Intracavity third-harmonic generation in Si:B pumped by intense terahertz pulses

Fanqi Meng, Mark D. Thomson, Qamar ul-Islam, Bernhard Klug, Alexej Pashkin, Harald Schneider, and Hartmut G. Roskos

Phys. Rev. B 102, 075205 – Published 25 August 2020

Abstract

We observe third-harmonic generation (THG) in boron-doped silicon (Si:B) upon pumping with picosecond 1.56-THz pulses from a free-electron laser with a peak electric field strength of up to 12 kV/cm. The measurements are performed at cryogenic temperatures where the majority of holes are bound to the acceptor dopants. The dependence of the THG on the pump intensity exhibits a threshold-free power-law behavior with an exponent close to 4. The observations can be explained by THz emission by free holes accelerated in the nonparabolic valence band, under the assumption that the density of free holes increases with the pump intensity. A quantitative treatment supports that these carriers are generated by impact ionization, initiated by the population of thermally ionized carriers, as opposed to direct tunneling ionization. In addition, we also observe intracavity THG by embedding the Si:B in a one-dimensional photonic crystal cavity. The THG efficiency is increased by a factor of eight due to the field enhancement in the cavity, with the potential to reach a factor of more than 100 for pump pulses with a spectrum narrower than the linewidth of the cavity resonance.

Received 18 June 2020
Revised 11 August 2020
Accepted 12 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.075205

Physics Subject Headings (PhySH)

High-order harmonic generation Nonlinear optics

Doped semiconductors

Terahertz spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Fanqi Meng ^1,*, Mark D. Thomson¹, Qamar ul-Islam¹, Bernhard Klug¹, Alexej Pashkin ², Harald Schneider², and Hartmut G. Roskos ^1,†

¹Physikalisches Institut, Goethe-Universität Frankfurt, 60438 Frankfurt am Main, Germany
²Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany

^*f.meng@physik.uni-frankfurt.de
^†roskos@physik.uni-frankfurt.de

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Vol. 102, Iss. 7 — 15 August 2020

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Images

Figure 1
(a) Experimental setup for the HHG measurements. The sample is positioned in a cryostat to enable temperature control. (b) Linear power transmission spectra of Si:B at three temperatures (150 K, 100 K, and 5 K), measured by FTIR spectroscopy. The ringing, most pronounced at low frequency, arises from multiple-reflection interference in the Si:B sample.
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Figure 2
(a) Transmittance/emittance spectra of the Si:B sample exposed to 1.56-THz radiation at the three pump pulse energies of 5.5, 12.5, and 31.2 nJ (power measured directly in front of the sample). Also included is the transmittance spectrum of the undoped HR Si sample for a pump pulse energy of 21.7 nJ (green curve, scaled down by a factor of 100 for better visibility in the logarithmic plot). (b) Black open diamonds: Measured THG intensity as a function of the pulse energy of the FEL beam, the error bars represent the power fluctuation of the FEL. Black dash-dotted line: Power-law dependence with an exponent of 3.9. The inset shows the results of a THG measurement using the TELBE facility where the pulse repetition rate is only 50 kHz (leading to reduced sample heating). The blue pentagons represent the measured THG intensity and the blue dashed line a power law with an exponent of 3.6. (c) Blue triangles: Normalized effective nonlinear susceptibility $χ_{eff}^{(3)}$ as a function of the electric radiation field $E_{ω}$ of the pump pulse in the sample. Red curve: Simulated $χ_{eff}^{(3)} = χ^{(3)} n_{h}$ due to impact ionization. Both are normalized to the respective values obtained at 12 kV/cm. Magenta-colored curve: Estimated density of light holes created by tunneling ionization.
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Figure 3
(a) Scheme of the 1D PC cavity. (b) Blue line: Transmittance spectrum of the 1D PC cavity at 20 K measured by THz time-domain spectroscopy (TDS); red line: transmittance spectrum calculated with the transfer matrix method (TMM). The spectra are as simulated respectively measured, without normalization.
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Figure 4
(a) Measured transmittance/emittance spectra of Si:B in the 1D PC cavity, pumped at three FEL pulse energies of 3.2, 8.4, and 21.5 nJ. (b) Measured intracavity THG intensity as a function of the pump pulse energy (red bullets). For comparison, the THG intensity for free-standing Si:B is shown by the black open diamonds. Dashed red and dash-dotted black lines: Power-law trends with an exponent of 3.9. The horizontal error bars in both data sets indicate the pump power fluctuation during the experiments.
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