Optical processes for middle atmospheric Doppler lidars: Cabannes scattering and laser-induced resonance fluorescence

Chiao-Yao She; Huailin Chen; David A. Krueger

doi:10.1364/JOSAB.32.001575

Journal of the Optical Society of America B
Vol. 32,
Issue 8,
pp. 1575-1592
(2015)
•https://doi.org/10.1364/JOSAB.32.001575

Optical processes for middle atmospheric Doppler lidars: Cabannes scattering and laser-induced resonance fluorescence

Chiao-Yao She, Huailin Chen, and David A. Krueger

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Chiao-Yao She, Huailin Chen, and David A. Krueger, "Optical processes for middle atmospheric Doppler lidars: Cabannes scattering and laser-induced resonance fluorescence," J. Opt. Soc. Am. B 32, 1575-1592 (2015)

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Abstract

The problem of light scattering from a monochromatic laser beam by an ensemble of atmospheric atoms or molecules in thermal equilibrium under ambient wind and temperature is revisited with two emphases. First, the essence of and difference between laser Cabannes scattering (CS) and laser-induced resonance fluorescence (LIF), which permit atmospheric temperature and wind measurements, are simply presented. A classical model is shown to yield the same angular distribution in scattered power for both, a factor of two larger Doppler shift for the former (CS), in the backward direction with the same line-of-sight (LOS) wind, and a dramatic 17 order larger backscattering cross section for the latter (LIF). Second, the LIF process is developed from first principles, and we present the relations between absorption cross section, differential scattering cross sections, and LIF emission spectrum for atoms with hyperfine structure. By doing this, we (1) equate the decoherence rate among the mixed excited substates to half of the Einstein coefficient to comply with energy conservation, and (2) present a clear physical insight into the origin of the Hanle effect, whose quantitative evaluation for these atoms requires quantum mechanical treatment. We then derive LIF emission rates for each of the eight and 10 pathways associated with the $D_{1}$ and $D_{2}$ transitions, and deduce the temperature and LOS wind dependence in differential backscattering cross sections of atmospheric sodium and potassium atoms. Using these cross sections allows retrieval of atmospheric parameters in the mesopause region (80–110 km in altitude) by a metal resonance lidar.

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Corrections

Chiao-Yao She, Huailin Chen, and David A. Krueger, "Optical processes for middle atmospheric Doppler lidars: Cabannes scattering and laser-induced resonance fluorescence: erratum," J. Opt. Soc. Am. B 32, 1954-1954 (2015)
https://opg.optica.org/josab/abstract.cfm?uri=josab-32-9-1954

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LIF Emission Pathway $ν_{f F f^{'}}$ ( $\| f 〉 \to \| F 〉 \to \| f^{'} 〉$ )	Level 3 ( $F = 1$ )	Level 4 ( $F = 2$ )
$(f, f^{'}) = (1, 1)$	$ν_{131} = 2 ν_{31} - ν$	$ν_{141} = 2 ν_{41} - ν$
(1, 2)	$ν_{132} = ν_{31} + ν_{32} - ν$	$ν_{142} = ν_{41} + ν_{42} - ν$
(2, 2)	$ν_{232} = 2 ν_{32} - ν$	$ν_{242} = 2 ν_{42} - ν$
(2, 1)	$ν_{231} = ν_{32} + ν_{31} - ν$	$ν_{241} = ν_{42} + ν_{41} - ν$

$ν_{f F f^{'}}$	Level 5 ( $F = 0$ )	Level 6 ( $F = 1$ )	Level 7 ( $F = 2$ )	Level 8 ( $F = 3$ )
(1, 1)	$ν_{151} = 2 ν_{51} - ν$	$ν_{161} = 2 ν_{61} - ν$	$ν_{171} = 2 ν_{71} - ν$
(1, 2)		$ν_{162} = ν_{61} + ν_{62} - ν$	$ν_{172} = ν_{71} + ν_{72} - ν$
(2, 2)		$ν_{262} = 2 ν_{62} - ν$	$ν_{272} = 2 ν_{72} - ν$	$ν_{282} = 2 ν_{82} - ν$
(2, 1)		$ν_{261} = ν_{62} + ν_{61} - ν$	$ν_{271} = ν_{72} + ν_{71} - ν$

$α_{f F f^{'}}^{π} (0, θ_{0}) = α_{F f^{'}} [1 + 3 g_{F} B_{f F f^{'}}^{(2)} / 10]$	$\| 3 〉$ ( $F = 1$ )	$\| 4 〉$ ( $F = 2$ )
$(f, f^{'}) = (1,1)$	1.125/6	1.175/2
(1, 2)	4.875/6	0.825/2
(2, 2)	5.025/6	1.175/2
(2, 1)	0.975/6	0.825/2

$α_{f F f^{'}}^{π} (0, θ_{0})$	$\| 5 〉$ ( $F = 0$ )	$\| 6 〉$ ( $F = 1$ )	$\| 7 〉$ ( $F = 2$ )	$\| 8 〉$ ( $F = 3$ )
(1, 1)	1	5.625/6	1.175/2	0
(1, 2)	0	0.975/6	0.975/2	0
(2, 2)	0	1.005/6	1.175/2	1.12
(2, 1)	0	4.875/6	0.825/2	0

$q_{f F}^{π} (0, θ_{0}) = \sum_{f^{'} = 1}^{2} α_{F f^{'}} [1 + 3 g_{F} B_{f F f^{'}}^{(2)} / 10]$	$\| 3 〉$ ( $F = 1$ )	$\| 4 〉$ ( $F = 2$ )
$\| 1 〉 : f = 1$	1	1
$\| 2 〉 : f = 2$	1	1

$q_{f F}^{π} (0, θ_{0})$	$\| 5 〉$ ( $F = 0$ )	$\| 6 〉$ ( $F = 1$ )	$\| 7 〉$ ( $F = 2$ )	$\| 8 〉$ ( $F = 3$ )
$\| 1 〉$ ( $f = 1$ )	1	1.1	1
$\| 2 〉$ ( $f = 2$ )		0.98	1	1.12

$e_{q_{1}} e_{q_{2}}$	$q_{2} = - 1$	1
$q_{1} = - 1$	$- 0.5 e^{- i 2 ϕ_{0}}$	0.5
0	0	0
1	−0.5	$- 0.5 e^{i 2 ϕ_{0}}$

$B_{f F f^{'}}^{(0)} = {(- 1)}^{f + f^{'}} [\begin{matrix} \begin{matrix} F & F & 0 \end{matrix} \\ \begin{matrix} 1 & 1 & f \end{matrix} \end{matrix}] [\begin{matrix} \begin{matrix} F & F & 0 \end{matrix} \\ \begin{matrix} 1 & 1 & f^{'} \end{matrix} \end{matrix}]$	$F = 3$	$F = 2$	$F = 1$	$F = 0$
$(f, f^{'}) = (1,1)$	1/21	1/15	1/9	0
(1, 2)	0	1/15	1/9	0
(2, 2)	0	1/15	1/9	0
(2, 1)	0	1/15	1/9	0

$B_{f F f^{'}}^{(2)} = (- 1)^{f + f^{'}} 5 [\begin{matrix} \begin{matrix} F & F & 2 \end{matrix} \\ \begin{matrix} 1 & 1 & f \end{matrix} \end{matrix}] [\begin{matrix} \begin{matrix} F & F & 2 \end{matrix} \\ \begin{matrix} 1 & 1 & f^{'} \end{matrix} \end{matrix}]$	$F = 3$	$F = 2$	$F = 1$	$F = 0$
$(f, f^{'}) = (1,1)$	2/35	7/60	1/180	0
(1, 2)	0	−7/60	−1/36	0
(2, 2)	0	−7/60	−1/36	0
(2, 1)	0	7/60	5/36	0

$e_{q_{1}} e_{q_{2}}$	$q_{2} = - 1$	0	1
$q_{1} = - 1$	$0.5 e^{- i 2 ϕ_{0}} \cos^{2} θ_{0}$	$- e^{- i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$	$- 0.5 \cos^{2} θ_{0}$
0	$- e^{- i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$	$\sin^{2} θ_{0}$	$e^{i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$
1	$- 0.5 \cos^{2} θ_{0}$	$e^{i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$	$0.5 e^{i 2 ϕ_{0}} \cos^{2} θ_{0}$

$e_{q_{1}} e_{q_{2}}$	$q_{2} = - 1$	0	1
$q_{1} = - 1$	$0.5 e^{- i 2 ϕ_{0}} \cos^{2} θ_{0}$	$- e^{- i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$	$- 0.5 \cos^{2} θ_{0}$
0	$- e^{- i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$	$\sin^{2} θ_{0}$	$e^{i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$
1	$- 0.5 \cos^{2} θ_{0}$	$e^{i ϕ_{0}} \cos θ_{0} \sin θ_{0} / \sqrt{2}$	$0.5 e^{i 2 ϕ_{0}} \cos^{2} θ_{0}$

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Equations (61)

Journal of the Optical Society of America B