7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Exploiting laser-induced fluorescence method with a single optical pathto multidimensional flow-velocity measurements

Shinji Yoshimura1,2, Kenichiro Terasaka3, Hiroki Minagawa4, Mitsutoshi Aramaki4
1
National Institute for Fusion Science, National Institutes of Natural Sciences, 2 Center for
Low-temperature Plasma Science, Nagoya University, 3 Interdisciplinary Graduate School ofEngineering Science, Kyushu University, 4 College of Industrial Technology, Nihon University
e-mail (speaker): yoshimura.shinji@nifs.ac.jp
The laser-induced fluorescence (LIF) method is widelyused as a versatile technique to measure the velocity
distribution functions of ions and neutrals from
low-temperature plasmas to magnetic-field confinement
plasmas. The LIF spectrum obtained by scanning thelaser wavelength (frequency) can be interpreted as avisualization of the density of the particles that satisfy
the resonant absorption condition. When the particles aremoving relative to the propagation direction of the laser
beam, the Doppler shift must be considered. For example,
when the wavenumber vector of the plane-wave laser
propagating in the z direction is 𝒌𝒌, and the velocity
vector of the particle is 𝝊𝝊, the Doppler shift of theabsorption frequency is given by 𝛿𝛿 = −𝒌𝒌 ∙ 𝝊𝝊 = −𝑘𝑘𝑧𝑧 𝜐𝜐𝑧𝑧 .
Only the velocity component parallel to the wavenumber
vector modifies the absorption condition, indicating that
this measurement is essentially one-dimensional.
Recently, it has been reported that the use of
Laguerre-Gaussian (LG) modes known as optical vortex
beams instead of plane-wave lasers may overcome thisone-dimensionality and extend the LIF method tomultidimensional measurements [1, 2]. The LG modesare cylindrically symmetric solutions of the Helmholtz
equation in the paraxial approximation and have a spatial
phase factor 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖 , where 𝑙𝑙 and 𝜑𝜑 denote thetopological charge and the azimuthal angle, respectively;
the beam center is a phase singularity, resulting in adoughnut-shaped intensity distribution, as shown in Fig.
1(a). In 1994, Allen et al. derived the expression of theDoppler shift for an atom moving in an optical vortex
beam [3]. The Doppler shift of the absorption frequency
𝑙𝑙has two primary terms as follows: 𝛿𝛿LG = −𝑘𝑘𝑧𝑧 𝜐𝜐𝑧𝑧 − 𝜐𝜐𝜑𝜑 .
𝑟𝑟
The first term is the translational Doppler shift used in
the conventional LIF method, while the second term isthe azimuthal one, i.e., perpendicular to the beam’s
propagation direction. Therefore, the LIF spectrum
obtained using the optical vortex beam contains
information on the velocity in the 𝜑𝜑 direction. When auniform flow traversing the LG beam exists, themagnitude of the second term varies with position in thebeam cross-section. If any arbitrary portion of the beam
could be used to obtain the LIF spectrum, theinterpretation of the center frequency shift of thespectrum would be straightforward; however, in theexperiment, the LIF photons from the entire beam would
be received. Consequently, the integrated LIF spectrum
will show an increase in width rather than a frequency
shift, and information on flow direction will be lost [1].

A beam with partially localized intensity while
maintaining the azimuthal phase gradient would allow
LIF measurements with sensitivity to the direction oftransverse flow across the beam. An asymmetric opticalvortex beam [4, 5] is a promising alternative with suchcharacteristics. Figure 1(b) shows an example of theintensity distribution of an asymmetric optical vortex
beam. In this case, the intensity is localized at the top of
the beam, while the phase gradient in the azimuthal
direction is retained. Therefore, the LIF spectrum
obtained with this beam is expected to show anadditional center frequency shift depending on thehorizontal flow velocity. By tailoring the intensity
distribution as desired, we can make the LIF spectrum
sensitive to any direction perpendicular to the beam
propagation direction. Since the translational Doppler
shift is maintained, the LIF method with asymmetric
optical vortex beams enables three-dimensional flow
velocity vector determination with a single optical path.
More details will be discussed in the presentation.
This work was supported by JSPS KAKENHI Grant
Numbers JP21H01058 and JP18KK0079.
References[1] S. Yoshimura et al., Jpn. J. Appl. Phys. 59, SHHB04(2020).
[2] S. Yoshimura et al., J. Adv. Simulat. Sci. Eng. 9, 151(2022).
[3] L. Allen et al., Opt. Commun. 112, 141 (1994).
[4] A.Ya. Bekshaev and A.I. Karamoch, Opt. Commun.
281, 3597 (2008).
[5] A. A. Kovalev et al., Phys. Rev. A 93, 063858 (2016).

(a)

(b)

Figure 1 (a) Intensity distribution of an experimentallygenerated optical vortex beam (𝑙𝑙 = 10), (b) Intensity
distribution of an experimentally generated asymmetric
optical vortex beam, where the laser incident position tothe hologram is intentionally misaligned.