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Polarization and angle dependence for hyper-Rayleigh scattering from local and nonlocal modes of isotropic fluids: erratum

David P. Shelton

Open Access Open Access

Abstract

This erratum gives corrections for the errors in a previously published paper [J. Opt. Soc. Am. B 17, 2032 (2000) [CrossRef]  ].

© 2017 Optical Society of America

Equations (10)–(13) of Ref. [1] for transverse mode hyper-Rayleigh scattering (HRS) are incorrect due to an error in Eq. (8) for one of the basis vectors. The correct transverse mode HRS expressions were derived and given as Eqs. (A4)–(A7) in the Appendix of Ref. [2]. Corrected Eqs. (7) and (8) for the basis vectors and Eqs. (10)–(13) for the transverse mode HRS intensities are given below.

Q^T1=λXY^+(1−λY)X^[(1−λY)2+λX2]1/2,
Q^T2=(1−λY)λZY^−λXλZX^+[(1−λY)2+λX2]Z^[(1−λY)2+λX2]1/2[2(1−λY)]1/2,
IVV/AT=sin2 θ sin2 ψ1+cos2 ψ−2 cos θ cos ψ+[(cos ψ−cos θ)sin2 ψ+R cos ψ(1+cos2 ψ−2 cos θ cos ψ)]22(1−cos θ cos ψ)(1+cos2 ψ−2 cos θ cos ψ),
IHV/AT=[1+(R−1)(1−cos θ cos ψ)]2 sin2 θ sin2 ψ1+cos2 ψ−2 cos θ cos ψ+[(cos ψ−cos θ+(R−1)sin2 θ cos ψ)sin2 ψ+cos ψ(1+cos2 ψ−2 cos θ cos ψ)]22(1−cos θ cos ψ)(1+cos2 ψ−2 cos θ cos ψ),
IVH/AT=[cos ψ−cos θ]21+cos2 ψ−2 cos θ cos ψ+sin2 θ sin2 ψ2(1−cos θ cos ψ)(1+cos2 ψ−2 cos θ cos ψ),
IHH/AT=[cos ψ−cos θ−(R−1)cos θ(1−cos θ cos ψ)]21+cos2 ψ−2 cos θ cos ψ+[1+(R−1)cos θ cos ψ]2 sin2 θ sin2 ψ2(1−cos θ cos ψ)(1+cos2 ψ−2 cos θ cos ψ).

REFERENCES

1. D. P. Shelton, “Polarization and angle dependence for hyper-Rayleigh scattering from local and nonlocal modes of isotropic fluids,” J. Opt. Soc. Am. B 17, 2032–2036 (2000). [CrossRef]  

2. D. P. Shelton, “Nonlocal hyper-Rayleigh scattering from liquid nitrobenzene,” J. Chem. Phys. 132, 154506 (2010). [CrossRef]  

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Equations (6)

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Q ^ T 1 = λ X Y ^ + ( 1 − λ Y ) X ^ [ ( 1 − λ Y ) 2 + λ X 2 ] 1 / 2 ,
Q ^ T 2 = ( 1 − λ Y ) λ Z Y ^ − λ X λ Z X ^ + [ ( 1 − λ Y ) 2 + λ X 2 ] Z ^ [ ( 1 − λ Y ) 2 + λ X 2 ] 1 / 2 [ 2 ( 1 − λ Y ) ] 1 / 2 ,
I V V / A T = sin 2   θ   sin 2   ψ 1 + cos 2   ψ − 2   cos   θ   cos   ψ + [ ( cos   ψ − cos   θ ) sin 2   ψ + R   cos   ψ ( 1 + cos 2   ψ − 2   cos   θ   cos   ψ ) ] 2 2 ( 1 − cos   θ   cos   ψ ) ( 1 + cos 2   ψ − 2   cos   θ   cos   ψ ) ,
I H V / A T = [ 1 + ( R − 1 ) ( 1 − cos   θ   cos   ψ ) ] 2   sin 2   θ   sin 2   ψ 1 + cos 2   ψ − 2   cos   θ   cos   ψ + [ ( cos   ψ − cos   θ + ( R − 1 ) sin 2   θ   cos   ψ ) sin 2   ψ + cos   ψ ( 1 + cos 2   ψ − 2   cos   θ   cos   ψ ) ] 2 2 ( 1 − cos   θ   cos   ψ ) ( 1 + cos 2   ψ − 2   cos   θ   cos   ψ ) ,
I V H / A T = [ cos   ψ − cos   θ ] 2 1 + cos 2   ψ − 2   cos   θ   cos   ψ + sin 2   θ   sin 2   ψ 2 ( 1 − cos   θ   cos   ψ ) ( 1 + cos 2   ψ − 2   cos   θ   cos   ψ ) ,
I H H / A T = [ cos   ψ − cos   θ − ( R − 1 ) cos   θ ( 1 − cos   θ   cos   ψ ) ] 2 1 + cos 2   ψ − 2   cos   θ   cos   ψ + [ 1 + ( R − 1 ) cos   θ   cos   ψ ] 2   sin 2   θ   sin 2   ψ 2 ( 1 − cos   θ   cos   ψ ) ( 1 + cos 2   ψ − 2   cos   θ   cos   ψ ) .
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