CC BY
20THz-I-6
Surprising nonlinear optics of pulsed terahertz radiation
A. Tcypkin1, A. Drozdov1, I. Artser1, A. Ismagilov1, M. Melnik1, I. Vorontsova1, M.
Zhukova1, S. Kozlov1
1-ITMO University, St. Petersburg, 197101, Russia kozlov@mail.ifmo. ru
Recently, it has been theoretically predicted and experimentally confirmed that the coefficient of the nonlinear refractive index of materials in the terahertz frequency range can be several orders of magnitude higher than its value in the visible and near-IR spectral ranges both for crystals [1,2] and for liquids [3, 4]. The mechanism of this nonlinearity is low-inertia one, which means that high-speed THz photonics devices based on nonlinear effects are promising. The values of nonlinear refractive index for some materials are presented in the Table 1.
Table 1. The nonlinear refractive index coefficients in the NIR and the THz frequency range
Medium n2 cm2/W in n2 cm2/W
THz range in NIR
range
ZnSe 1x10-13 3.8x10-14
LiNbOs 7x10-11 1.7x10-15
Water 5x10-10 1.9x10-16
Ethanol 9x10-9 7.7x10-16
CO, (THz)
Fig. 1. Spectrum of the generated THz field. Black solid line is the experimental data, red dotted line is the analytical results, blue dashes line shows the error for experimental data
Moreover, well-known nonlinear effects in the field of pulsed THz radiation can qualitatively change their appearance. For example, the self-focusing phenomenon may not be observed even when the radiation power is significantly exceeded the critical self-focusing power [5].
Also, we discovered another amazing modification of one of the classical phenomena of nonlinear optics. The interaction of a THz pulse containing only one full oscillation of the electrical field with a medium with cubic nonlinearity can generate radiation at quadruple frequencies relative to the frequency of the power spectral density maximum, instead of radiation at triple frequency as expected. Illustration of this effect is present in the Fig.1.
It can be seen in Fig.1, that both for experimental and for theoretical results no generation of radiation at triple frequencies is observed in the spectrum of pulsed THz radiation at the output of the medium during the interaction of the generated THz field with a crystal, which also has cubic nonlinearity. Moreover, in the THz radiation spectrum instead of the triple frequency, according to the frequency of its spectral density maximum, a pronounced dip is observed. In this case, radiation of significant energy is generated at a quadruple frequency, which is not observed for similar experiments in the visible and near-IR frequency ranges. This effect is analytically proven and is determined by the asymmetry of the spectrum of such pulse.
However, some of the aspects of the measurements and calculations of z-scan curves were not completely discussed [6]. Here, we introduce some clarity to the raised issues of implementation of broadband single-cycle THz pulses for z-scan method. We are considering issues related to the spatiospectral representation of strongly focused single-cycle THz pulse with extremely broad spectrum 0.12.5 THz, its nonparaxiality of propagation and influence the results measured by the z-scan technique. We also estimate the influence of ellipticity in the shape of the collimated THz beam to the beam profile close to the focus. We note that within an order of magnitude there is a very good agreement between the calculated and measured values even considering features of broadband single-cycle THz pulses.
The study is funded by RFBR project No. 19-02-00154.
[1] K. Dolgaleva, et al., Prediction of an extremely large nonlinear refractive index for crystals at terahertz frequencies, Physical Review A, vol. 92, p. 023809, (2015).
[2] M. Zhukova, et al., Estimations of Low-Inertia Cubic Nonlinearity Featured by Electro-Optical Crystals in the THz Range, Photonics, vol. 7, p. 98, (2020).
[3] A. Tcypkin, et al., High Kerr nonlinearity of water in THz spectral range, Optics express, vol. 27, pp. 10419-10425, (2019).
[4] A. Tcypkin, et al., Giant Third-Order Nonlinear Response of Liquids at Terahertz Frequencies, Physical Review Applied, vol. 15, p. 054009, (2021).
[5] S.A. Kozlov, et al., Suppression of self-focusing for few-cycle pulses, JOSA B, vol. 36, pp. G68-G77, (2019).
[6] M. Melnik, et al., Methodical inaccuracy of the Z-scan method for few-cycle terahertz pulses, Scientific reports, vol. 9, pp. 1-8, (2jC7l(9).
