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20THz-I-7
The nonlinearity of the refractive index of optical media in the terahertz spectral range
S.A. Kozlov1, M.V. Melnik1, ZhukovaM.O.1, O. Vorontosova1, S.E. Putilin1, A.N. Tcypkin, Xi-Cheng Zhang1,2
international Laboratory of Femtosecond Optics and Femtotechnologies, ITMO University,
St. Petersburg, 197101, Russia, [email protected]
2The Institute of Optics, University of Rochester, Rochester, NY 14627, USA
Terahertz (THz) frequency range has become an active research area due to its perspective applications. Recent advances in research have brought high intensity broadband sources of THz radiation into play (1013 W/cm2 or higher) into play [1], that it gets which make it possible to observe nonlinear effects in this spectral range [2]. The most important parameter characterizing the nonlinearity of the material response in the field of intense waves is the coefficient of its nonlinear refractive index n2. There is number of different techniques for n2 estimation. The most widespread is Z-scan [3]. This method was originally designed for strictly monochromatic radiation. However, it is become common in the case of femtosecond pulsed radiation with a broad spectrum [4]. Thus, this approach can be used for broadband THz radiation as well [2, 5].
This work presentation will gives a brief overview on the theory of low-inertia mechanisms of nonlinearity of the polarization response of condensed matter in THz spectral range and then introduce new results, both analytical and experimental, on estimations of n2 of some liquids and direct measurements of the coefficient of water in this spectral range.
We estimate the nonlinear refractive index coefficient n2 of optical media through the use of a recent theoretical treatment [6]. This treatment ascribes the THz nonlinearities in media to a vibrational response that is orders of magnitude larger than typical electronic responses. This model assumes that the nature of the nonlinearity of optical media refractive index in THz spectral range is caused by the anharmonicity of molecular vibrations. We find that the predicted value of n2, for example, for water in the low-frequency limit is n2 = 5.0*10-10 cm2/W, which is 6 orders of magnitude higher than for the visible and IR ranges. It is interesting that theoretical estimates of the coefficient n2 of vibrational nature for liquids show that the quadratic nonlinearity of anharmonic vibrations of each molecule determines the main contribution to the cubic nonlinearity of the polarization response of these isotropic media.
We present the direct measurement of water nonlinear refractive index coefficient for the broadband pulsed THz radiation with the conventional Z-scan methodtechnique. Since the Z-scan this method works with plane-parallel samples only, flat water jet was used. The experimental setup for measuring n2 of a liquid jet was based on TERA-AX source of THz radiation. The THz pulse energy was 400 nJ, the pulse duration was 0.5 ps and the spectrum width was from 0.1 to 2.5 THz. Pulsed THz radiation was focused and collimated by two parabolic mirrors. The spatial size of the THz radiation at the output of the generator was 25.4 mm. Caustic diameter was 1 mm (FWHM) and the radiation intensity of the THz beam 108 W/cm2. Flat water jet was moved along the caustic area using a motorized linear translator. The water jet had a thickness of 0.1 mm and was oriented along the normal to the incident radiation. The jet was obtained using the nozzle which combines the compressed-tube nozzle and two razor blades. The pressure was created by the pump and the hydroaccumulator which reduces the pulsations. The rate of laminar flow was enough for a complete renewal of water in the area of interaction at a laser repetition rate of 1 kHz. For n2 determination Z-scan curves measured with closed aperture were used. The direct
measurement of the nonlinear refractive index coefficient n2 = 7.0*10-10 cm2/W of water in the THz frequency range is shown. These results are consistent with the theoretical estimateions above.
We have discussed the correctness of the known Z-scan method for calculating the nonlinear refractive index coefficient for broadband THz radiation regarding the pulse number of cycles pulses have. We have demonstrated that the error in determining the nonlinear refractive index coefficient is always greater than 70% for true single-cycle pulses. With the increase in the number of oscillations up to three the measurement error shows strong dependence on the sample thickness and can vary from 2% to 90% depending on the chosen parameters. It is demonstrated that the decrease in the sample thickness leads to the reduction of the nonlinear refractive index coefficient determination error, and this error is <2% when the ratio between the sample thickness and the pulse longitudinal spatial size is <1.
The study is funded by RFBR project No. 19-02-00154.
References
[1] M. Shalaby, C. Hauri, Nature Communications, 6, 5976 (2015);
[2] A. Tcypkin, M. Melnik, M. Zhukova, I. Vorontsova, S. Putilin, S. Kozlov, X. Zhang,et al. Optics express, 27 (8), 10419-10425 (2019);
[3] M. Sheik-Bahae et al. IEEE journal of quantum electronics, 26 (4), 760-769 (1990);
[4] X. Zheng et al., Optics Letters, 40 (15), 3480 (2015);
[5] M. Melnik, et al., Scientific Reports, 9 (1), 9146 (2019);
[6] K. Dolgaleva et al,, D. Materikina, R. Boyd, S. Kozlov, Physical Review A., 92 (2), 023809 (2015).
