination. The laser power was 21.3 W.

Equations (2)

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F s u r = 0 π 2 π r 0 2 sin θ cos θ p ( T ) d θ = 4 π r 0 0 π sin θ cos θ σ ( T ( t c , r 0 , θ ) ) d θ .
σ ( T ) = 5.38 × 10 5 T + 0.333

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