Methodical inaccuracy of the Z-scan method for few-cycle terahertz pulses

Abstract

Modern sources of THz radiation generate high-intensity pulses allowing to observe nonlinear effects in this spectral range. To describe many nonlinear effects theoretically, it is necessary to know the nonlinear refractive index coefficient of optical materials. The work studies the applicability of the Z-scan method to determine the nonlinear refractive index coefficient in the THz frequency range for few-cycle pulses. We have discussed the correctness of the known Z-scan method for calculating the nonlinear refractive index coefficient for broadband THz radiation regarding 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 to the measurement error shows strong dependence on the sample thickness and can vary from 2% to 90% regarding the parameters chosen. The fact that such radiation dispersion length is commensurate with the nonlinear length or even less than the latter results in the discrepancy mentioned. 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. This can relate to the fact that the nonlinear effects in such a thin sample occur faster than the dispersion ones.

Estimations of Low-Inertia Cubic Nonlinearity Featured by Electro-Optical Crystals in the THz Range

“…The magnitude of the difference between the maximal and minimal values allows to calculate the nonlinear refractive index coefficient. Earlier we have shown that this technique is applicable for THz frequency range featuring a very broad spectrum with the correct ratio of the crystal thickness to the spatial size of the pulse [40]. Regarding water as the nonlinear medium, we obtained theoretically a value of n 2 = 5×10 −10 cm 2 /W and experimentally n 2 = 7 ± 5 × 10 −10 cm 2 /W.…”

Nonlinear TeraHertz Transmission by Liquid Water at 1 THz

“…Routine z scan measurements are obtained either with an open or a partially closed aperture in front of the detector [23]. Often, z scan experiments measure only the transmitted intensity with, e.g., a bolometer or a diode, and not the field transmittance [26][27][28]. An open aperture intensity z scan allows to quantify only the nonlinear absorption (α NL ) [26], while a partially closed aperture intensity z scan is sensitive both to the nonlinear absorption as well as the nonlinear refraction [26].…”

“…Tcypkin et al [23] reported the nonlinear transmission of almost single-cycle pulses centered at 0.75 THz by a liquid water jet. They performed typical z scan measurements [26], whereby the sample is moved through the beam focus and the intensity transmission is measured with a power detector, both with an open as well as with a partially closed aperture [27,28]. This experimental approach is restricted to the large sample volume required to run a recirculating liquid jet, which to our knowledge needs at least hundreds of milliliters of liquid sample [29].…”

Intense terahertz radiation: generation and application

“…The rapid progress of intense THz sources and detectors has motivated researchers to use intense THz radiation for various applications. Since intense THz pulses can provide higher energy for photoexcited carriers, many studies use intense THz radiation for THz time-domain spectroscopy (TDS) to characterize the carrier dynamic properties of semiconductors and other condensed matter systems [106][107][108][109][110][111][112][113][114][115][116][117][118][119]. Additionally, intense THz radiation has a relatively high peak electric-field strength that allows various traditional optical nonlinear effects such as high-order harmonic generation [110,111], saturation and anti-saturation absorption [112][113][114][115][116], and four-wave mixing.…”