Abstract

We correct several clerical errors of a previously published paper and provide a material loss Q factor formula with improved accuracy.

© 2013 Optical Society of America

We have found several clerical errors for the material loss Q factor derived in Appendix B of a previously published paper [1]. Equations (B3 )–(B9) should read as

δ[1εx]=2(1η)ε0(1ωp2/ω2)2ωp2ω2δωiγd/2ω=Γxε0(δωωiγd2ω),
δ[1εy]=2(1η)ε0(ηε1+(1η)ε0(1ωp2/ω2))2ωp2ω2δωiγd/2ω=Γyε0(δωωiγd2ω),
Γx=2(1η)(1ωp2/ω2)2ωp2ω2,
Γy=2(1η)(ηε1/ε0+(1η)(1ωp2/ω2))2ωp2ω2,
2ωδω=π2μ0(Γyε01Lx2Γxε01Ly2)(δωωiγd2ω),
δω=(1+2ω2π2μ0(Γyε01Lx2+Γxε01Ly2))1·iγd2(1+4λp2Lx211η+λp2Ly2(1η))1·iγd2,
and
Qmat(1+4λp2Lx211η+λp2Ly2(1η))ωγp,
where, in the last step of the derivation of Eq. (B8), Γx2(1η)ω2/ωp2 and Γy2(1η)1ω2/ωp2 have been used. Note that, when η1, Eq. (B9) presented here reduces to Eq. (B9) of the previously published paper [1].

We emphasize that the formulas provided in this errata improve the accuracy of the analytic calculation of the material loss Q factor. To demonstrate this point, we numerically evaluate the material loss Q factor of a dielectric–plasmonic bilayer resonator (consisting of 10 pairs) using COMSOL Multiphysics and compare the results with those obtained using the two analytic formulas. For this purpose, we fix the resonator width, the resonator height, the dielectric permittivity, and the plasmonic damping rate as Lx=Ly=λp, ε1=12.96ε0, and γ=0.002ωp, and sweep the dielectric filling ratio η from 0.01 to 0.5. The obtained results of the material loss Q factor are plotted in Fig. 1, where the squares correspond to the numerical values from COMSOL Multiphysics, the solid line corresponds to the analytic value from Eq. (B9) of the previously published paper [1], and the dashed line corresponds to the analytic value from Eq. (B9) of this errata. From Fig. 1, the accuracy improvement of the material loss Q factor formula of this errata is confirmed.

 figure: Fig. 1.

Fig. 1. Material loss Q factor as a function of the dielectric filling ratio. Solid line: analytic result from Eq. (B9) of the previously published paper [1]. Dashed line: analytic result from Eq. (B9) of this errata. Squares: numerical results from COMSOL Multiphysics.

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REFERENCE

1. G. Zhu, “Analytical design of quasi-closed subwavelength electromagnetic rectangular resonators using stacks of dielectric–plasmonic bilayers,” J. Opt. Soc. Am. B 29, 2575–2580 (2012). [CrossRef]  

References

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  1. G. Zhu, “Analytical design of quasi-closed subwavelength electromagnetic rectangular resonators using stacks of dielectric–plasmonic bilayers,” J. Opt. Soc. Am. B 29, 2575–2580 (2012).
    [Crossref]

2012 (1)

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Figures (1)

Fig. 1.
Fig. 1. Material loss Q factor as a function of the dielectric filling ratio. Solid line: analytic result from Eq. (B9) of the previously published paper [1]. Dashed line: analytic result from Eq. (B9) of this errata. Squares: numerical results from COMSOL Multiphysics.

Equations (7)

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δ [ 1 ε x ] = 2 ( 1 η ) ε 0 ( 1 ω p 2 / ω 2 ) 2 ω p 2 ω 2 δ ω i γ d / 2 ω = Γ x ε 0 ( δ ω ω i γ d 2 ω ) ,
δ [ 1 ε y ] = 2 ( 1 η ) ε 0 ( η ε 1 + ( 1 η ) ε 0 ( 1 ω p 2 / ω 2 ) ) 2 ω p 2 ω 2 δ ω i γ d / 2 ω = Γ y ε 0 ( δ ω ω i γ d 2 ω ) ,
Γ x = 2 ( 1 η ) ( 1 ω p 2 / ω 2 ) 2 ω p 2 ω 2 ,
Γ y = 2 ( 1 η ) ( η ε 1 / ε 0 + ( 1 η ) ( 1 ω p 2 / ω 2 ) ) 2 ω p 2 ω 2 ,
2 ω δ ω = π 2 μ 0 ( Γ y ε 0 1 L x 2 Γ x ε 0 1 L y 2 ) ( δ ω ω i γ d 2 ω ) ,
δ ω = ( 1 + 2 ω 2 π 2 μ 0 ( Γ y ε 0 1 L x 2 + Γ x ε 0 1 L y 2 ) ) 1 · i γ d 2 ( 1 + 4 λ p 2 L x 2 1 1 η + λ p 2 L y 2 ( 1 η ) ) 1 · i γ d 2 ,
Q mat ( 1 + 4 λ p 2 L x 2 1 1 η + λ p 2 L y 2 ( 1 η ) ) ω γ p ,

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