Broadband and narrowband laser-based terahertz source and its application for resonant and non-resonant excitation of antiferromagnetic modes in NiO

A versatile table-top high-intense source of terahertz radiation, enabling to generate pulses of both broadband and narrowband spectra with a tunable frequency up to 3 THz is presented. The terahertz radiation pulses are generated by optical rectification of femtosecond pulses of Cr:forsterite laser setup in nonlinear organic crystal OH1. Electric field strengths of broadband and narrowband terahertz pulses were achieved close to 20 MV/cm and more than 2 MV/cm, correspondingly. Experiments on excitation of spin subsystem oscillations of an antiferromagnetic NiO were carried out. Selective excitation of 0.42 THz mode was observed for the first time at room temperature by a narrowband terahertz pulses tuned close to mode frequency. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
In recent years, sources of single-cycle and multi-cycle pulses of terahertz (THz) radiation have been increasingly used for both fundamental and applied research. Numerous new experiment in THz science have become possible due to the recent availability of THz sources with high values of energy and strength of electric and magnetic fields [1][2][3][4]. High-intense terahertz pulses are generated by various methods, in particular down-frequency conversion, optical rectification of femtosecond laser pulses [1,2,[5][6][7], radiative phenomena of ultra-short, highly charged electron beams in modern linear accelerators [3,8].
Single-cycle THz pulses are generated in table-top setup by optical rectification of femtosecond laser pulses in nonlinear organic [1,9] and inorganic [10,11] crystals, in gas-plasma driven by two-colour laser [12], and in large scale accelerator facilities using relativistic charged particle beams [3]. The advantages of optical rectification in highly-nonlinear crystal are a conversion efficiency of a few percents, shot-to-shot radiation stability, and high beam quality, which allows tight focus and highest field [1,2], but has several limitations. In particular, radiation spectral bandwidth ranges up to 10 THz and pulse energy is limited by the size of the nonlinear crystal and the pump energy density, at which its destruction occurs. Compared with optical rectification, the gas-plasma THz generation scheme has a very wide spectral bandwidth (up to 50 THz) [13], as well as the theoretical possibility of achieving a field strength of up to 1 GV/cm [5]. Systems that allow generation of THz radiation using charged particle beams make it possible to realize high pulse energy at high repetition frequencies (up to 100 kHz) [3]. A significant disadvantage of these sources is the inability to obtain generation of broadband and narrowband radiation in a single setup. In addition, it is difficult to implement synchronization with probe laser radiation for the pump-probe schemes used in THz spectroscopy.
Multi-cycle THz pulses are generated in laser-based sources by mixing two delayed linearly chirped pulses in a nonlinear medium [14]. The THz pulses close to microjoule energy tunable in the frequency range of 0.3-1.3 THz were obtained in LiNbO 3 crystal by tilted-pulse-front pumping [15]. The generation of THz pulses with a tunable central radiation frequency in the range from 0.3 to 0.8 THz in an HMQ-TMS organic crystal by collinearly phase matched optical rectification of temporally shaped 800 nm pulses was obtained in [16]. Optical rectification of the spatial forms of femtosecond laser pulses in a lithium niobate crystal was used to generate THz pulses tunable in the frequency range 0.3-1.2 THz [17]. Extreme narrowband (quasi monochromatic), multi-cycle THz generation (1%-bandwidth, 0.361 THz) with high pulse energy (0.6 mJ) using a large-aperture periodically-poled lithium niobate was demonstrated in [4].
To carry out experiments covering linear and nonlinear THz spectroscopy, resonant pumping and control of material properties, the capability to control the number of oscillations of the electric field strength from one to several oscillations is required, which corresponds to the broadband and narrowband spectrum, with the maximum possible electric field strength up to several tens of MV/cm. Despite the numerous of studies in the field of generation of intense terahertz pulses, nowadays there is no versatile THz source with high conversion efficiency and providing both broadband and narrowband THz generation with a tunable central frequency.
In this paper we present a versatile table-top laser-based easy-to-implement THz source that allows to generate both broadband and narrowband pulses with tunable center frequency with high energy. In addition, the resonant and non-resonant effects of THz radiation pulses of our source on the spin subsystem of a typical NiO antiferromagnetic at room temperature are demonstrated.

Versatile broadband and narrowband laser-based THz source
The versatile spectrally tunable source of THz radiation pulses has been developed on the unique chromium-forsterite laser system [18] based on chirped pulse amplification scheme and it consists of a seed oscillator, stretcher, amplifying stages and a temporal compressor ( Fig. 1(a)). The laser system delivers femtosecond optical pulses at a wavelength of 1240 nm with an energy up to 40 mJ, a duration of 100 fs (FWHM Fig. 1(b)) and a repetition rate of 10 Hz. Broadband THz pulses are produced by optical rectification of femtosecond laser pulses in an organic crystal [1,9]. It is necessary to form optical pulses with a given temporal shape (Figs. 1(c) and 1(d)) to generate THz radiation pulses with a specific spectral band (narrowband) [14,19]. We used two alternative devices to implement this mode of operation that were included in the optical scheme of the femtosecond laser system: the first one was based on an acousto-optic dispersion delay line (AODDL) [20,21], the second one was based on the Mach-Zehnder interferometer (MZI) [22] (Fig. 1(a)).
The advantage of using AODDL before the amplifier is the possibility to recover the diffraction losses in the acousto-optic crystal. In fact the subsequent amplifier stages operate in the saturation mode and are not sensitive to the input seed energy. Moreover, the AODDL allows to control the frequency and width of the spectrum of the generated terahertz pulses radiation in real time. However, the use amplification of multi-peaked laser pulse requires careful adjustment of the gain of amplifiers, since, instead of a single pulse stretched in time, a sequence of shorter pulses is used that connected with potential risk to exceed the optical damage threshold of the laser components. Unlike a device that uses AODDL, the pulse energy loss is at least 50% with the Mach-Zehnder interferometer and cannot be compensated since this pulse forming system is placed after the amplifiers. The advantage of the scheme with the interferometer is a larger adjustment range for the duration of the laser pulse (up to the duration of the chirped pulse). This makes possible to obtain a narrower spectral line of THz radiation, and its center frequency [22] can be varied by changing the beat frequency via delaying the pulse replica.
In recent works, [1,9] it was shown that the method of optical rectification of femtosecond laser pulses with a wavelength of 1240 nm allows to generate linearly polarized THz pulses in various nonlinear organic crystals (DAST, DSTMS, OH1) with high pulse energy (from tens to hundreds of µJ) and conversion efficiency (a few percents). Typical waveform of single-cycle THz pulse generated in an OH1 crystal, and the corresponding spectrum calculated by Fourier transformation are shown in Figs. 2(a) and 2(c). In order to obtain multicycle (narrowband) THz pulse shown in Figs. 2(b) and 2(d), the laser beam is directed towards the above-mentioned pulse-forming scheme of versatile THz radiation source. Waveforms were measured by electro-optical sampling in a 100 µm thick GaP electro-optical crystal with (110) orientation (on a 2 mm-thick GaP substrate with (100) orientation).

Excitation of spin subsystem oscillations of an antiferromagnetic NiO
To demonstrate the benefit to use a versatile THz source, we have carried out experiments on the excitation of spin subsystem oscillations of an antiferromagnetic NiO. To excite antiferromagnetic modes in NiO, high intensity THz pulses at a frequency close to the resonance were used. Spin dynamics controlled by the magnetic field of the THz pulse has been investigated by the magneto-optical Faraday effect using infrared femtosecond laser pulses.
The scheme of the experiments is shown in Fig. 3. The main part of the laser system radiation (95%) at the fundamental wavelength of 1240 nm was directed to a nonlinear organic OH1 crystal (Rainbow Photonics). The OH1 crystal was 6 mm in diameter and 425±10 µm thick with an antireflection coating at the pump laser wavelength. After the OH1 crystal, a low pass filter (LPF8.8-47, Tydex) with cut off frequency at 10 THz was used to reject the residual laser pump radiation. The filter reduced the laser radiation more than 10 8 times. High conversion efficiency (∼3%) was achieved at the fluence of 6 mJ/cm 2 of transform-limited pump laser pulse. The maximum THz radiation pulses energy was obtained at the pump energy density of 15 mJ/cm 2 . To achieve the maximum strength of the electric and magnetic fields, the THz radiation beam size was expanded 6 times with a telescope consisting of two off-axis parabolic mirrors with reflected focal lengths of 25.4 mm and 152.4 mm. The THz radiation was focused on the sample by an off-axis parabolic mirror with a reflected focal length of 50.8 mm.
A probe pulse with a duration of 100 fs at a wavelength of 1240 nm passed through a hole in the parabola and was focused on the NiO sample's surface by a positive lens with a focal length of 100 mm in a 20 µm spot (at a level of 1/e 2 ). The energy of the probe pulse was 1 µJ. Then, the radiation passed through a half-wave plate, a Wollaston prism, and was recorded by balanced diodes (Thorlabs PDB210C/M). A delay line installed in the pump beam of the OH1 crystal was used to implement the temporal overlap between the probe and THz pulses. The experimental scheme for the THz radiation generation and the spin dynamics study in a NiO crystal was placed in a housing with dried air to reduce the absorption of a THz radiation by water vapor (absolute humidity at a temperature of 23 • C was 0.41 g/m 3 ). The THz radiation polarization was parallel to the probe pulse polarization. Table 1 shows the parameters of the THz radiation pulses that have been used in the experiment, where f -frequency, ∆f -spectral line width, r e −2 -focusing spot radius at 1/e 2 level, W -energy, E -electric field strength, B -magnetic field induction. The last row of Table 1 displays the parameters of a single-cycle THz pulse (broadband) (Figs. 2(a) and 2(c)). The temporal and spectral characteristics of the THz pulses were measured using electro-optical sampling. The THz beam size in the focal plane was estimated using the "knife-edge" method, and a calibrated Golay cell (GC-1D, Tydex) was used to measure the THz pulse energy. The electric field strength of THz pulses E was estimated taking into account the measured energy, duration, and size of the spot, keeping in mind that the THz pulse was of Gaussian distribution [23][24][25]. The corresponding magnetic field induction was calculated by the well-known expression: B = E/c, where c is the speed of light.
In the experiments, we have used a double-side polished monocrystalline sample of a NiO (111) crystal of 45 µm thick and 5 mm in diameter. Nickel oxide (NiO) crystallizes in a cubic structure and below the Neel temperature T = 523 • C is an antiferromagnetic [26]. The magnetic field of the THz pulse was applied parallel to the (111) surface of the NiO sample and had direct access to the degrees of freedom of the spin system of the antiferromagnetic. In this case, a Zeeman torque is created on the magnetic dipole associated with each spin at a frequency that can be tuned in resonance with the collective mode of the NiO magnons [27][28][29][30].
The time dependences of the rotation of the probe pulse polarization plane in the NiO sample due to the magneto-optical Faraday effect under action of broadband and narrowband THz pulses with different frequencies are shown on Fig. 4. We can see an increasing amplitude of oscillations and subsequent exponential decay with time constant of the order of 40 ps under the action of either the broadband (Fig. 4(a)) or the narrowband (at a frequency of 1 THz, Fig. 4(b)) THz pulses. In both cases, a quasi-permanent period of 1 ps can be observed, which corresponds to the 1 THz antiferromagnetic resonant mode in NiO. However, the oscillations have a rather sharp front and reach their maximum amplitude about 4 ps after exposure to the broadband THz pulse. In case of the narrowband pulse with a frequency of 1 THz, the oscillations develop more smoothly and reach their maximum amplitude about 8 ps after the THz pulse. Despite the ratio of the magnetic fields for the broadband and narrowband THz pulses is 16, the ratio of amplitude of oscillations is only 2, indicating that more effective excitation is reached with narrowband resonant stimulus. The Faraday signals induced by narrowband THz pulses at frequencies of 0.5 THz and 2 THz (Figs. 4(c) and 4(d)) are 10 times less than the maximum amplitude under the action of the broadband THz pulse, and it is very difficult to find any periodicity in the observed signal.
In [31] it was shown that at low temperature ( 273K) five antiferromagnetic resonant modes could be observed in NiO: three modes at low frequency in the range up to 0.5 THz (0.028; 0.198; 0.42 THz) and two high-frequency modes in the range from 1 to 2 THz (1.14; 1.29 THz). At room temperature (273K), the splitting of high-frequency modes degrades, and the two modes merge into one at a frequency of ∼1.07 THz (mode softening occurs). The mode with a frequency of ∼0.4 THz is weakly dependent on temperature and almost does not change in frequency, unlike the low-frequency pair 0.028 and 0.198 THz, which merges into the mode at a frequency of ∼0.2 THz. Thus, at room temperature, according to [31], we can observe three antiferromagnetic modes out of five in the vicinity of frequencies 0.2, 0.4, and 1 THz.
In addition, the experimental detection of the nonlinear response of the NiO spin system as a weak signal (about 1% of the maximum amplitude) in the spectrum of magnon oscillations at the double frequency of the main antiferromagnetic resonant mode (∼1 THz), when the sample was excited at room temperature by broadband and narrowband THz pulses tuned to the frequency of the resonant mode, was reported in the works [28,29], respectively.
The amplitude spectra obtained using the Fourier transform of time dependences of the magneto-optical signals presented in Fig. 4 are shown in Fig. 5. We can clearly see two magnon modes at frequencies of 0.25 and 1 THz (indicated by arrows) under the action of a broadband THz pulse with a peak amplitude of the magnetic field of 6.5 T (Fig. 5(a)) on the sample, which have been previously observed in [27,28]. In this mode of exposure, we could not resolve the feature associated with higher order nonlinear effects such as a component of the second harmonic of the antiferromagnetic mode with a frequency of ∼1 THz due to the low signal-to-noise ratio [28] despite the high THz field (the last line in Table 1). However, when using a narrowband THz pulse with a frequency of ∼1 THz and a peak magnetic field amplitude of 0.4 T, the second harmonic spectral feature is traced (Fig. 5(b)), as in [29]. The second harmonic signature is visible although the pulse repetition rate of our THz source is 10 4 times lower compared with the work of [29], and the signal-to-noise ratio is 10 2 worse. The obtained result agrees well with the excitation theoretical model of nonlinear spin oscillations in an antiferromagnetic NiO under the action of a picosecond THz pulse with a frequency of 1 THz and an amplitude of the magnetic field of 0.4 T [32]. Figure 5(c) shows two low-frequency modes 0.27 and 0.42 THz in the spectrum of spin oscillations induced by a narrowband THz pulse with a frequency of 0.5 THz (peak amplitude of the magnetic field ∼0.1 T). Note that the antiferromagnetic resonant mode with a frequency of 0.42 THz is observed for the first time in experiments on excitation of spin oscillations under the action of THz pulses at room temperature. Previously, a mode at a frequency of 0.5 THz was observed experimentally only using Brillouin spectroscopy [31] and in the time-domain terahertz spectroscopy [33].
The spectrum of magnon oscillations when a NiO sample is excited by a narrowband THz pulse with a frequency of 2 THz (magnetic field amplitude 0.8 T) is shown in Fig. 5(d). As it can be seen from the figure, no lines in the range from 0.5 to 2.2 THz are detected in the spectrum, the signal is a white noise. This suggests that the effect of a THz pulse tuned at frequencies out from the main antiferromagnetic resonances does not induce excitation of spin subsystem of the antiferromagnetic NiO. Consequently, the interaction of the THz pulse with the NiO spin system has a strictly resonant character.
In addition, we can see two local maxima with frequencies of 0.86 and 1.14 THz, which are symmetrically located relative to the resonant frequency of 1 THz (see Fig. 5(a)). In [28], the presence of local maxima at 0.77 and 1.23 THz was interpreted as the process of mixing the difference and sum frequencies of magnon oscillations in the plane and outside the plane with a frequency of 0.23 and 1 THz. In our experiment, we assume that the appearance of local maxima is not related to the propagation effect (∆f = 0.14 THz not 0.25 THz), but may be due to splitting of the resonant mode of 1 THz in the magnetic field of the THz pulse, by analogy with [30,34].

Conclusion
We present a versatile table-top high-intensity source of THz radiation, enabling the generation of pulses with a broadband and narrowband spectra with a tunable center frequency in the range of 0.1-3 THz. The THz generation based on optical rectification in OH1 organic crystal provides up to 300 µJ in the broadband mode and up to 7 µJ in the narrowband mode with high conversion efficiency. High values of field strength, reaching several tens of MV/cm (for one cycle) and several MV/cm (for several cycles) open new scientific ways for selective and nonlinear excitation of low-energy modes in condensed matters.
An experimental demonstration of the capabilities of this versatile THz source was carried out by excitation of the spin subsystem of a typical NiO antiferromagnetic by broadband and narrowband THz pulses at room temperature. Two modes were recorded at 0.25 and 1 THz under action of a broadband THz pulse. A mode at 0.42 THz was observed for the first time due to selective excitation by narrowband THz pulses tuned close to this resonance. Our observations agree well with theoretical predictions of the antiferromagnetic resonant modes in NiO. It was shown that the interaction of THz pulses with the NiO spin subsystem had a strictly resonant character.

Funding
Ministry of Education and Science of the Russian Federation .