1. Introduction

Optical rectification of femtosecond laser pulses in electro-optic (EO) crystals is an established method for generating pulsed terahertz radiation. In this method, the pump laser pulse induces in the crystal a nonlinear polarization that follows the optical intensity envelope. The nonlinear polarization copropagates with the laser pulse and acts as a source of terahertz radiation. Depending on the crystal type and laser wavelength, different generation regimes are used, including the standard collinear phase matching [1–4], Cherenkov radiation [5–7], and tilted-pulse-front pumping [8–10]. In all these regimes, the generated terahertz waves lag behind the pump laser pulse. Only weak transient radiation from the entrance boundary of the crystal can propagate ahead of the laser pulse [11]. At high pump intensities, multiphoton ionization leads to the generation of free carriers behind the laser pulse that absorb the generated terahertz waves. This limits the efficiency of terahertz generation.

Recently, the effect of generating unipolar electromagnetic precursors propagating ahead of the pump laser pulse was predicted [12]. In this effect, multiphoton ionization plays counterintuitively a crucial positive role. Free carriers, produced by the ionization, are accelerated by the electric field copropagating with the nonlinear polarization. This creates a current surge, which in turn generates electromagnetic fields. In subluminal materials, with ${n_g} > {n_0}$ [11], where ${n_g}$ is the optical group refractive index and ${n_0}$ is the low-frequency phase refractive index, the generated low-frequency fields propagate faster than the laser pulse and form a unipolar electromagnetic precursor ahead of the laser pulse. The quasi-constant electric and magnetic fields in a precursor can exceed the terahertz fields behind the laser pulse [12,13]. In superluminal materials, with ${n_g} < {n_0}$ [11], the generation of unipolar precursors as strong as hundreds of MV/cm and thousands of G by laser pulses with tilted pulse front was predicted [14]. However, the precursor generation has not been observed experimentally. At the same time, generation of strong unipolar and quasi-unipolar pulses is a subject of current interest [15]. Such pulses can be beneficial, for example, for particle acceleration [16,17], ultrafast control of electron wavepacket dynamics [18] and magnetic order in matter [19], molecular orientation and alignment [20,21], nonlinear terahertz spectroscopy [22], and terahertz streaking [23].

Here we report the experimental evidence for the phenomenon of unipolar precursors. The experiments were performed with a GaP crystal excited by a Ti:sapphire laser of 790 nm wavelength. For this wavelength, GaP is a subluminal crystal at the terahertz wave frequencies below ω/(2π) ≈ 7.4 THz [24], which makes it well suited for observing the precursor generation in a convenient collinear geometry. At low pump intensities, terahertz emission from a GaP crystal consists of two pulses of opposite polarity, which are generated at the crystal boundaries as transient radiation [24,25]. At high pump intensities, a plateau-like (quasistatic) part is predicted to appear in the emission waveform between the two terahertz pulses as a precursor of the laser pulse [12]. Detecting this plateau-like part is the purpose of this work.

2. Experimental setup

The experimental setup is depicted in Fig. 1. For generating the precursor, <110>-cut GaP crystals with thicknesses of 1, 3, and 5 mm were pumped by an amplified Ti:sapphire laser (790 nm wavelength, 1 kHz repetition rate, 0.65 mJ maximum pulse energy, and 65 fs Fourier limited pulse duration). To optimize the precursor generation [13], the pump pulse duration was increased to 450 fs by negatively chirping the Fourier limited laser pulse. The standard collinear configuration with normal incidence of the pump laser beam on the crystal boundary was used. The beam was parallel, and its diameter (full-width at half maximum, FWHM) was varied in the interval from 2.3 to 14 mm by means of two-lens telescopes.

 

Fig. 1. Schematic of the experimental setup. The pump laser beam from an amplified Ti:sapphire laser is incident normally on the generator GaP crystal. The detector crystal (a 50-µm thick ZnTe layer) is placed near the exit surface of the GaP crystal and separated from it by a 100-µm thick sheet of black paper. The probe laser beam propagates in the detector ZnTe crystal towards the generated low frequency radiation and is reflected from the back surface of the crystal. The standard EO sampling scheme with a quarter-wave plate (QWP), Wollaston prism (WP), and balanced detector (BD) is used for the ellipsometric detection of the low frequency waveform.

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A crucial part of the experimental setup is its detection arm. The usual terahertz schemes with focusing optics are inapplicable for detecting the quasistatic unipolar precursors. Indeed, the electric field in the focus is proportional to the time-derivative of the incident field, and, therefore, focusing destroys unipolarity [15,26]. Similarly, propagation from the near- to far-field also leads to reshaping effects [27]. For these reasons, the generated electric field was measured immediately after it exited from the GaP crystal. A 50-µm thick <110>-cut ZnTe crystal on a 1-mm thick glass substrate was used as a detector. The substrate suppresses multiple reflections in the ZnTe crystal to ensure high spectral resolution of the detection. The detector (ZnTe) crystal was placed at the exit surface of the generator (GaP) crystal. To shield the detector from the pump laser beam, a 100-µm thick sheet of black paper was clamped between the crystals (Fig. 1). Complete blocking of the pump beam by the paper was confirmed by zero signal from the balanced detector in the absence of the probe beam and by means of an IR-viewer. Black paper was used instead of commonly used Si wafer to avoid optically generating free carriers that could prohibit the low frequency radiation from penetrating into the detector crystal. Another reason for using paper instead of Si is the requirement of proper reflection conditions for the probe optical beam at the back surface of the ZnTe crystal. Namely, the beam should be reflected from the interface with a medium that has a lower, as compared to ZnTe, refractive index. Otherwise, the probe pulse polarity will flip over due to reflection and the reflected probe beam will experience an EO modulation of the opposite sign with respect to the incident beam modulation. This can strongly reduce or even completely cancel the net EO signal. The rest of the experimental setup is the standard ellipsometric scheme (Fig. 1) that allows for detecting the birefringence induced in the ZnTe crystal by the low frequency electric field generated in the GaP crystal.

It should be taking into account that forth and back propagation of the probe pulse in the terahertz field can cause waveform distortions. For the terahertz signals longer than ∼1.2 ps, which is the round-trip time of the probe pulse propagation in the 50-µm thick ZnTe detector crystal, the EO signal is enhanced twice as compared to a single-pass propagation. This reduces the relative magnitude of sharp picks (shorter than 1.2 ps) in the waveform with respect to the smooth features. When calculating the absolute value of the terahertz field, we take into account the two-fold enhancement of the EO signal (divide it by two) thus underestimating (up to two times) the sharp features of the waveform.

3. Results and discussion

Figure 2(a) shows the experimental waveforms obtained with 5-mm thick generator crystal for different intensities of the pump laser beam. The variations of the optical intensity were provided by changing the pump beam diameter at a fixed pump pulse energy. The waveforms have three distinctive features including a leading pulse of negative polarity, a wide plateau-like part of the same (negative) polarity behind it, and a pulse of positive polarity in the rear. The leading pulse is the transient radiation produced by the pump laser pulse at the entrance surface of the GaP crystal. Due to the condition ${n_g} > {n_0}$ in GaP, this pulse propagates faster than the laser pulse and arrives first at the detector crystal. The lagging pulse of positive polarity is the transient radiation produced by the laser pulse at the exit surface of the GaP crystal and, therefore, it arrives at the detector crystal with a delay $\Delta t = L({{n_g} - {n_0}} )/c$, where c is the speed of light and L is the crystal thickness. For L = 5 mm, ${n_g} = 3.61$ [28], and ${n_0} = 3.36$ [29], we obtain $\Delta t \approx 4$ ps, which agrees well with Fig. 2(a). Due to pump depletion and distortion, the lagging pulse is substantially weaker and broader than the leading pulse. The plateau-like part of the waveform is the quasistatic precursor generated in the volume of the GaP crystal and propagating ahead of the laser pulse, in accord with the theoretical predictions [12,13].

 

Fig. 2. (a) Experimental oscillograms of the electric field for different focusing conditions (the laser beam diameter and corresponding optical intensity are shown in the legend) and fixed optical pulse energy of 0.47 mJ in the crystal. The pump pulse duration is 450 fs (negative chirp), the generator GaP crystal is 5-mm thick. The arrow indicates the arrival time of the laser pulse at the crystal exit surface. (b) Numerically calculated oscillograms for the same parameters as in (a).

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In Fig. 2(a), the strongest precursor, with the electric field of ∼1 kV/cm, is generated at the pump beam diameter of 3.5 mm (7 GW/cm² optical intensity in the crystal). This result agrees rather well with Ref. [13], where maximum precursor magnitude was predicted for a ∼2-mm wide (FWHM) two-dimensional (2D) pump laser beam of a fixed laser pulse energy. The difference can be attributed to only limited application of the 2D model to the experimental configuration with a round laser beam. The precursor duration ∼2.4 ps is substantially longer than the leading pulse duration, the latter is about the duration of the pump laser pulse (450 fs).

To interpret the experimental results more accurately, we performed 2D numerical modeling of the precursor generation for the parameters of Fig. 2(a). We used the physical model and FDTD code developed in Ref. [13] with slightly different indices ${n_g}$ and ${n_0}$ (see above), which fit better the experimental time delay between the leading and lagging pulses in Fig. 2(a). Due to time consuming calculations, the effects of linear dispersion and Kerr nonlinearity on the pump laser pulse were omitted, only pump depletion caused by two-photon absorption was included. The numerical results, shown in Fig. 2(b), are in good general agreement with the experiment. Some discrepancies between Figs. 2(a) and 2(b) in the magnitude and width of the lagging positive pulses can be attributed to the pump pulse distortion due to dispersion and Kerr nonlinearity. Indeed, according to 1D modeling [12,13], these factors can substantially affect the pump pulse duration and intensity on the distances of a few mm for the parameters of Fig. 2(a).

To study experimentally the dynamics of the precursor formation in the generator GaP crystal, crystals of different thicknesses (1, 3, and 5 mm) were used for generation. The measured waveforms are compared in Fig. 3(a). It is seen that the main part of the precursor forms at the distance of about 3 mm. Increasing the crystal thickness to 5 mm adds little to the precursor length, only slight elongation of its weak rear part is observed. This can be explained by the dispersive and nonlinear distortion of the pump laser pulse at the distances larger than 3 mm. Indeed, the numerically calculated oscillograms [Fig. 3(b)], with the pump depletion included, show a further elongation of the precursor for a 5-mm thick crystal. Therefore, the factor of pump depletion is not sufficient to explain Fig. 3(a), and the factors of dispersion and Kerr nonlinearity need to be accounted for.

 

Fig. 3. (a) Experimental oscillograms of the electric field for different thicknesses of the generator GaP crystal. The pump beam diameter is 7 mm, the optical intensity is 1.73 GW/cm2, the pump pulse duration is 450 fs (negative chirp). (b) Corresponding numerically calculated oscillograms.

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A substantial effect of the pump depletion and distortion on the precursor generation is confirmed by Fig. 4(a) where the experimental oscillograms [Fig. 2(a)] are shown normalized to their maximal values. The length of the plateau-like part in the normalized waveforms increases monotonically with the increase of the pump beam diameter (decrease of the optical intensity). This can be explained by a lower pump depletion and distortion at lower optical intensities, that is confirmed by a larger amplitude of the positive polarity pulse in the rear part of the oscillograms in Fig. 4(a). Indeed, this pulse, which is generated at the exit surface of the generator crystal, can serve as an indicator of the pump depletion and distortion.

 

Fig. 4. (a) The same oscillograms as in Fig. 2(a) but normalized to their maximal values. (b) Experimental oscillograms for different distances between the generator (GaP) and detector (ZnTe) crystals. In (b), the laser beam diameter is 7 mm and the GaP crystal is 5-mm thick.

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An interesting question is how long can the precursor preserve its unipolarity after exiting the generator crystal? Indeed, for the dc component of the precursor with the wavelength $\lambda \to \infty $ there is no near-field region in terms of the Fraunhofer distance ${L_F}\sim {D^2}/\lambda $ ($D$ is the transverse size of the precursor). Therefore, one can expect the precursor to experience strong reshaping effects while propagating in free space. To study experimentally the precursor reshaping, we measured the generated electric field at different distances from the exit surface of the generator crystal for the pump beam diameter of 7 mm [Fig. 4(b)]. It is seen from Fig. 4(b) that the plateau-like part of the oscillogram substantially decreases at the distance of 1 mm and completely disappears at 5 mm. The oscillogram acquires a typical quasi-unipolar shape with a leading half-cycle peak and a long weak tail of opposite polarity [15]. For generating longer propagating precursors, wider pump laser beams should evidently be used, according to the theoretical predictions [13]. Reducing the crystal thickness from 5 to 3 mm can also be beneficial due to shortening of the idle propagation distance in the crystal.

4. Conclusion

We have observed experimentally the phenomenon of generating a unipolar electromagnetic precursor propagating ahead of a high-intensity Ti:sapphire laser pulse in a GaP crystal. The precursor appears as a plateau-like part in the radiation waveform emitted from the crystal. The experimental results are in good agreement with 2D numerical FDTD modeling performed for the conditions of the experiment. Both the experimental and numerical results demonstrate the significance of pump depletion and distortion due to the linear dispersion and Kerr nonlinearity. The precursor with the electric field of ∼1 kV/cm was obtained for the pump intensity of several GW/cm². Much higher intensities can be used for tilted-pulse-front pumping of a LiNbO₃ crystal, thus allowing for the generation of much stronger unipolar precursors [14].