Intense terahertz radiation and their applications

Historically, GaAs has been the popular choice as the substrate for PCAs, due to its suitable electrical and optical properties. GaAs crystals have very high carrier mobility and a band gap of 1.44 eV, which allows it to be pumped above the band gap with Ti:sapphire lasers. However, its relatively low breakdown field (around 10 kV cm⁻¹) when used as the substrate for LAPCA limits the maximum bias field that could be applied, thus also limiting the maximum intensity of the radiated THz pulse. It should be noted that while high (>100 kV cm⁻¹) bias fields have been used in low-temperature GaAs PCAs [24], such high fields are only possible with small (∼10 μm) gap sizes. For LAPCAs with gaps sizes of few mm, carriers would be accelerated to energies high enough to cause damage to the semiconductor substrate. Another limitation of GaAs LAPCAs is its degradation with usage and subsequent failure [25], resulting primarily from increased temperature due to Joule heating.

Recent studies have focused on overcoming these limitations and to increase the intensity of the THz pulses from LAPCAs. One solution involves the use of a wide bandgap semiconductor with suitable thermal as well as electrical properties. For example, diamond [26], ZnO [27] and GaN [28] semiconductor crystals have been tested in the past. However, these crystals have bandgaps larger than 3.1 eV, which in turn require at least the third harmonic of a Ti:sapphire laser to excite the carriers above the bandgap, thus decreasing their attractiveness. ZnSe is another wide bandgap semiconductor crystal that has been intensively studied. Its 2.7 eV band gap allows the ZnSe LAPCAs to be pumped above the bandgap by the second harmonic (400 nm) of a Ti:sapphire laser [29] and below the bandgap via two-photon absorption with an 800 nm laser pulse [29, 30]. One drawback of ZnSe for use in LAPCA is that it has thermal properties similar to GaAs, which can lead to rapid degradation of the performance of the LAPCA with time. Recently, LAPCAs using 6H- and 4H-SiC semiconductor crystals have also been studied [31], taking notice of its superior thermal quality compared with ZnSe crystals. In this work, they have demonstrated that when the LAPCA is excited with the second harmonic of a Ti:sapphire laser, carrier excitation requires two-photon absorption for 4H-SiC crystals, while 6H-SiC crystals require one-photon absorption. This difference is attributed to the slight difference in their bandgaps, which is 3.03 eV for 6H-SiC and 3.26 eV for 4H-SiC. These studies have also shown that the 6H-SiC is a good candidate for the LAPCA substrate, resulting in 2.3 times higher THz yield under optimum conditions compared with ZnSe crystals.

To generate THz pulses with large peak electric fields, simple coplanar stripline LAPCAs (with two electrodes) require large photo-excited surfaces and high-voltage sources that operate in the range of tens of kV, which is difficult to use. To avoid such difficulties, the interdigitated LAPCA is an alternative way to reduce the bias voltage (and thus the requirement for the high-voltage source), while maintaining a large aperture for illumination [32]. Figure 1 shows a schematic diagram of a typical interdigitated LAPCA. In interdigitated LAPCAs, adjacent antennas emit THz radiation with opposite polarity, and thus in the far field, they cancel each other out, resulting in zero or very low THz fields. Therefore, conventional LAPCAs have used methods to cancel out THz emission from every other antenna, such as using a shadow mask to eliminate irradiation of the excitation laser. Interdigitated LAPCAs have many advantages in comparison with simple LAPCAs. They (i) increase the THz efficiency due to the trap field enhancement near the multiple anodes [33], (ii) allow the possibility to apply higher bias fields [34], and (iii) limit Joule heating since the interdigitated structure typically uses a shadow mask that allows the illumination of less than half of the LAPCA [34, 35]. On the other hand, these structures have some limitations. For example, if the gap size is too small (below 100 μm for a GaAs LAPCA), the LAPCA works in the space-charge screening regime, which saturates the radiated field [36, 37]. The application of the shadow mask also limits the maximum efficiency of the LAPCA, since at least half of the total area is shadowed. As a consequence, when one compares the performance of a conventional LAPCA with an interdigitated LAPCA with the same effective area, the same bias field and excited with the same excitation fluence, the conventional LAPCA will radiate THz waves with a larger peak electric field [34]. Despite these limitations, the highest optical-to-THz conversion efficiency obtained with a GaAs interdigitated LAPCA with 5 μm gap size is 2 × 10⁻³ [25].

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Some solutions have been proposed for increasing the performances of the interdigitated LAPCA. For example, Ropagnol et al used a phase mask instead of a shadow mask, to make full use of the total aperture of the interdigitated LAPCA [35]. The phase mask consists of replacing the shadow mask with glass plates positioned on to every other antenna. The binary phase mask results in a time-delayed excitation of the adjacent antennas, which allows subsequent antennas to produce an additive field, thus increasing the THz conversion efficiency. The other benefit of the phase mask is that the timing of THz emission from adjacent antennas could be varied by varying the thickness of the phase mask, thus allowing some simple THz pulse shaping. Another potential solution for increasing the THz conversion efficiency is the use of plasmonic electrodes. Nanoscale plasmonic contact electrodes reduce the average photo-carrier transport path, allowing the collection of a large number of carriers on a sub-picosecond time scale that contribute to increased THz emission [38]. Using this technique increases the radiated THz power by a factor of 50 compared with conventional PCAs. This structure is very promising, and a GaAs interdigitated LAPCA with plasmonic electrodes has demonstrated an exceptionally high efficiency of 1.6% [39]. However, the challenge is to fabricate such plasmonic electrodes over a large area, and to test the generation of intense THz pulses from such structures.

The various techniques described above have been combined together, to demonstrate intense THz generation from LAPCA. In 2013, Ropagnol et al demonstrated the generation of THz pulses with an estimated peak THz field of 143 kV cm⁻¹, from a ZnSe interdigitated LAPCA excited above the bandgap with 400 nm laser pulses at 10 Hz repetition rate [40]. The total surface of the antennas was 5.5 cm², and the gap size of the interdigitated structure was 0.6 mm, which ensures operation in the THz-field-screening regime, so that the radiated THz field is not limited by space-charge-screening. A pulsed high voltage source that provides 20 ns pulses was used for biasing the LAPCA. Different masks were used with this LAPCA: (i) a traditional shadow mask, (ii) 0.65 mm and 1 mm thick binary masks, (iii) a mix of shadow masks and phase masks, obtained by exchanging some shadow plates with phase plates. These different masks have allowed the generation of various THz waveforms, from an asymmetric half-cycle pulse to a symmetric single-cycle pulse. Figure 2 shows the different waveforms generated by the ZnSe interdigitated LAPCA covered by the different masks. The maximum energy of these THz pulses was 3.6 μJ when the antenna was covered with a binary mask and biased with a field of 47 kV cm⁻¹.

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Following this approach, Ropagnol et al further increased the surface of the ZnSe interdigitated LAPCA up to 12.2 cm². This source generated quasi-single cycle THz pulses with energies of 12.5 ± 0.3 μJ when the LAPCA was covered with a phase mask, and half-cycle THz pulses with an energy of 8.3 ± 0.2 μJ when the LAPCA was covered with a shadow mask. Figure 3(a) shows the scaling of the THz energy and (b) the optical-to-THz conversion efficiency as a function of the optical energy, when the LAPCA is covered with the phase and the shadow mask. At low optical energy, the THz energy follows a sub-linear relationship and then saturates when the optical energy is higher than 15 mJ. Maximum optical-to-THz conversion efficiency of 2 × 10⁻³ with the phase mask and 1.1 × 10⁻³ with the shadow mask is obtained when the LAPCA is excited with 2.5 mJ, 400 nm lasers. The calculated THz field was estimated to be 331 ± 5 kV cm⁻¹. Considering that the median frequency of these THz pulses was 0.28 THz, we estimated the ponderomotive energy of these pulses to be 15 ± 1 eV, which is higher of what can be obtained with a 1 MV cm⁻¹ field at 1 THz [41].

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One 'unsung' characteristic of intense THz sources via LAPCA is its relatively good shot-to-shot stability. There are several reasons behind this. First, THz generation from PCA is basically a linear process when pumped above the bandgap, with one laser photon exciting one carrier in the semiconductor substrate. Second, the LAPCA can be operated in the saturation regime, where THz yield is less affected by changes in the laser intensity. Therefore, instability in the driving laser has less effect on the THz output from LAPCAs, compared with THz generation techniques that make use of nonlinear optical effects. As such, it has been demonstrated that, although time consuming, clean waveforms with low noise could be obtained with intense THz sources via LAPCA, even with relatively low (10 Hz) repetition rates.

The use of large-aperture crystals for intense THz generation is an approach that can reduce saturation effects (due to effects such as two-photon absorption) and minimize damage to the crystal surface induced by the high laser intensity. In the case of 〈110〉 ZnTe crystal, the azimuthal angle dependence of THz radiation energy is essential as well. As shown in figure 4, θ is the angle between the y'-direction [001] of the lab reference coordinates and the polarization vector of the incident optical field.

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The emitted THz field ${E}_{{\rm{THz}}}$ will be projected on to the reference plane x'y', where x' is the [-110] direction. According to the formula derived for the OR process [47]:

$$\begin{eqnarray}&&\left(\begin{array}{c}{E}_{{\rm{THz}}}^{x}\\ {E}_{{\rm{THz}}}^{y}\end{array}\right)\propto \left(\begin{array}{c}\sin (2\theta )\\ {\sin }^{2}(\theta )\end{array}\right).\end{eqnarray} \tag{ 10 }$$

From equation (10), we see that the THz energy has an angular dependence with a maximum value at $\theta =54.7^\circ ,$ corresponding to the polarization direction of the emitted THz beam at $54.7^\circ$ [47].

We show in figure 5 a typical experimental setup for large aperture ZnTe THz generation, which was built at the Canadian Advanced Laser Light Source (ALLS) facility, on a beam line providing 800 nm, 40 fs laser pulses with energies as high as 70 mJ per pulse (after the vacuum compressor) at a repetition rate of 100 Hz. The detailed description of the experimental setup is given in [49]. The THz pulse profile is detected by free-space EO sampling using a detector ZnTe crystal, and the delay between the probe pulse and the THz pulse is scanned by using an optical delay stage. The emitted THz energy was measured by a calibrated pyroelectric detector (Coherent-Molectron J4-05), and the image of the THz beam at the focus was observed using a pyroelectric IR camera (ElectroPhysics), so that the THz electric field can be estimated. The azimuthal angle dependence was also studied to verify that the intense THz radiation is generated via OR. Up to 1.5 μJ of THz energy and about 230 kV cm⁻¹ peak THz electric field at focus was measured with this setup, with the THz spectrum covering the range from 0.1 to 3 THz, using ZnTe pumped by a 48 mJ pump beam with a conversion efficiency of 3.1 × 10⁻⁵.

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Despite the high THz energy obtained, the conversion efficiency of the ZnTe emitter was still limited by free-carrier-induced absorption. On the other hand, with the apparent advantage of its high EO coefficient and high damage threshold, OR from titled-pulse-front lithium niobate (LiNbO₃) source is now one of the most promising approach for intense few-cycle THz generation, which has been very well developed experimentally [52–54] and theoretically [55–57]. Optical-to-THz conversion efficiency of about 0.35% at room temperature has been reported with this technique, using 800 nm central wavelength pump lasers [54]. By cooling the LiNbO₃ crystal down to cryogenic temperatures, energy conversion efficiencies up to 3.8% was achieved with 0.68 ps pump pulses centered at 1.03 μm wavelength [42].

Equation (11) is the phase matching condition in this crystal, which is fulfilled by introducing a tilt angle γ in the pulse front with respect to the phase front, as shown in figure 6(a)

$$\begin{eqnarray}&&{\upsilon }_{{\rm{THz}}}^{{\rm{ph}}}={\upsilon }_{{\rm{pump}}}^{{\rm{gr}}}\,\cos (\gamma ).\end{eqnarray} \tag{ 11 }$$

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The pulse front of the optical pulse is titled typically using a diffraction grating, and a telescope is then used to image the titled-pulse at the crystal position with an appropriate demagnification ratio M. Figure 6(b) shows a schematic diagram of the setup for ultrafast THz pulse generation using a titled-pulse-front configuration, employing a single lens and a diffraction grating. Moreover, the crystal is cut at $\gamma$ to fulfill the phase matching condition inside the crystal. In this configuration, the angle $\gamma$ is given by [47]:

$$\begin{eqnarray}&&\tan \,\gamma =\displaystyle \frac{m\,N\,{\lambda }_{{\rm{pump}}}M}{{n}_{{\rm{pump}}}\,\cos \,\beta }.\end{eqnarray} \tag{ 12 }$$

Here, m is the diffraction order, N is the grating groove number density, ${n}_{{\rm{pump}}}$ is the refractive index of the LiNbO₃ crystal at the pump laser wavelength and $\beta$ is the diffracted angle of the incident beam on the grating.

Typical experimental setups of the LiNbO₃ THz source based on the titled-pulse-front technique use an amplified Ti:sapphire laser, which delivers several mJ, femtosecond pulses at kHz repetition rates [47]. It is worth mentioning that the LiNbO₃ crystal was 1 mol% Mg doped, so as to avoid the photorefractive effect in the crystal and to reduce THz absorption [58]. Typical tilted-pulse-front LiNbO₃ THz sources provide peak electric fields of >200 kV cm⁻¹ in the 0.1–2.5 THz spectral range, with conversion efficiencies of ∼10⁻³, which is ∼30 times higher than large aperture ZnTe sources.

Several additional methods [42, 53] have been proposed to improve the OR efficiency in LiNbO₃, such as (i) cooling of the LiNbO₃ crystal; (ii) optimizing the Fourier-limited (FL) pump pulse duration; (iii) reducing the imaging errors by using contact-grating setup. High conversion efficiency is the result of sufficiently long effective THz generation length, which is determined by various loss mechanisms and dispersion. Several techniques have been implemented to the tilted-pulse-front THz source to reduce such unfavorable effects, thus increasing THz output. For example, Mg-doping of the LiNbO₃ crystal reduces the photorefractive effect (resulting in lower loss of the pump laser), and cooling the LiNbO₃ crystal decreases phonon absorption of THz waves, thus significantly improving the conversion efficiency [42]. Another technique that has been implemented is the optimization of the pulse duration of the driving laser. In the past, relatively short (<100 fs) Ti:sapphire lasers had been used to pump the LiNbO₃ THz source. However, studies have shown that a longer, optimized Fourier transform limited pulse could maximize the effective THz generation length, giving rise to higher conversion efficiencies [42, 54, 56]. Another factor that needs to be considered is the sensitivity of the conversion efficiency to the pump imaging errors, which could cause asymmetric intensity profiles as well as huge divergence of the THz beam. Several new configurations have been proposed to overcome these problems, such as using contact-grating setups [56] to eliminate imaging errors and obtain a larger pump area. More recently, optical pump pulses with elliptical beam profiles have also been suggested, so that high conversion efficiency can be preserved in the case of high optical pump energies [57].

Even after incorporating such methods, there is an ultimate limit at which the LiNbO₃ crystal could be pumped, which turns out to be much lower than the damage threshold of the crystal or the grating. As the optical pump pulse propagates within the crystal and generates THz photons, a frequency redshift of the optical pump occurs, especially in cases of high conversion efficiency. Such cascaded frequency redshift can further result in a large spectral broadening of the pump beam. Even though cascading effect is responsible for conversion efficiencies that exceed the Manley–Rowe limit, the induced spectral broadening combined with the influence of self-phase modulation effect will prevent further THz generation due to phase mismatching in the presence of group velocity dispersion from material dispersion and from angular dispersion [56].

We show in figure 7 a typical experimental setup used to study these effects and improve the THz radiation energy. In this work, a high-energy 100 Hz repetition rate Ti:sapphire laser was used [54]. Using such a setup, record energy conversion efficiency up to 0.36% has been demonstrated, which saturates for >240 fs pulse durations. A combination of short-pass (f1) (Model FF01-842/SP-50, Semrock) and long-pass filters (f2) (Model BLP01-785R-50, Semrock) was placed prior to the optical compressor 1, to adjust the Fourier transform limited pulse duration. The cutoff wavelength of both filters can be tuned by changing the angle of incident laser. Optical compressor 2 was used to obtain a probe pulse (45 fs pulse width and <0.1 μJ) for EO sampling detection. The emitted THz energy was measured at the EO sampling position (D1) by a pyroelectric sensor. The measured THz energy and the corresponding energy conversion efficiency as a function of the Fourier transform limited pulse duration are shown in figure 8, while the peak intensity and the central wavelength of the pump beam were kept constant during the measurement.

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To understand the increase in the THz conversion efficiency as a function of the Fourier transform limited pulse duration due to the cascading effect, a setup as shown in figure 9(a) was built to reveal this asymmetric redshift. Figure 9(b) shows the measured normalized spectra of the pump laser, as a function of the translation detection position x. Results show that the redshift varies with the propagation distance of the pump beam within the LiNbO₃ crystal, suggesting that the position and the area of the pump beam on the incident surface of the LiNbO₃ crystal should also be adjusted to optimize efficiency. However, despite this high THz energy and conversion efficiency, the maximum peak electric field measured in this experiment is 720 kV cm⁻¹, which is well below the theoretical limit. This is because the cascaded redshift effect induces spatially asymmetric extreme broadening and segmentation of the optical pulse [54, 59]. It has also been experimentally identified that free-carrier absorption of THz radiation due to multi-photon absorption of the 800 nm radiation would also limit the scaling of optical-to-THz conversion efficiencies. Therefore, further theoretical and experimental investigations at high pump intensities are essential to further increase THz output from the titled-pulse-front LiNbO₃ THz source.

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In addition to its use with LiNbO₃ crystal, the tilted-pulse-front technique can be also applied to other materials, which is significant for exploring new, highly efficient nonlinear crystals. For example, THz generation in room temperature gallium arsenide (GaAs) crystal using pump laser at a wavelength of 1.8 μm has been reported with the tilted-pulse-front technique [60].

As we have seen above, high THz energies with THz electric fields exceeding 1 MV cm⁻¹ have been demonstrated from title-pulse-front LiNbO₃ sources. However, the spectrum of the LiNbO₃ source is typically confined around 1 THz, due to absorption at high frequencies [2] and very high THz electric field is always challenging to reach. Several novel nonlinear organic crystals [43, 61–63] have been explored for high field THz generation. These materials provide low THz absorption and much higher second-order optical susceptibility than room temperature LiNbO₃. Typically, the phase matching condition of such organic materials can be fulfilled in a simple collinear geometry with pump wavelengths between 1.35 and 1.5 μm. In addition, owing to the naturally collimated emitted THz waves free of aberrations [64], tight focusing becomes much easier and thus extremely high electric field strengths can be achieved. The experimental setup of THz generation with a 4-N-methylstilbazolium tosylate (DAST) crystal is shown in figure 10(a), in which the THz waveform is characterized using the EO sampling method with a GaP crystal. The disadvantage of these organic crystals is the low laser damage threshold in comparison with mostly used inorganic crystals.

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The ionic organic crystal DAST was developed in the '90s and then attracted much attention for its large second order nonlinearity. The optimal pump wavelength that is required for phase matching of OR in DAST for THz generation is at 1500 nm. Therefore, for intense THz generation, an optical parametric amplifier (OPA) pumped by a Ti:sapphire laser is usually used to generate pump beams at this wavelength. High-quality THz beams with maximum electric field of 6.3 MV cm⁻¹ has been demonstrated, with a conversion efficiency of 2.1% at room temperature [61]. However, the THz spectrum is inevitably distorted around 1.1 THz, corresponding to the absorption resonance from transverse optical phonon modes in DAST. The single-cycle THz pulse shape as well as its spectrum is shown in figures 10(b) and (c), where absorption at 1.1 THz could be clearly seen [61].

To solve this phonon absorption problem at 1.1 THz, one method is to cool the crystal, to suppress the vibration modes and reduce distortion. Another way is by making an appropriate modification of the crystal or by exploring other similar highly nonlinear organic crystals, such as OH1. The organic nonlinear crystal DSTMS (4-N, N-dimenthylamino-4'-N'-methyl-stilbazolium2, 4, 6-trimethylbenzenesulfonate) has very large second order nonlinear susceptibility and best phase matching condition for OR at a wavelength of 1500 nm, similar to DAST. Furthermore, DSTMS has several unique advantages, including significant reduction of phonon absorption at 1.1 THz, due to minor changes of substituents of the counter-anion to DAST. DSTMS also has favorable crystal growth characteristics [65] to fabricate large-area bulk crystals. Vicario et al [66] have recently proposed a large-size partitioned DSTMS crystal with negligible influence of the discontinuity in the whole crystal surface. This new approach opens up the avenue for further scaling up the THz field strength and energy radiated from such nonlinear organic crystals. Another promising organic crystal for THz generation is 2-[3-(4-hydroxystyryl)-5.5-dimethylcyclohex- 2-enylidene] malononitrile OH1. The velocity-matching condition for pump wavelength is in the range of 1200–1460 nm, resulting in high efficiency THz generation from 0.3 to 3 THz.

In general, Ti:sapphire lasers with central wavelength at 800 nm is not suitable for realizing phase matching condition for these organic crystals. However, by utilizing other nonlinear susceptibility coefficients, THz generation from DAST and DSTMS pumped at 800 nm wavelength is feasible, but with rather low energy conversion efficiency [67]. An OPA system is typically used to generate pump wavelengths between 1350 and 1500 nm, but the generated pump beam is always affected by drawbacks of using an OPA, such as instability and beam profiles irregularities [68]. To overcome the non-uniformity of the pump beam and the irregularity of a typical thin organic crystal, Shalaby et al have proposed an optimization method based on pump wavefront-divergence control combined with an improved imaging system to significantly enhance the generated THz beam quality [69]. Furthermore, instead of using OPA, Vicario et al have demonstrated a new approach by utilizing the direct output of a femtosecond Cr:forsterite laser at central wavelength of 1250 nm [43, 68] and peak fields of more than 42 MV cm⁻¹ and 14 T were reached using DSTMS crystal pumped by this Cr:forsterite laser.

Yoshii et al have proposed a mechanism for THz generation in which short pulses of GHz to THz frequencies are generated by the interaction between a laser wakefield and a static magnetic field, through a mechanism named Cherenkov wake radiation [104, 120]. Normally, electrostatic wakefield oscillation does not convert to electromagnetic radiation in cold plasma. However, the situation is completely different in the presence of transverse magnetic field. The wakefield then has both electrostatic $({\boldsymbol{k}}\cdot {\boldsymbol{E}}\,\ne 0)$ and electromagnetic $({\boldsymbol{k}}\times {\boldsymbol{E}}\,\ne 0)$ components in the magnetized plasma. Furthermore, the magnetized wakefield has nonzero group velocity. This enables the wake to propagate through the plasma and couples radiation into the vacuum at the plasma vacuum boundary. This phenomenon is called Cherenkov wake radiation, and emits electromagnetic pulses with frequency close to the plasma frequency, whose radiation amplitude is (ω_c/ω_p) times the amplitude of the wakefield amplitude. GW level THz power generation has been predicted by using the wakefield excited using currently available laser systems and the appropriate transverse magnetic field. Yugami et al have experimentally observed this electromagnetic emission in the THz and GHz frequency domain, in a low density magnetized plasma [105]. However, the observed conversion efficiency was small, due to not satisfying experimental conditions favorable for THz generation.

It has been found from numerical simulations by Sheng and his group that intense radiation around the plasma frequency can be produced from the wakefield in inhomogeneous plasma, although the mechanism involved yet to be solved. One possible explanation could be linear mode conversion [116]. It is well known that an electromagnetic wave can convert into an electrostatic wave through linear mode conversion, which leads to the resonance absorption of light in inhomogeneous plasmas [98, 99]. Similarly, linear mode conversion from the laser wakefield to electromagnetic pulses can occur in inhomogeneous plasma under certain conditions. The energy conversion efficiency from the driving laser pulse to the THz pulses scales as (ω/ω₀)³, where ω and ω₀ are the angular frequency of the generated THz pulse and driving laser. The THz pulse energy conversion efficiency also depends on the laser intensity and the plasma density scale length [107, 108, 116].

Singh et al have proposed a different mechanism for intense THz pulse generation. In this scheme, the high-intensity driving laser propagates perpendicular to the background magnetic field. This laser wave decays in to a large amplitude upper hybrid wave and a low frequency THz wave via nonlinear parametric decay process [112]. Various laser and plasma parameters were optimized and an efficiency of about 1.4 × 10⁻² has been predicted.

Intense THz pulses can also be generated from relativistic electron beams, either by bending the electron beams in an external magnetic field or by sending the e-beam through medium boundaries with discontinuities in the dielectric constant. This technique has been successfully used in electron accelerators to generate high average power THz pulses [121, 122]. High-intensity laser–plasma interaction also produces relativistic electrons with more than nC charge per pulse, and is suitable for intense THz pulse generation. An experimental attempt by Leemans et al has generated THz pulses with energies of 3–5 nJ pulse⁻¹ within a collection angle of 30 mrad and in the spectral range of 0.3–3 THz, which scales up with electron charge [106, 123]. 1.5 nC electron bunches with relativistic energies are produced by the interaction of the high-intensity laser with helium gas jet inside a vacuum chamber and THz pulses are generated when these electrons pass through a 5 μm thick metal coated nitrocellulose foil, which is placed 30 cm from the gas jet.

High-intensity THz pulse generation via high-intensity laser-solid interaction has been demonstrated experimentally by Li et al [109, 112], using maximum peak laser intensities of ∼5 × 10¹⁸ W cm⁻². The THz pulse energy peaks at an incident angle of 67°, and THz generation is explained by transient surface current produced during laser plasma interaction [109, 112]. It was also found that the THz pulse energy scales up with incident laser intensity and strongly depends on the preplasma scale length [114] or laser contrast ratio and follow a power scaling law E_THz ∼ (Iλ²)^1.0. Figure 12 [112] shows that the THz pulse energy scales up with laser intensity. THz pulses are detected by a pyroelectric detector and for 67° incident angle. The solid angle for THz collection was 0.07 sr.

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Electron currents are generated during high intensity laser plasma interaction via various absorption mechanisms that are responsible for THz pulse generation. Hence it is expected that THz pulse generation will be closely related to absorption mechanism. THz pulses generated by this mechanism are expected to be ultrabroadband, ranging GHz to infrared. The generated THz pulses are also polarized in the plane of incident laser irrespective of the polarization of the incident laser.

Sagisaka et al and Gopal et al have reported intense THz pulse generation via the interaction of high-intensity laser with foil targets [110, 113, 124]. Sagisaka et al proposed the antenna mechanism for THz emission, whereas Gopal et al mentioned that a fast decaying current at the rear side of the foil is responsible for the THz generation. In the antenna mechanism for THz pulse generation, THz pulses are generated by electrons moving along the target surface. This electron current could be either oscillatory or highly energetic, so that they can escape from the target. Figure 13 [124] explains the antenna mechanism. The laser–plasma interaction generates a time dependent surface current. This current has a lifetime equal to the ratio of half of the target size to the velocity of electrons, which generates THz pulses. The polarization of the generated THz pulses is similar to that of the TM mode. In the laser incidence plane, the TM mode is seen as a p-polarized wave. The total THz pulse energy can be estimated by the following equation

$$\begin{eqnarray}&&{E}_{{\rm{THz}}}=\displaystyle \frac{{B}^{2}}{4\pi }\displaystyle \frac{4\pi {r}^{3}}{3}.\end{eqnarray} \tag{ 18 }$$

Here, B is the magnetic field generated by the laser–plasma interaction and r is the electron displacement length. According to the antenna mechanism, the spectrum of the THz emission is determined by the target size. However, no clear experimental evidence was found to show that the target size has any impact on the THz spectrum [109].

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In summary, the various techniques of intense THz generation have been accelerated by advances in Ti:sapphire laser technology. Table 2 summarizes the various techniques reviewed above and provides a comparison among them in terms of the merits and demerits of each technique. As an intense short laser pulse is a common requirement, we included in our table only additional requirements that differ among the various techniques.

LAPCAs generate asymmetric quasi-half-cycle THz pulses at low THz frequencies. These pulses can result in large ponderomotive potential, due to their relative low peak electric field. LAPCAs are the only THz source that covers efficiently THz frequencies below 0.5 THz. As a consequence, this source may be used for example to induce strong resonance in materials that have resonances at low THz frequencies. However, its strongest applications should be in the non-resonant control of matter where electron acceleration has strong effects. Indeed, the large ponderomotive potential of the THz pulses from LAPCA could accelerate electrons to kinetic energies that may induce various effects, such as bleaching, ionizations, field emission and high harmonic generations. In the future, the main challenge would be to increase the peak electric field of LAPCA THz sources above 1 MV cm⁻¹, by adding for example plasmonic structures to the large interdigitated structure, and by overcoming the thermal problems of LAPCAs to allow the use of amplified Ti:sapphire laser with higher repetition rate.

Intense THz generation by OR benefits from its simple experimental configuration, as well as its high conversion efficiency. As a result, this technique has been widely used in THz spectroscopy and imaging systems with high repetition rate. THz generation from LiNbO₃ and organic crystals is still far from their limits, and many efforts have been made to further increase the THz field and energy. Meanwhile, it is of great interest to develop other potential nonlinear mediums with superior properties for THz generation.

Air-plasma generation for intense THz pulses based on two-color laser field has been studied and developed since 2000, with some recent strong improvement using the laser filamentation method. The air-plasma generation technique was developed on one hand for potential imaging applications, like in security imaging, where the use of THz waves was impractical, due to strong attenuation by water vapor after propagation through air for a long distance. On the other hand, the nonlinear THz spectroscopy profits significantly from this technique, covering a wide THz band compared with other THz generation techniques. A study of carrier dynamics in graphene has been done by air plasma generation [125], which offer an interesting field of application for condense matter physics regarding the large THz band covered.

Intense THz pulses generated by high-intensity femtosecond laser–plasma interaction are still in its early stage of research, and knowledge on the characteristics of these pulses is limited. It has been predicted in numerical simulations and also seen in the experiments that they produce high THz pulse energy and electric field. There is also the possibility to further increase the THz yield, which could open many new areas in THz science. This THz generation technique is new compared to other THz generation techniques. Since high-power, low repetition rate lasers are used, single-shot THz detection techniques should be used for the complete characterization of these THz pulses.

PCA described in section 2.1 was also the first technique developed for coherent terahertz wave detection [126]. The mechanism of THz detection by PCAs is similar to THz generation from PCAs, but is an inverse process without the bias voltage. In PCA detectors, a femtosecond probe laser pulse illuminates the gap of a PCA and excites carriers in to the conduction band. However, PCA detectors do not have any external bias field. Instead, the THz field to be measured accelerates the carriers, leading to a transient photocurrent inside the PCA detector. The measured photocurrent I(t) depends not only on the incident THz electric field, but also on the transient surface conductivity σ_s(t) [127]:

$$\begin{eqnarray}&&I(t)\propto \,\displaystyle {\int }_{-\infty }^{t}{\sigma }_{s}(t-t^{\prime} ){E}_{{\rm{THz}}}(t^{\prime} ){\rm{d}}t^{\prime} .\end{eqnarray} \tag{ 19 }$$

The time dependent conductivity implies that the current cannot flow instantaneously in response to the THz field. The photocurrent is a convolution of the THz field with the conductivity. As a consequence, the characteristics of the laser pulse and the semiconductor substrate will affect the detected THz waveform. In order to limit the effects of conductivity, materials with short carrier lifetime (such as low-temperature grown GaAs (LT-GaAs) and doped GaAs) are usually selected [128–130]. LT-GaAs has a carrier lifetime that is shorter than 0.5 ps. For increasing the maximum detected bandwidth, one should also combine a substrate with short carrier lifetime and an optical pulse with short duration. For example, the detection of THz pulses with frequencies up to 30 THz from a doped GaAs PCA has been reported, by using a 15 fs laser pulse for the probe [131]. More recently, THz pulses with bandwidths extending up to 100 THz have been demonstrated with an LT-GaAs PCA and a 10 fs optical probe [132].

Another factor that influences the bandwidth of the detected THz pulse is the geometry of the PCA. Currently, there are four kinds of PCAs that are mainly used for THz detection: strip-line, bowtie, butterfly and logarithmic antennas. These PCAs each have different characteristics. For example, the butterfly PCA will be very efficient for detecting low THz frequencies, while a strip-line PCA will be very sensitive for detecting high THz frequencies. Another factor that will greatly influence the detected signal is the dimension of the PCA. For example, a smaller gap size will allow the detection of higher frequencies and larger amplitude signals, while longer electrodes will increase the amplitude of the detected signal but will be more sensitive to low frequencies [133].

Free-space EO sampling technique utilizes the linear Pockels effect in an EO crystal together with a femtosecond optical gating pulse, to probe the electric field of the THz pulse [127, 134, 135]. The Pockels effect induces birefringence in the nonlinear crystal, which is directly proportional to the THz electric field. By measuring the birefringence, or the change in the polarization state of the probe beam, the THz electric field strength can then be determined. A typical schematic diagram of the balanced measurement using this technique is shown in figure 14.

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Without the THz pulse, a linearly polarized optical probe pulse traverses the EO crystal without experiencing birefringence, which then passes through a quarter-wave plate and becomes circularly polarized. A polarization-state analyzer, such as a Wollaston prism, is then used to separate the orthogonal polarization components, and each is sent to one of the photodiodes of a balanced detector. The detector connected to a lock-in amplifier, measures the difference signal ${I}_{y}-\,{I}_{x}$ from the two photodiodes, giving zero reading without the THz pulse. On the other hand, when the probe pulse and the THz pulse co-propagate through the EO crystal in time, the THz field induced birefringence rotates the polarization of the probe pulse, making it elliptical, thus introducing a signal imbalance between ${I}_{y}$ and ${I}_{x}.$ This difference between the two signals can directly give the electric field amplitude information of the THz pulse [127] by using the following equations:

$$\begin{eqnarray}&&{I}_{{\rm{s}}}={I}_{y}-{I}_{x}={I}_{0}{\rm{\Delta }}\phi \propto {E}_{{\rm{THz}}}.\end{eqnarray} \tag{ 20 }$$

Here

$$\begin{eqnarray}&&{I}_{x}=\displaystyle \frac{{I}_{0}}{2}(1-\,\sin \,{\rm{\Delta }}\phi )\approx \displaystyle \frac{{I}_{0}}{2}(1-{\rm{\Delta }}\phi ),\end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray}&&{I}_{x}=\displaystyle \frac{{I}_{o}}{2}(1+\,\sin \,{\rm{\Delta }}\phi )\approx \displaystyle \frac{{I}_{0}}{2}(1+{\rm{\Delta }}\phi ).\end{eqnarray} \tag{ 22 }$$

${I}_{0}$ is the total intensity of the probe beam and ${\rm{\Delta }}\phi$ is phase retardation between the two polarization components. Note that in these equations, an approximation of ${\rm{\Delta }}\phi \ll 1$ is used, and thus a linear relationship between the THz electric field and the signal is seen in equation (20). Therefore, the dynamic range (DR) of the EO sampling technique is limited. For the detection of intense THz radiation, to assure linearity of the measurement, several high-resistivity float-zone silicon plates are often used to reduce the THz field to an appropriate value. However, dispersion and wavelength-dependant absorption of such plates would modify the THz waveform, thus complicating the correct measurement of intense THz waves using conventional EO sampling [136].

The entire THz waveform can be mapped in time by employing an optical delay stage to scan the time delay between the femtosecond probe pulse and the THz pulse. The quasi-DC THz electric field approximation used above is reasonable for femtosecond optical probe pulses. However, for an ultra-short THz pulse with broad spectrum, temporal walk-off due to velocity mismatch between the probe pulse and the THz pulse should be considered carefully. THz detection sensitivity will increase as the crystal thickness increases, but the corresponding detection bandwidth will decrease because of this walk-off. For this reason, the thickness of the EO crystal should be chosen properly. Thinner crystals are used for broadband detection, such that velocity matching can be fulfilled. In addition, phonon absorption is also a crucial factor that limits the detection bandwidth. For example, phonon absorption at 1.6 and 3.7 THz and the transverse optical phonon at 5.31 THz in commonly used ZnTe crystal typically limit its use to low THz frequency detection [137]. As such, other EO crystal alternatives like GaP and GaSe are generally better choices for broadband detections. Thus, the selection of the detection crystal and optimizing the detection scheme requires a good understanding of the THz optical properties of the crystal material, such as its linear dispersion and absorption [138] in the THz frequency range.

Advances in tabletop, intense, few-cycle broadband THz sources have pushed the achievable peak THz electric fields from the sub-MV cm⁻¹ level to well into the several MV cm⁻¹ regimes [40, 49, 53, 139]. Such intense THz fields are of great interest, since they enable studies of fascinating nonlinear phenomena in materials within the THz frequency range, at picosecond and even sub-picosecond timescales. High-intensity THz sources and their detection methods are the main tools that are driving such technology to boom. As we have seen in the previous sections, coherent detection of such intense THz electric fields is currently performed by various methods [134, 140]. However, these conventional techniques for THz detection have several challenges when trying to detect intense THz fields.

For example, with the EO sampling technique, if the THz electric field is intense enough, a phase difference of more than π/2 will be introduced to the optical probe beam, which leads to reversal in the intensity modulation of the probe pulse. This in turn leads to ambiguities in the measured THz field, hence posing a limitation in detecting intense THz electric fields using conventional EO sampling technique [141]. This limitation is known as over-rotation. Over-rotation poses several other restrictions in THz detection via the EO sampling technique. For example, higher spectral resolution in THz-TDS requires longer temporal scans, which could be achieved by using thicker EO detection crystals. Moreover, using thicker EO crystals result in measurements with higher signal-to-noise ratio (SNR), due to the longer interaction length in the crystal. However, using a thicker crystal increases the chance for over-rotation, since the birefringence introduced in the detection crystal is proportional to both the THz electric field and the thickness of the crystal. The increased availability of robust high-intensity THz sources and the urgent need to characterize their peak electric fields and waveforms has become a challenge for conventional EO sampling techniques. This is because high power THz measurements require high DR detection techniques, where DR is defined as the ratio of the maximum measurable signal to the standard deviation of the noise signal. Conventional EO sampling has achieved DR of only a few hundred.

PCA detectors are not commonly used for detecting intense THz pulses, despite their quality. One reason for this is that the PCA detector is very sensitive to the ambient electro-magnetic noise, which could be relatively high when using high-energy amplified laser systems. However, the major disadvantage of using PCA for the detection of intense THz pulse is the possible presence of nonlinear effects in the semiconductor substrate induced by the intense THz field [142], thus leading to incorrect interpretation of the detected signal.

In this section, we will review two methods of coherent THz detection that are especially well adapted to intense THz sources, the air-based THz detection technique, and the spectral-domain interferometry (SDI) technique. We will also review single-shot THz detection techniques, which are useful when the repetition rate of the THz source is limited.

Compared with THz generation in air, this process is well described by a four-wave mixing model with the generation of a second harmonic field, which depends on the THz pulse shape [143, 144]. The interaction of the fundamental laser field ω and the THz pulse can be described by the following equation:

$$\begin{eqnarray}&&{E}_{2\omega }\propto {\chi }_{{\rm{air}}}^{(3)}{E}_{\omega }{E}_{\omega }{E}_{{\rm{THz}}}.\end{eqnarray} \tag{ 23 }$$

Here, ${E}_{2\omega },$ ${E}_{\omega }$ and ${E}_{{\rm{THz}}}$ are the electric field amplitude of the second harmonic 2ω, the fundamental ω and the THz waves, respectively. The term ${\chi }_{{\rm{air}}}^{(3)}$ is the third-order susceptibility of air. From this equation, one can see that the second harmonic electric field is proportional to the THz electric field. However, in practice we measure the intensity or power of the second harmonic, but not its electric field. From equation (23), we see that the intensity of the second harmonic ${I}_{2\omega }$ is proportional to the intensity of the THz wave ${I}_{{\rm{THz}}}.$ The consequence is that the measured signal would be proportional to the square of the THz field, and thus phase information cannot be extracted, resulting in an incoherent measurement. To realize coherent measurements, the authors have devised a clever method, to mix a local oscillator at the 2ω frequency ${E}_{2\omega }^{{\rm{LO}}}.$ This local oscillator interferes with the second harmonic induced by the THz field, as expressed in the following equation:

$$\begin{eqnarray}&&{I}_{2\omega }\propto {|{E}_{2\omega }|}^{2}={({E}_{2\omega }^{{\rm{THz}}}+{E}_{2\omega }^{{\rm{LO}}})}^{2}\\ &&\quad ={E}_{2\omega }^{{{\rm{THz}}}^{2}}+2{E}_{2\omega }^{{\rm{THz}}}{E}_{2\omega }^{{\rm{LO}}}+{E}_{2\omega }^{{{\rm{LO}}}^{2}}.\end{eqnarray} \tag{ 24 }$$

Here, ${E}_{2\omega }^{{\rm{LO}}}$ is the second harmonic local oscillator, which is provided by the second-harmonic component of the white light in the laser-induced air plasma. The second cross term in this equation is the key term for coherent THz detection. The local oscillator ${E}_{2\omega }^{{\rm{LO}}}$ depends on the probe beam intensity. In the case of low probe energy, the first term of this equation is dominant, leading to ${I}_{2\omega }\propto {I}_{{\rm{THz}}},$ which results in incoherent detection. With probe intensity higher than the air ionization threshold, the local oscillator becomes sufficiently strong and the second term of equation (24) becomes dominant, and thus ${I}_{2\omega }\propto {E}_{{\rm{THz}}},$ which leads to coherent detection. As the probe intensity has to be high enough to break down the air for coherent detection, this technique was first named THz air breakdown coherent detection (which is also THz-ABCD in short) [143].

Later, Karpowicz et al [144] applied an AC bias voltage at the focus point of the collinear THz and optical beams, as shown figure 11 (see section 2.3). The AC bias voltage was synchronized with the laser repetition rate. The bias voltage breaks the symmetry, providing an additional source of second harmonic, which could be used as the local oscillator ${E}_{2\omega }^{{\rm{LO}}}.$ The THz field induced second harmonic (TFISH) ${E}_{2\omega }^{{\rm{THz}}}$ and the AC bias second harmonic ${E}_{2\omega }^{{\rm{LO}}}$ can be written as

$$\begin{eqnarray}&&{E}_{2\omega }^{{\rm{THz}}}\propto {\chi }_{{\rm{air}}}^{(3)}{I}_{\omega }{E}_{{\rm{THz}}},\\ &&{E}_{2\omega }^{{\rm{LO}}}\propto {\chi }_{{\rm{air}}}^{(3)}{I}_{\omega }{E}_{{\rm{bias}}}.\end{eqnarray} \tag{ 25 }$$

Here, ${E}_{{\rm{bias}}}$ is the bias electric field. Then equation (24) becomes:

$$\begin{eqnarray}&&{I}_{2\omega }\propto {({\chi }_{{\rm{air}}}^{(3)}{I}_{\omega })}^{2}({E}_{{\rm{THz}}}^{2}+2{E}_{{\rm{THz}}}{E}_{{\rm{bias}}}+{E}_{{\rm{bias}}}^{2}).\end{eqnarray} \tag{ 26 }$$

In practice, the first and third terms of equation (26) can be eliminated when the AC bias voltage is synchronized with the lock-in amplifier. Only the cross term is measured, thus resulting in ${I}_{2\omega }\,\propto \,{E}_{{\rm{THz}}}{E}_{{\rm{bias}}}$ and allowing coherent measurements. This method has the great advantage to reduce the probe power needed to generate the second harmonic and detect the THz pulse. Furthermore, the SNR has been improved by one-order of magnitude [144] compared to the method without AC biasing [143], and the DR is larger as well. Finally, another important feature of THz-ABCD is that the THz bandwidth is only limited by the optical pulse duration. Ho et al [145] demonstrated a continuous measurable spectral range covering from 0.2 to over 30 THz, with the help of sub-35 fs laser pulses from a Ti:sapphire amplified laser.

The second method developed to detect intense THz field in air is based on plasma fluorescence emission. The interaction of the THz pulse with the induced-laser plasma can generate TFISH, but also enhances the fluorescence emission of the plasma. Liu et al [146] used this latter effect for the first time to coherently detect intense broadband THz fields, and named it THz radiation-enhanced emission of fluorescence (THz-REEF). Compared with the other well-developed detection techniques, this method has an omnidirectional emission pattern. One can notice that this technique can be used for plasma characterization as well [147]. Its first demonstration has been realized with a single-color optical probe beam that results in an induced-fluorescence enhancement ${\rm{\Delta }}{I}_{{\rm{FL}}},$ which is proportional to the THz intensity, as described by the following equation [146]:

$$\begin{eqnarray}&&\underset{\tau \ll {\tau }_{{\rm{THz}}}}{\mathrm{lim}}{\rm{\Delta }}{I}_{{\rm{FL}}}\propto {n}_{e}\displaystyle \frac{{e}^{2}\tau }{2m}\displaystyle {\int }_{{t}_{{\rm{d}}}+{t}_{\varphi }}^{+\infty }{\vec{E}}_{{\rm{THz}}}^{2}(t){\rm{d}}t\end{eqnarray} \tag{ 27 }$$

Here, $\tau$ and ${\tau }_{{\rm{THz}}}$ are the electron relaxation time and the THz pulse duration, and ${n}_{e},$ $e$ and $m$ are the electron density, charge and mass, respectively. The term ${t}_{{\rm{d}}}$ is the time delay between the THz pulse peak and the laser pulse peak, ${t}_{\varphi }$ is the phase delay caused by the plasma formation. From equation (27), we see that the time-resolved signal extracted from REEF cannot be directly used for coherent detection of the THz pulse. To realize coherent detection using REEF, Liu et al applied an external bias field parallel to the THz field on the plasma as a local oscillator, allowing the THz waveform to be retrieved [148].

Another solution to realize coherent detection is to apply an AC bias voltage at the common focus point of the THz pulse and the laser pulse, as proposed by Dai et al [148]. This bias voltage field is applied parallel to the THz field onto the plasma as a local oscillator ${E}_{{\rm{LO}}}.$ If this AC bias voltage is synchronized at the half of the laser repetition rate, the measured component of the enhanced fluorescence signal can be expressed as:

$$\begin{eqnarray}&&{\rm{\Delta }}{I}_{{\rm{FL}}}\propto \tau \displaystyle {\int }_{{t}_{{\rm{d}}}+{t}_{\varphi }}^{+\infty }2{\vec{E}}_{{\rm{LO}}}{\vec{E}}_{{\rm{THz}}}(t){\rm{d}}t\propto \,{\vec{E}}_{{\rm{LO}}}{\vec{A}}_{{\rm{THz}}}({t}_{{\rm{d}}}+{t}_{\varphi }).\end{eqnarray} \tag{ 28 }$$

Following this approach, the THz field can be retrieved through ${\vec{E}}_{{\rm{THz}}}={\rm{d}}{\vec{A}}_{{\rm{THz}}}/{\rm{d}}t,$ with ${\vec{A}}_{{\rm{THz}}}$ being the vector potential of the THz pulse.

Finally, Lui et al [149] demonstrated an 'all-optical' technique for THz wave remote sensing with a two-color laser-induced air plasma. This is based on symmetry-broken laser fields in order to control electron momentum, which leads to coherent measurement of the THz field ${\vec{E}}_{{\rm{THz}}}.$ They reported a THz detected signal enhancement by one order of magnitude [149], compared with the first THz-REEF demonstration [146].

The third THz detection method in air plasma, named TEA, is based on photoacoustic emission from laser-induced plasma. Focusing a femtosecond laser pulse with high peak energy in air provokes an instantaneous heating of this focus point and produces a shock wave that relaxes into an acoustic wave. The addition of a THz field into the laser-produced plasma induces an acceleration of free electrons. The collisions of these electrons with the surrounding molecules lead to higher heating of the plasma and enhancement of the local pressure where the acoustic wave is generated [150]. This variation of acoustic pressure, measured with a microphone, permits to reconstruct the THz pulse. Unlike THz-REEF, where the induced fluorescence enhancement is measured, the theory behind the plasma behavior in the presence of a THz field is the same for TEA, which considers the acoustic pressure variations [151–152]. Furthermore, coherent detection can be realized with asymmetrically ionized gases obtained with two-color laser pulses [152, 153].

In OPTP experiments, the material sample is first pumped with laser pulses in the visible to the near-infrared range, and then its photo-induced dynamics is probed by THz pulses. In semiconductors, photoexcitation of electrons from the valence band into unoccupied states in the conduction band takes place linearly only when the exciting photon-energy exceeds the bandgap energy. On the other hand, the photoexcitation of carriers in zero-bandgap graphene from the valence band to the conduction band requires the photon energy of the pump beam to exceed twice the Fermi-level energy of the graphene sample; otherwise the interband transition will be blocked (Pauli blocking effect) [170–172]. After photoexcitation of the material sample in OPTP experiments, the THz probe field then reveals the transport dynamics of the free carriers (holes in the valence band and electrons in the conduction band), through transmission and/or reflection measurements. In OPTP experiments, the THz probe beam is sufficiently weak so that the THz interaction is in the linear regime. However, by using OPITP spectroscopy, new and interesting phenomena are beginning to evolve, such as the nonlinear THz-induced carrier dynamics of various materials. Here, we review two materials that have been studied by the OPITP technique, namely bulk GaAs semiconductor and two-dimensional graphene.

Su et al [173] employed intense THz probe field to study the nonlinear transport properties of photoexcited carriers in GaAs. The GaAs sample is pumped optically with 800 nm, 30 fs Ti:sapphire laser pulses with a pump fluence of 8 μJ cm⁻², while the induced dynamics has been probed coherently at the peak of a single-cycle intense THz pulse generated by OR in 〈001〉 ZnTe crystal [49]. The OPITP response of the sample was measured through transmission of the intense THz probe field, as shown in figure 20. Two THz probe field levels have been studied, with peak field strengths of 4 (low) and 173 kV cm⁻¹ (high).

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After the photoexcitation, the 4 kV cm⁻¹ THz probe field experienced transient absorption that resulted in reduction in the THz field amplitude transmitted through the GaAs sample as a function of the delay time between the pump and probe pulses, as shown in figure 21(a). Remarkably, the induced THz absorption is found to decrease when the THz probe field is increased, indicating that a nonlinear THz field-induced effect has taken place. This phenomenon has been attributed to THz absorption bleaching due to THz field-induced intervalley scattering of the photoexcited electrons from the high-mobility Γ-valley to the low-mobility L-valley of the conduction band, as shown schematically in figure 21(b). Thus, the intense THz probe field experiences less absorption due to this reduction in the carrier mobility via the intervalley scattering process. The authors have developed a simple intervalley scattering based Drude model and extracted the carrier dynamic parameters, such as the carrier population in the two valleys, scattering times, and the THz photoconductivity of the photoexcited GaAs sample, which reproduced the experimental transmission measurements, as shown in figure 22.

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Sharma et al [142] extended this study to account for the effect of increasing the photoexcited carrier density on the THz-field induced nonlinearity. The optical pump fluence has been varied from 2 to 40 μJ cm⁻², leading to a change in the photoexcited carrier density from 1 × 10¹⁷ to 10.6 × 10¹⁷ cm⁻³. The carrier dynamics has been probed at two THz field levels with peak field strengths of 9 kV cm⁻¹ (low) and 133 kV cm⁻¹ (high). The THz field-induced absorption bleaching α_b (the nonlinearity) is expressed as

$$\begin{eqnarray}&&{\alpha }_{{\rm{b}}}=\,\displaystyle \frac{{T}_{{\rm{high}}}}{{T}_{{\rm{low}}}}-1,\,T=\,\displaystyle \frac{{\int }^{}{|{E}_{{\rm{pump}}}(t)|}^{2}{\rm{d}}t}{{|{E}_{{\rm{ref}}}(t)|}^{2}{\rm{d}}t}.\end{eqnarray} \tag{ 32 }$$

Here, ${E}_{{\rm{pump}}}$ and ${E}_{{\rm{ref}}}$ are the THz electric field transmitted through the photoexcited (pump) and unexcited (ref) sample, and T_high and T_low are the normalized transmission at the high (133 kV cm⁻¹) and the low (9 kV cm⁻¹) THz peak fields, respectively. Figure 23 shows the dependence of the THz field-induced nonlinearity on the photoexcited carrier density. The trend is divided into two regions; at low carrier densities, the induced nonlinearity increases with the carrier density, which reaches a maximum at a carrier density of 4.7 × 10¹⁷ cm⁻³, while at higher densities, we see a reduction in the induced nonlinearity with the carrier density. The authors have used the intervalley scattering model to interpret this trend and attributed it to variation in the inter- and intravalley carrier scattering rates with increasing carrier density. Below 4.7 × 10¹⁷ cm⁻³, absorption bleaching increases with increasing the carrier density as long as more carriers can undergo intervalley scattering from the Γ- to the L- valley. Above this carrier density, the increase in the carrier density leads to an increase in the electron–hole scattering that suppresses the carrier kinetic energy in the Γ-valley and in turn reduces the intervalley scattering to the L-valley, leading to a reduction in absorption bleaching with increasing carrier density.

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Another example of a highly interesting application of OPITP spectroscopy is to reveal the carrier dynamics of graphene. Graphene, a monolayer of carbon atoms covalently bound in a hexagonal honeycomb lattice structure, has shown unique quantum properties exemplified by relativistic massless Dirac-fermion physics [174–178]. The band structure of graphene has shown a zero-bandgap and an energy spectrum described by a linear dispersion relation, i.e. $\varepsilon ={v}_{{\rm{F}}}|{\bf{P}}|=\hslash {v}_{{\rm{F}}}|{\bf{k}}|,$ where ${v}_{{\rm{F}}}\approx 1.1\times {10}^{6}\,{\rm{m}}\,{{\rm{s}}}^{-1}$ is the Fermi velocity, ${\bf{P}}=\hslash {\bf{k}}$ is the momentum and $\hslash$ is the reduced Planck's constant, and k is the wave vector. Since its first successful preparation in 2004 [174], graphene has attracted great interest to study its exceptional properties. Within five years just after the first preparation of graphene, more than 5000 publications on graphene have appeared [179].

Using the LiNbO₃-based THz source [47] available at the multi-kHz beam line of the ALLS facility at the INRS-EMT, Hafez et al [180, 181] performed various experiments of nonlinear THz spectroscopy of graphene. Using OPITP spectroscopy with highly n-doped monolayer epitaxial graphene (with a high Fermi level of ∼350 meV) on SiC, the effect of increasing the free carrier density on the THz nonlinear transmission of graphene has been studied. The graphene sample has been pumped optically by 800 nm, 40 fs laser pulses and the induced dynamics has been probed by the peak field of intense THz pulses, as shown schematically in figure 24.

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After photoexcitation and probing with a fixed THz probe field, a transient enhancement in the THz transmission (defined by a positive THz differential transmission ΔT/T₀) has been observed, as shown in figure 25(a). This observation was attributed to suppression in the photoconductivity of the graphene sample after photoexcitation, due to the increase in the carrier scattering rate. After the response peaks, a subsequent relaxation takes place over a picosecond timescale due to carrier cooling via optical phonon emission and carrier recombination. Interestingly, with increasing THz probe field, the authors have observed a reduction in ΔT/T₀, leading to a reduction in the overall increase in the THz transmission after photoexcitation. Figure 25(b) shows the THz peak field transmission as a function of the peak field strength after photoexcitation, relative to that before photoexcitation. Before photoexcitation, the increase in the THz field itself induces transparency in graphene, giving rise to increase in transmission, indicating a nonlinear response of graphene to the THz field. Photoexcitation led to a further increase in transmission. However, the relative increase in transmission after photoexcitation is decreased when the THz field is increased. This observation has been attributed to the combined effects from both the THz field and the optical pump fluence on the graphene photoconductivity.

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THz-pump/THz-probe (TPTP) spectroscopy using an intense THz pump beam, is an efficient but quite challenging technique for exploring the nonlinear THz properties of materials. The TPTP technique is commonly used in studying impact ionization [181] and intervalley scattering in doped semiconductors [182].

Blanchard et al [183] performed TPTP experiments to study the effective mass anisotropy of hot electrons in non-parabolic conduction bands in n-doped InGaAs. For most III–V semiconductors, the conduction band energy at the Γ point is considered to be isotropic (i.e. spherically symmetric so that ${\varepsilon }_{{\rm{k}}}={\varepsilon }_{|{\rm{k}}|})$ but non-parabolic (i.e. the curvatures of the band along k_x and k_y are different). This nonparabolicity leads to an anisotropy in the electron effective mass [i.e. ${m}_{x}({\bf{k}})\ne {m}_{y}({\bf{k}})].$ However, this mass anisotropy only appears away from the Γ point, and thus requires intense electric field to drive the electrons to sufficiently high k points to observe this effect. Thus, a polarization-dependent TPTP experiment has been implemented for this purpose. Figure 26 illustrates the TPTP scheme for exploring mass anisotropy in n-doped InGaAs. A strong THz pump pulse accelerates the conduction band electrons in the x direction, which are then probed by another weaker THz pulse polarized either in the x (collinear, CL in plane A) or y (cross-linear, XL in plane B) direction. The anisotropy of the electron effective masses induced by the THz-pump pulse was expected to yield distinctly different THz-probe responses for the CL and XL configurations, because the measured THz-probe signal is supposed to be proportional to the corresponding component of ${m}_{i}^{-1}({\boldsymbol{k}})$.

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In the experiment, a sample of n-doped In_0.53Ga_0.47As epilayer (carrier concentration of ∼2 × 10¹⁸ cm⁻³) on a 0.5 mm thick [100] semi-insulating InP substrate has been pumped at the focus of an intense THz beam (∼200 kV cm⁻¹ peak field) generated by OR in a large-aperture ZnTe crystal. The experimental setup was constructed on the 100 Hz ALLS THz facility [49]. A smaller ZnTe crystal is used to generate the weaker probe THz beam (∼2 kV cm⁻¹ peak field) that overlaps non-collinearly with the pump beam at the focus on the sample surface, as shown in figure 27(a). We also show in figure 27(b) the temporal waveform of the incident THz-pump beam and (c) the waveform of the THz-probe beam at various delay times between the main positive peaks of the THz-pump and THz-probe pulses. The amplitude of the transmitted THz-probe waveform was found to increase when it overlaps the THz-pump pulse at zero relative time delay, while the phase is relatively unchanged.

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Figure 28(a) shows the normalized transmission of the main peak of the THz-probe pulse. The presence of the THz-pump pulse results in an increase in transmission of the probe pulse. The blue shaded area shows the transmission change for XL polarizations of the pump and probe beams, while the red line shows the same measurement for the CL polarizations. The CL case yields a much larger amplitude oscillation than the XL case (blue area) indicating that the TPTP method can indeed access the mass anisotropy.

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A microscopic model was developed, based on coupling the equation of motion of carriers in intense THz field to a wave equation describing the propagation of the field through the n-doped InGaAs film. The transmission of the weak THz-probe field in the presence of the intense THz-pump field was computed, assuming an initial Fermi–Dirac distribution at 300 K and taking into account the effect of back coupling due to reflection effects. The results are shown in the upper part of figure 28(b), showing good agreement with the experimental results in figure 28(a). The solid line in figure 28(b) shows that the transmission is strongly enhanced for CL polarization due to increased effective mass, while the XL case (the blue shaded area) produces a much smaller effect since the effective mass is changed only moderately (see figure 26(d)). On the other hand, omitting the back coupling in the simulation resulted in a behavior opposite to that observed in the experiment, as shown in the lower part of figure 28(b). Thus, a complete understanding required the inclusion of the complex self-consistent back-coupling effects.

Hwang et al [184], performed TPTP experiments with monolayer CVD graphene and observed THz field-induced transparency. The THz generation was based on OR in a LiNbO₃ crystal. The crystal was pumped with two laser beams produced by splitting the incoming laser beam from an amplified laser source, to generate the THz-pump and the THz-probe beams with field strength ratio of 20:1. The two THz beams were focused collinearly onto the graphene sample and EO sampling detection was performed on transmission through the sample. In the experiment, two graphene samples on two different substrates; namely 1.4 mm thick fused silica 1.4 mm thick and high resistivity 1 mm thick silicon, were examined. The two samples were hole-doped with an approximately equal Fermi level of ∼−270 meV.

Figure 29 shows the THz field-induced transparency in graphene. Figure 29(a) shows the spectral transmission for various THz field strengths as a function of frequency, indicating induced transparency that increases with increasing THz pump fluence. The inset of figure 29(a) shows the THz time and frequency profiles measured in the experiment. Figure 29(b) shows the power transmission of the entire THz pulse plotted versus THz fluence. The average power transmission increased from 54% at low fluence to 79% at the highest THz fluence (corresponding to 73% and 89% average field transmission), and was fit to a saturable power transmission function.

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Figure 30 shows the time-resolved collinear-TPTP response of the two tested graphene samples. A transient change in transmission is measured as a function of the pump–probe delay time. The unreliable signal at t = 0 was due to temporal overlapping of the pump and probe pulses inside the LiNbO₃ crystal. However, the back-reflection of the THz pump pulse from the substrate−air interface, upon its return to the graphene layer, was sufficiently intense to produce a significant change in probe pulse transmission. Thus, the second signal from each sample in figure 30 occurs when the pump−probe delay time matches the THz round-trip time (roughly 20 ps) in the substrate. Through the second signal components, we observe THz field-induced transparency in the graphene samples, defined by a transient increase in the differential transmission ΔT/T₀. The response then exponentially decays with relaxation times of 1.7 ps for graphene on fused silica and 2.9 ps for graphene on silicon, using a single exponential decay fit.

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These observed THz field-induced transparency in graphene has been interpreted to be due to suppression in the intraband THz photoconductivity of graphene as a result of increasing the carrier scattering rate with increasing THz pump field. The effect of the intense THz pump beam results in thermalizing the carrier distribution. Thus, both the carrier and lattice temperatures increase with increasing THz field, leading to an increase in the optical-phonon population and in turn increase in the carrier-phonon scattering rate that suppresses the carrier mobility.

In TPOP experiments, the material sample is pumped with intense THz pulses, and the THz field-induced dynamics is probed by a very low power optical beam. In a very interesting study employing TPOP experiment, Tani et al [125] revealed ultrafast THz field-induced carrier dynamics in hole-doped monolayer CVD graphene. The graphene sample was pumped with intense broadband THz pulses generated by air-plasma THz source providing intense THz pulses with peak electric field strength up to 300 kV cm⁻¹. The induced THz dynamics was probed by a weak optical beam. In this work, the THz field-induced change in the optical-probe transmission of the graphene sample was defined by the normalized differential optical density ${\rm{\Delta }}{\rm{OD}}/{{\rm{OD}}}_{{\rm{ref}}}$ $=\,({{\rm{OD}}}_{{\rm{ex}}}-{{\rm{OD}}}_{{\rm{ref}}})/{{\rm{OD}}}_{{\rm{ref}}}\,$ $\simeq \,{\rm{\Delta }}T/{{\rm{OD}}}_{{\rm{ref}}},$ where OD_ref is the optical density of graphene at 800 nm without THz pulse excitation, and OD_ex is that with THz pulse excitation. The value of −ΔOD/OD_ref corresponds to the population occupation at the energy of an 800 nm transition. After THz pulse excitation, ΔOD/OD_ref immediately becomes negative (that is, graphene becomes transparent in the NIR region under THz pulse excitation) followed by a subsequent relaxation over a sub-picosecond time scale, as shown in figures 31(a) and (b). The large induced transparency was attributed to electron filling or hole depletion of the corresponding energy levels due to THz field-induced impact ionization.

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Using a theoretical model based on the semi-classical Boltzmann equation, incorporating THz field-induced impact ionization (II) and Auger recombination (AR) into the scattering term, the experimental results have been reproduced, as depicted by the solid lines in figures 31(a) and (b). The II process creates an extra electron–hole pair while losing the kinetic energy of another electron or hole, while the AR process reduces the number of carriers. The observed large induced transparency indicated that efficient carrier multiplication by II prevails over AR under the high THz field condition. The carrier density calculations presented in figures 31(c) and (d) show that for a peak THz field of 300 kV cm⁻¹, the number of carriers is increased by almost five times compared with the initial number of carriers. The calculations qualitatively reproduce the field dependent relaxation time, which confirm the longer relaxation time at higher excitation density, which was attributed to the hot phonon effect.

In summary, various techniques of THz spectroscopy along with intense THz sources have been employed to explore the carrier dynamics of condensed matter in the THz frequency range. The selection of a technique for a certain study depends on the nature of the dynamics to be explored. With OPTP spectroscopy one can study carrier dynamics of free carriers generated by photoexcitation, especially in undoped semiconductors. It can also reveal information about the interaction of hot photoexcited carriers and cold carriers in doped semiconductors. On the other hand, pumping with intense THz fields and probing with a weaker optical or THz field can reveal nonlinear THz effects such as impact ionization in doped semiconductors. Such THz spectroscopic techniques have a great advantage of being noninvasive.

Intense THz pulses can generate and accelerate ultrashort and ultrabright electron bunches from a metal surface [185–187], analogous to earlier microwave [188] and femtosecond laser [189–192] field emission. In the THz regime, the electron emission is induced by acquiring energy from a local enhanced THz field that enables modulation of the metal work function Φ (Schottky effect), and allows electrons to tunnel through such a potential barrier. The intense field can further provide kinetic energy, producing an accelerated electron beam. The process is thus considered a nonperturbative nonlinear THz field-metal interaction. The THz local field enhancement can be achieved by a metal nanotip [185, 186] or micro antenna [187].

Hernik et al [186] demonstrated THz-induced field emission from a sharp tungsten tip (10 nm in diameter, biased at 40 V) for local THz fields exceeding 20 MV cm⁻¹, and using a time-of-flight (TOF) electron spectrometer for detection. Figure 32(a) shows the field emission map acquired by scanning the tip through the THz focal plane and recording the electron yield. Figure 32(b) shows the generated electron energy spectra for two local THz field strengths of 31 and 53 MV cm⁻¹, with a sharp cutoff that blue-shifts by increasing the THz field strength.

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Iwaszczuk et al [187] demonstrated THz-induced electron field emission from a gold nanoantenna on high resistivity silicon in a nitrogen purged environment. It has been shown that the generated photoelectrons ionize the nitrogen molecules surrounding the sample, giving rise to the generation of UV radiation. The incoming THz beam has a peak electric field of 200 kV cm⁻¹ and a peak intensity of 0.1 GW cm⁻², illuminating one side of the substrate first, and the emitted UV radiation detected on the other side. The emitted UV spectrum (photon energies 2.7–5 eV) has been found to consist of emission lines of excited N₂ and singly ionized ${{{\rm{N}}}_{2}}^{+},$ as shown in figure 33. The process is described by a four-step model, consisting of (i) electron field emission, (ii) electron ballistic acceleration, (iii) excitation and ionization of N₂ molecules and (iv) UV emission.

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Further, Wimmer et al [185] and Hernik et al [186] independently, demonstrated THz control of electron dynamics using OPTP spectroscopy. Optical pump at 800 nm induced nonlinear photoelectron emission from biased metal nanotips, which is gated and streaked by locally enhanced THz fields. The effect of the THz field, with polarization parallel to the tip line, resulted in enhancement in the photoemission-streaking maximum, caused by a THz field-induced reduction in the work function.

The Rydberg state of an atom or molecule is an electronically excited state. The most important property of Rydberg states is the large orbital radius, and hence dipole moment. As a result, Rydberg atoms have typical properties such as small binding energy, high state density and long lifetime, which make them easy to ionize under the action of an external electric field [193–195]. Working with Rydberg atoms is very interesting for studying the different ionization mechanisms. For example, different mechanisms dominate the ionization process if we excite the Rydberg atoms with radio frequencies, micro- and THz waves. The first example of nonlinear nonresonant control of matter by intense THz pulses was the ionization of Na atoms in a Rydberg state by asymmetric half-cycle THz pulse generated by GaAs LAPCA in 1993 [193]. The threshold electric field required to ionize a Rydberg state with effective quantum number n is found to scale as n⁻² for states with n > 13, in contradistinction to the n⁻⁴ threshold scaling for static field ionization and high order multiphoton ionization. Bensky et al [194] studied the process of ionization of Na Rydberg atoms with intense quarter cycle circularly polarized THz pulses. However, it was found that the ionization probability is remarkably insensitive to the time-varying polarization of the THz field. Recently, the ionization of atoms in a low Na Rydberg states, $6\leqslant n\leqslant 15,$ by a low frequency, long single-cycle THz pulse was demonstrated [195]. Figure 34(a) shows the THz field dependence of the ionization probability for $6\leqslant n\leqslant 15.$ Working in that regime revealed three surprising results: (i) the adiabatic ionization occurred for higher field threshold, which scales as n⁻³, as shown in figure 34(b), (ii) it has been found that the electrons originating from the most tightly bound Rydberg states left the atoms with the highest energies, and (iii) the kinetic energy of electrons largely exceeds the limit of ${\rm{\Delta }}{E}_{\max }=2{U}_{{\rm{p}}}$ where U_p is the ponderomotive energy of the pulse.

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In solids, the electronic transport of free carriers under the action of a static field is described by the Drude model. The Drude model is still valid until the carrier moves ballistically between scattering events. A description as free carriers is well justified if the carriers stay close to the lower band edge. If the field is large enough that the carriers in a crystalline solid reach the edge of the Brillouin zone before scattering takes place, Bragg reflection occurs and the electron traverses the Brillouin zone again, causing the electron to oscillate in the real and reciprocal space [196–203]. This effect is well known as BOs. For a crystalline structure with a lattice period d, in an electric field E, the carrier can oscillate with a period ${\tau }_{{\rm{BO}}}=\hslash /eEd.$ The first experimental observation of BO has been verified in semiconductor superlattices using optical excitations [197].

In the THz frequencies, Schubert et al [203] reported intense (72 MV cm⁻¹ peak electric field, and central frequency at 30 THz) THz field-induced BOs in a bulk crystal of GaSe semiconductor, leading to THz HHG up to the 22nd harmonic order, as shown in figure 35(a). The effect is thus nonlinear and nonresonant. Proper detection techniques of EO sampling, InGaAs diode array and a Si CCD camera have been employed to detect this wide range of the whole spectrum. The THz field dependence of the generated harmonics, the 13th order for example, is shown in figure 35(b). The intensity scales initially asymptotically as ${I}_{13}\propto {E}^{26}$ (dashed line) and then a slower increase as ${I}_{13}\propto E$ is observed for higher fields (dotted line), confirming the nonperturbative nature of HHG. The experimental observations have been justified quantitatively by considering BOs combined with coherent interband excitations, i.e., accounting for nonresonant excitation of interband polarization and intraband acceleration of electronic wavepackets throughout the Brillouin zone. In contrast to the three-step model for HHG in atoms, the THz acceleration of electrons in a periodic lattice potential in a crystalline solid is dominated by Bragg reflection. The model also accounted for the generation of even harmonics by assuming THz field-induced dynamical band mixing including three valence and two conduction bands (see figure 35(c)), incorporating the broken inversion symmetry of GaSe.

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It has been reported a few years ago that intense THz fields can lead to a breakup of Cooper pairs in superconductors, providing a switching from superconductor to normal metal properties [13, 204–206]. Matsunaga et al [204] studied ultrafast dynamics of the BCS state in a conventional NbN superconductor (with a BCS gap of 2Δ(0) = 5.2 meV (1.3 THz)) after impulsive injection of quasiparticles (QP) at the edge of the BCS gap by using intense THz pulses and employing TPTP spectroscopy. Rapid THz field-induced switching off of superconductivity was observed within the duration of a single-cycle THz pulse with a peak electric field exceeding 50 kV cm⁻¹ and a spectrum located at the BCS gap region. At that pump level, high-density QPs as much as 10²⁰ cm⁻³ were estimated. The temporal evolution of the probe THz field E_probe transmitted through the NbN sample and the pump–probe change ΔE_probe as functions of the pulse gating time t_g and the pump–probe delay time t_pp is shown in figures 36(a)–(c), for a pump THz peak field of 100 kV cm⁻¹ at 4 K. Figure 36(d) shows the temporal evolution of the peak of ΔE_probe (t_g = 0) as a function of t_pp for various THz pump peak fields. At low THz pump field, a rapid transient increase in ΔE_probe with a peaklike signal is induced after pump as a result of Cooper pair breakup via direct photoinjection of QPs, leading to a change in the BCS state. Although the effect is linear and resonant, the switching from superconductor to normal metal phase requires high density of photoinjected QPs, which in turn requires high THz field. In addition, the THz field effect is highly distinguished from that induced by optical pump that generates hot electrons with excess energy transferred to the creation of high-frequency optical phonons, which in turn cause the pair breaking [204, 205]. The transient change becomes constant after t_pp = 1.6 ps, indicating that the BCS state reached a quasiequilibrium state. As the THz pump field increases, the peaklike signal disappears and the transient change shows a steplike signal and the rise of ΔE_probe becomes earlier. The origin of the former effect is not clearly understood, while the latter effect was attributed to a change in the BCS state induced by the precursor part of the THz pump pulse before the main peak in the high pump regime. Moreover, the decay time of ΔE_probe was found to increase by increasing temperature and THz pump field.

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In contrast to the above study with NbN superconductor in which the BCS gap was analogous to the THz photon energy, Glossner et al [206] reported Cooper pair breakup in high-temperature YBa₂Cu₃O_7−δ [∼20 meV gap energy] induced by intense THz field with photon energies much lower than the superconducting gap energy of the material. The process is thus nonlinear and nonresonant. Figure 37 shows THz pulses transmitted through a 45 nm YBa₂Cu₃O_7−δ O thin film on 500 μm (LaAlO₃)_0.3(Sr₂AlTaO₆)_0.7 (LAST) substrate and normalized to the peaks of the corresponding THz pulses transmitted through bare LAST substrate, at various temperatures below and above the critical temperature [T_C = 80 K] and various incident THz fields with peak electric fields up to 30 kV cm⁻¹. For a fixed THz field, we observe reduction in transmission as the temperature reduces below T_C, i.e. by reaching the super conductor phase. Interestingly, the low-temperature transmission increases and a time shift is observed by increasing the exciting THz field (the upper two panels of figure 37) indicating suppression in the superconductivity of the material, while no field-induced change is observed for T > T_C. These observations provide further control of THz response of metamaterials on superconducting substrate, which will be discussed in the next section.

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In contrast to THz field-induced Cooper pair breakup, Dakovski et al [207] demonstrated THz field-induced charge density wave (CDW) in an underdoped single crystal YBa₂Cu₃O_6+δ (T_C = 75.2 K and doping level p = 0.133), demonstrating that low photon energy fields can induce pronounced coherent, collective excitations in the superconducting state. In their experiments, intense THz pulses with peak electric field of ∼400 kV cm⁻¹ is used to pump the sample, while the induced excitations have been probed by an 800 nm beam of 100 fs pulse duration, by employing reflection measurements via TPOP spectroscopy. Figures 38(a) and (b) show THz field-induced transient optical reflectivity at low temperatures, for two cases of the optical probe polarization with respect to the a and b axes of the sample. The transient peak is followed by coherent oscillations, closely following the THz pulse intensity profile, which have been Fourier analyzed in figures 38(c) and (d). The sign of the transient reflectivity was found to be dependent on the relative orientation of the optical probe beam with respect to the sample axes, while the polarization of the THz pump beam did not show any effect. For optical probe polarization parallel to the b-axis, only one single mode of 1.8 THz is observed, similar to observations obtained by 800 nm optical pump [207, 208]. For the probe beam polarization parallel to the a-axis, two additional modes at 0.6 and 2.7 THz are observed. The THz field-induced effects are thus resonant. The 1.8 and 2.7 THz modes match CDW oscillations measured by x-ray scattering, while the 0.6 THz mode still needs more investigations.

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Figure 39 shows the temperature dependence of the THz field-induced transient reflectivity and the coherent oscillations. As the temperature increases, the coherent oscillations diminish and vanish at temperatures close to the transition temperature T_C, consistent with the behavior of the CDW transition. Moreover, a change in the sign of the transient reflectivity is induced by increasing temperature above T_C.

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The magnetic field is an excellent way to control the quantum-mechanical spin S of an electron. Since S is associated with the magnetic dipole moment, it couples to B through the Zeeman Hamiltonian γ S · B, where γ denotes the gyromagnetic constant [209]. A direct control of spin is provided by a time dependent magnetic field that exert a Zeeman Torque given by γ S × B, which leads to spin precession [210]. In antiferromagnets, the spin precessions, called magnon, occur at THz frequencies. With the development of intense THz sources, it is now possible and very promising to manipulate and control the spin by intense THz electromagnetic transient in antiferromagnets. A THz pump-optical probe experiment was tested onto NiO [209, 210], whose magnon resonance is located at 1 THz [211]. NiO was chosen because the Heel temperature is set at 523 K, allowing all the experiments to be at ambient temperature, and also because it is considered to be a centrosymmetric medium, which allows the driving of spin dynamics only by the THz magnetic field. Figure 40 shows the trace of the incident magnetic THz transient (a), Faraday rotation as a function of the pump–probe delay time with a period of 1 ps (b), the spectrum of the THz pulse and the spectrum of the Faraday rotation induced by the intense THz pulse into the NiO substrate (c) and the Faraday rotation as a function of the pump–probe delay time for a double pulse excitation with the second pulse in (d) or out (e) of phase with the spin precession induced by the first intense THz pulse.

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The intense THz transient was generated by OR of 5 mJ, 800 nm, 100 fs laser pulse in a large aperture ZnTe crystal and focused onto a Twin domain, which is in the order of 100 μm. The peak electric field and peak magnetic field were estimated to be about 0.4 MV cm⁻¹ and 0.13 T, respectively and cover a spectral range from 0.1 up to 3 THz. The induced spin precession was measured by measuring the Faraday rotation of the 8 fs probe pulse. When using single pulse excitation, the authors observed that the Faraday rotation oscillates with a period of 1 ps corresponding to a narrow spectrum centered around 1 THz. The maximum amplitude is reached at 3 ps, which then decays exponentially with a time constant of 39 ps. Following the idea introduced by Yamaguchi et al [212] who have induced quasiferromagnetic and quasiantiferromagnetic spin precession in a YFeO₃ crystal using a double THz pulses excitation with an adequate time delay, and taking advantage of the long life time of the spin procession, Pashkin et al [209] controlled (switch on–switch off) the spin precession with a succession of two excitation pulses with different time delay between them. If the second pulse arrives 6 precession cycles after the first pulses, the two torques induced by the two pulses will be in phase, which induce an almost two times stronger Faraday rotation, resulting from a two times stronger spin precession. However, if the second pulse arrives 6.5 precession cycles after the first pulse, the torques will be out of phase, which switches off the spin precession.

Control of magnetization dynamics is also possible in ferromagnetic material. However, since the resonant modes are typically lower than 100 GHz, intense THz magnetic transients allow nonresonant control of the spin [213]. The biggest advantage of THz wave over optical pulse is that the former induces an adiabatic process, thus avoiding cooling, which in general limits the speed of the magnetization manipulation [214]. Recently, Vicario et al [215] studied off-resonant magnetization dynamics induced by an intense THz pulse in a 10 nm thin cobalt film. They showed that the magnetization variations were phase locked to the THz magnetic transient. Before the THz excitation, the magnetic moment was driven to saturation by applying an external magnetic field. The THz pulses were generated via OR in an organic crystal excited with a 1550 nm laser pulse. The THz pulse was 1.5 cycles and the magnetic peak field was 0.4 T. A 50 fs, 800 nm optical probe sampled the magnetization dynamics via the magneto-optical Kerr effect (MOKE).

Figure 41 shows the THz magnetic transient, the MOKE signal and the signal obtained with the simulations as a function of time (a) and their respective spectrums (b). The simulations were calculated using the Landau–Lifschitz–Gilbert formalism. We observe that the magnetism dynamics are phase locked with the magnetic transient with a phase shift of 50 fs corresponding to a quarter of a cycle. As a consequence, the two spectra show good agreement. This was the first time that such fast magnetic dynamics was induced by an exciting pulse. The speed of the magnetization dynamics was the fastest ever observed. This phenomenon is possible because the photon energy of the THz waves is at least 3 orders lower than the photon energy of an optical pulse, which limits the heating of the substrate.

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As extremely high THz magnetic field is required for inducing magnetic switching effects, using metallic structures that can enhance the THz magnetic field could be essential. Engineered structures such as metamaterials, which will be discussed in the next section, could be of a great importance. To the best of our knowledge, no applications based on employing metamaterials in THz magnetic switching effects are reported to date.