Mechanism of relativistic Doppler reflection from a photoinduced moving plasma front studied by terahertz time-domain spectroscopy

Nanase Kohno, Ryuji Itakura, and Masaaki Tsubouchi

Phys. Rev. B 94, 155205 – Published 27 October 2016

Abstract

We applied terahertz (THz) time-domain spectroscopy to reveal the mechanism of the relativistic Doppler reflection of THz light from a photoinduced plasma front in a silicon wafer. The frequency upshift caused by the Doppler reflection was identified by measurement of the reflected THz waveforms and compared to the calculated results obtained using the one-dimensional finite-difference time-domain method. The relation between the energy density of the pump light and the frequency upshift was also explored. We found that the interaction time of the moving plasma front and the reflected THz pulse is a key factor in understanding the mechanism of the relativistic Doppler reflection.

Received 11 July 2016
Revised 4 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.155205

Physics Subject Headings (PhySH)

Terahertz generation in plasmas

Finite-difference time-domain method Ultrafast pump-probe spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Nanase Kohno, Ryuji Itakura, and Masaaki Tsubouchi^*

Kansai Photon Science Institute, National Institutes for Quantum and Radiological Science and Technology, 8-1-7 Umemidai, Kizugawa, Kyoto 619-0215, Japan

^*tsubouchi.masaaki@qst.go.jp

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Vol. 94, Iss. 15 — 15 October 2016

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Images

Figure 1
Schematic diagram to realize the Doppler reflection. The time sequence of the THz and optical pump pulses and their propagation in the Si wafer are shown from (I) to (III).
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Figure 2
Schematic diagram of the experimental apparatus. $λ / 2$ and $λ / 4$ , half and quarter wave plates, respectively; ND, neutral density; ITO, indium-tin-oxide; WP, Wollaston prism; PD, photodiode; L1, L2, and L3, plastic lenses for THz light (PAX, Tsurupica) with focal lengths of 50, 100, and 100 mm, respectively. (b) Example of the THz waveform transmitted from the Si wafer. (c) Fourier transformed spectrum of Pulse B.
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Figure 3
Waveforms of the reflected THz pulse [Pulse $B$ in Fig. 2] as a function of pump-probe delay time $Δ t$ (solid lines). The Si wafer was irradiated by the optical pump pulse with an energy density of $2.7 μ J m m^{- 2}$ . The horizontal axis corresponds to the roundtrip time within the 1 mm thick Si plate. The dotted line indicates the equivalent phase position of the reflected pulse. The red dashed lines correspond to the waveforms calculated using the 1D-FDTD method.
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Figure 4
(a) Time-resolved THz waveforms measured with a fine scan step of 67 fs. The Si wafer was irradiated by the optical pump pulse with an energy density of $2.7 μ J m m^{- 2}$ . The horizontal axis corresponds to the roundtrip time within the Si plate. The arrow indicates the temporal advance of the waveforms. (b) Time-dependent power spectra $I (ν_{THz}, Δ t)$ obtained by a Fourier transform of the THz waveforms shown in (a). (c) Time-dependent average frequency of spectra $〈 ν_{THz} (Δ t) 〉$ . The upshift factor is indicated by the right axis. (d)–(f) The corresponding results obtained by the 1D-FDTD calculation for the THz waveforms, the power spectra, and the average frequency, respectively. In (c) and (f), the horizontal dashed lines show $Γ = 1$ .
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Figure 5
Time-resolved (a) THz waveforms and (b) Fourier transformed spectra measured with a fine scan step of 67 fs at seven pump energy densities, 0.19, 0.38, 0.79, 1.3, 2.7, 4.1, and $8.6 μ J m m^{- 2}$ .
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Figure 6
Pump energy dependences of (a) effective plasma thickness $d_{eff}$ , (b) speed of the plasma front $v_{p}$ , (c) maximum upshift factor $Γ_{\max}$ , (d) interaction time $t_{int}$ , and (e) modified upshift factor $\tilde{Γ}$ . In (a), the dashed line is the result calculated by Eq. (7) using the average frequency of the incident THz pulse, and the solid line is the fitted result of Eq. (7) to the experimental data. In (c) and (e), the solid lines are the fitted results of the logarithmic curve to the upshift factors as a function of the pump energy density. Note that, in (c), the data at $8.6 μ J m m^{- 2}$ was excluded in the fitting. In (d), the horizontal dashed line shows the period of the THz waveform at the frequency of 0.52 THz.
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