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Abstract
We demonstrate a table-top high-field terahertz (THz) source based on optical rectification of a collimated near-infrared pulse in gallium phosphide (GaP) to produce peak fields above 300 kV/cm with a spectrum centered at 2.6 THz. The experimental configuration, based on tilted-pulse-front phase matching, is implemented with a phase grating etched directly onto the front surface of the GaP crystal. Although the THz generation efficiency starts showing a saturation onset as the near-infrared pulse energy reaches 0.57 mJ, we can expect our configuration to yield THz peak fields up to 866 kV/cm when a 5 mJ generation NIR pulse is used. This work paves the way towards broadband, high-field THz sources able to access a new class of THz coherent control and nonlinear phenomena driven at frequencies above 2 THz.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-field terahertz (THz) sources [1] are widely applied to explore nonlinear THz properties of various materials including semiconductors [2], 2D materials [3], and gases [4]. These sources also allow experimentalists to access new regimes of high-harmonic generation [5], free electron acceleration [6], and coherent control [7–9]. Most research groups working on these topics have employed the tilted-pulse-front technique based on an ultrafast near-infrared (NIR) laser to generate high-field THz pulses by optical rectification inside a LiNbO3 nonlinear crystal [10,11]. Generally, this table-top technique provides a THz electric field on the order of several hundreds of kV/cm, with a record value of 6.3 MV/cm [12], featuring a spectrum which peaks around 1 THz and then gradually decreases in amplitude as frequencies approach the phonon resonance of LiNbO3 at 4.5 THz [13,14]. Modifications to this standard configuration have recently led to a more efficient generation of high-field THz pulses with spectral components up to 4 THz [15]. However, 98% of the pulse energy in this configuration is still contained within the frequency range below 2 THz, limiting most high-field applications requiring a spectrum centered at higher frequencies. Cooling the LiNbO3 crystal down to cryogenic temperatures can increase the field strength by a factor up to 2.7 [16,17] and, in some cases, extend the spectrum towards higher frequencies by reducing losses due to the phonon absorption tail. This latter approach was notably used to enable the generation of a spectrum centered at 4 THz with a peak field around 10 kV/cm [16]. However, the use of cryogenic equipment adds another level of complexity to an already complicated experimental setup. Furthermore, a THz peak field evaluated to about 150 kV/cm from power measurements was produced in a 1 mm-thick GaP crystal with a spectral peak below 2 THz [18]. There is therefore a general lack of a straightforward table-top experimental configuration based on high damage threshold crystals, able to generate high-field THz pulses with a spectrum centered at frequencies exceeding 2 THz. Such a system is crucial for providing experimentalists with access to a new range of phenomena such as phonon-assisted nonlinearities [2,19], coherent control of Bose-Einstein condensation in semiconductor microcavities [20], and saturable transitions in molecular gases [4]. Other high-field THz generation techniques using air plasma or metallic spintronic emitters have reported peak fields above 1 MV/cm [21–24], the spectral bandwidth of these sources typically extends from 0.5 to 30 THz. Recent work on air plasma THz sources have demonstrated high-energy pulses covering a large spectral range [24,25]. Such systems, if combined with spectral filters [26], can potentially yield THz pulses with peak field amplitudes reaching several 100’s of kV/cm within a specific spectral region. Finally, organic materials, such as DAST and DSTMS, display great potential for generating high-field THz above 20 THz [27–29]. High conversion efficiencies in the region between 2 and 4 THz [30–32] can notably be achieved with a pump source centered between 1.2 and 1.6 µm, relying on a nonlinear wavelength conversion stage [33]. BNA and HMQ-TMS crystals can generate high-field THz up to 6 THz with a NIR pump laser centered at 800 nm or 1030 nm, however most of the THz pulse energy is still contained within a spectral range below 2 THz [34,35]. In those spectra, phonon absorption lines are common due to the organic nature of the THz generation crystal, but those lines can be reduced with cryogenic cooling [30,35,36]. The typical damage threshold of organic crystal is however relatively low, typically below 20 mJ/cm2 [35,37,38], which is about 60 times lower than that of semiconductor crystals, such as GaP [39,40]. This may be a limiting factor for long-term stability of a THz source relying on high near-infrared power.
In this work, we demonstrate a scheme to generate high-field THz pulses centered at 2.6 THz using a phase grating directly etched onto the surface of a nonlinear crystal to enable non-collinear phase-matched tilted-pulse-front THz generation. This technique has been proposed theoretically [41–47] and then demonstrated experimentally [48–50] with surface gratings on ZnTe and LiNbO3 crystals to achieve high THz generation efficiencies at frequencies <2 THz. In comparison to the standard tilted-pulse-front technique in LiNbO3, this configuration eliminates imaging distortions of the diffracted generation pulse, hence improving THz beam quality as well as THz generation efficiency [41,44,48]. Recently, broadband THz generation was demonstrated from 0.1 to 6 THz with a phase grating etched on the surface of a 2 mm-thick GaP crystal [50]. In this geometry the generation NIR pulse was focused onto the generation crystal. Here we use the same material, but we rely instead on a different geometry using a collimated 0.57 mJ NIR pulse from a standard commercial 1035 nm femtosecond laser amplifier to generate a THz pulse with a peak field reaching 303 kV/cm at a central frequency of 2.6 THz. This is the first report of a high-field source based on a high damage threshold crystal to target the hard-to-access region immediately above 2 THz. The confined spectral bandwidth, free of phonon absorption lines, can be efficiently used to drive a resonant system into a nonlinear regime. More importantly, there are two indications that our configuration is able to yield much larger THz peak fields: (1) NIR pulse energies to generate THz radiation can be increased by two orders of magnitude before reaching the GaP damage threshold, and (2) we observe a quasi-linear relationship between the incident NIR pulse energy and the emitted THz amplitude, with a slight saturation onset only observed at the highest energies reached in our experiments.
2. Experiments
Figure 1 shows a diagram of the experiment apparatus for high-field THz generation in a GaP crystal. This crystal is patterned with a surface phase grating to efficiently diffract the incident NIR beam and enable tilted-pulse front phase-matching conditions [10,51]. The optical source is a commercial Yb:KGW regenerative amplifier system generating 265 fs pulses with a center wavelength of 1035 nm, a pulse energy of 1 mJ and a repetition rate of 3 kHz. The output laser beam is focused in air with a 1 m focal length lens. A 1 mm-thick BK7 window is placed before the focus to broaden the NIR spectrum from a bandwidth of 3.5 THz to 7.2 THz through self-phase modulation (SPM). The NIR spectra of the pulse before and after the BK7 window are shown in Fig. 1(a). The laser beam is then guided through a set of chirped mirrors, providing a total dispersion of -3000 fs2, to compensate for the positive dispersion in the SPM process and compress the pulse to ∼80 fs (FWHM) in the time domain. The autocorrelation traces of the NIR pulses before and after the BK7 window and chirped mirrors are shown in Fig. 1(b).
Fig. 1. (a) and (b) Spectra and corresponding autocorrelation traces of the NIR laser pulses measured at the laser output (black line) and after spectral broadening in BK7 and temporal compression with chirped mirrors (CMs) (red line). We observe a spectral broadening from 3.5 THz to 7.2 THz (FWHM) and a reduced pulse duration from 265 fs to 81 fs (FWHM). The reference frequency ν0 corresponds to the center wavelength of 1035 nm. (c) Schematic of the high-field THz setup. The focused NIR pulses are first passed through a 1 mm-thick BK7 window to broaden the spectrum by self-phase modulation. A THz-TDS scheme is then used to generate and detect THz radiation where the NIR generation beam is collimated onto the THz generation crystal. The germanium wafer (Ge) can be used to block the small (1.4%) residual fundamental NIR beam. The system is operated in a dry-air purged environment. Optical components to build the setup are labelled above as follows: L1: lens, f = 100 cm; L2: lens, f = 70 cm; CMs: -250 fs2 each; BS: beamsplitter; TS: translation stage; PG on 1 mm GaP: 110-oriented 1 mm-thick GaP crystal with a phase grating on the incident surface; Si: silicon wafer; PM: Parabolic mirror; 0.1 mm GaP: 110-oriented 0.1 mm-thick GaP crystal; L3: lens, f = 5 cm; λ/4: quarter-wave plate; WP: Wollaston prism; PD: photodetector.
The NIR beam in the first arm is collimated at normal incidence onto a 1 mm-thick 110-oriented GaP semiconductor crystal with a surface-etched phase grating [52] to enable efficient THz generation by optical rectification.This NIR beam has a 1/e2 diameter of 3.2 mm and a pulse energy of 0.57 mJ. The highly uniform grating with an average pitch of Λ = 1.60 µm yields first diffraction orders at angles of ±12° inside the GaP crystal. The standard deviation of this average grating pitch is measured to be ±0.03 µm. This configuration enables non-collinear phase-matching conditions leading to broadband THz generation from 0.5 to 6 THz with a geometry allowing both the incident NIR pulses and generated THz pulses to propagate along a direction normal to the crystal plane. In this geometry, the 1st order diffraction angle of the NIR pulse is also equal to its pulse-front-tilt angle [42]:
where ng(ωNIR) is the group index of the NIR generation beam centered at 1035 nm and n(ω4THz) is the phase index at 4 THz inside of the generation crystal. The grating filling ratio is 50%, and the target height modulation is 245 nm. This corresponds to an optical π-phase difference between optical light rays passing through the top and bottom sections of the grating, which reduces the 0th diffraction order because of destructive interference. In a transmission geometry, we measure a total of 44% of the incident power (87% of the total transmitted NIR power) in ±1 diffraction orders, while only 0.7% of the incident power (1.4% of the transmitted power) remains in the 0th diffraction order. Note that the presence of the grating also creates an effective index layer at the air-GaP interface reducing the Fresnel reflection coefficient by about 5% at the front crystal surface [52,53]. The presence of the grating on a 1 mm-thick GaP crystal increases the energy contained in the region between 2 and 3 THz by a factor of 4. The generated THz radiation is collected by an off-axis gold parabolic mirror PM1 in Fig. 1(c) with 1.27 cm diameter and a short (1.27 cm) focal length to minimize the spot size at the focus. The ±1st diffracted NIR beams leave the generation crystal with an exiting angle of 40°. Since these beams are not collected by PM1, this allows a sample to be positioned at the first THz focus to perform high-field experiments while the NIR background illumination remains relatively weak. In the same figure, the subsequent parabolic mirrors, with a 5.08 cm diameter and 5.08 cm focal length (PM2-PM5), are arranged in a standard terahertz time-domain spectroscopy (THz-TDS) configuration. The gating pulse in the second arm is first reflected by the Si wafer and then focused by the PM5 on a 0.1 mm-thick 110-oriented GaP detection crystal, overlapped with the focused THz transient to resolve the oscillating THz transient with electro-optical sampling (EOS) detection. The thin GaP detection crystal enables a broad detection bandwidth >6 THz.3. Results and discussion
Figure 2 shows the measured high-field THz transient and corresponding spectral amplitude, obtained with the Fourier transform. The spectral bandwidth extends up to 6.3 THz with a peak centered at 2.6 THz. The multi-cycle pulse is attributed to group velocity dispersion in the 1 mm-thick GaP generation crystal stretching the pulse in time. We evaluate the electric field strength of the THz pulse at the focus between PM1 and PM2 since this is a practical position to insert a sample in the setup. We evaluate the THz electric field ETHz with the following equation [54]:
Fig. 2. (a) Time-resolved high-field THz transient. The inset shows the corresponding spectral amplitude calculated with the Fourier transform. (b) THz spectral intensity (black curve) and noise floor (blue curve). The dashed blue line is the noise floor fitted with the model A*(1/f + B), considering the 1/f noise, where f is the frequency and both A and B are fitting parameters. The dynamic range (red curve) is calculated based on [61].
The dynamic range of our system reaches 80 dB at 2.6 THz and remains above 60 dB between 0.6 THz to 5.3 THz (Fig. 2(b)). We do not expect THz radiation to be generated at frequencies exceeding the range shown in Fig. 2(b) due to a drop in the second order nonlinear coefficient at 8 THz and a phonon absorption at 11 THz [62].This figure of merit is calculated by dividing the THz spectral intensity by the noise floor, which is measured by blocking the THz beam and then fitted to a model A*(1/f + B), where f is the frequency, and A and B are fitting parameters [61].
To confirm the THz field strength, we also measure the THz power with a thermal detector. A Golay cell, calibrated using a blackbody source, measures a power corresponding to a THz pulse energy of 2.8 nJ immediately after the detection crystal since the space after PM1 in our setup is too small to accommodate the Golay cell or a mirror able to deflect the beam. Considering the Fresnel transmission coefficients of all optical components between the Golay cell placed after the GaP detection crystal and THz focus located between PM1 and PM2, the pulse energy at that position corresponds to 41.1 nJ. Based on this value, the conversion efficiency from the diffracted NIR beam to THz radiation is relatively low (0.023%), but could be improved with an anti-reflection coating and an optimized grating design [63]. We then calculate the peak THz field strength based on this Golay cell measurement. First, we use the time-resolved THz transient and consider the highest THz half cycle containing 45% of the full pulse energy to extract a precise value of the THz peak electric field [60]. The peak intensity of the highest THz half cycle can be calculated by
Finally, we look into the possibility to combine our configuration with a more powerful NIR source to achieve even higher THz peak fields. We first determine the crystal damage threshold to the incident NIR pulse, which is a critical parameter to allow the use of higher pulse energies. We perform this test at a wavelength of 1035 nm and a repetition rate of 50 kHz by placing a non-patterned and patterned GaP window at the focus of a 15 cm lens. For both samples, we only notice visible damage on the crystal accompanied by an abrupt drop in the generated THz signal when the incident power exceeds 0.8 W, which corresponds to a peak fluence of 5.6 J/cm2. For comparison purposes, the highest peak fluence used in this work is 14.2 mJ/cm2, which is a factor of 400 lower than this damage threshold. These results indicate that it is indeed possible to significantly increase the incident NIR pulse energy to enable the generation of higher THz peak fields. We also investigate the dependence of the THz peak field $E_{THz}^{Peak} $ as a function of the NIR generation peak fluence FNIR. Figure 3(a) shows the THz signal as FNIR is varied from 1.5 mJ/cm2 to 14.2 mJ/cm2 while keeping the same NIR spot size on the generation crystal. The experimental results are displayed along with two simple models: (1) a linear relationship (red dashed line) fitting the data collected at low fluence <5.1 mJ/cm2: $E_{THz}^{Peak}$ = aFNIR, where the slope a = 27.5 kV cm mJ-1 is related to the conversion efficiency, and (2) a modification of the first model (blue dashed curve): $E_{THz}^{Peak}$ = aFNIR / (1 + bFNIR), where a is the same as that in the first model, and b = 0.024 mJ-1 cm2 accounts for saturation effects, which can be caused by multiple-photon absorption [10] and thermal effects [65]. We observe that the generated THz peak amplitude is linear with FNIR until 5.1 mJ/cm2. The observation of a saturation onset at this NIR fluence is consistent with previous work using an unpatterned GaP crystal [66]. Figure 3(b) shows THz spectra generated with different NIR incident pulse energies, which all peak at 2.6 THz. However, we observe a gradual decrease of the THz spectral amplitude around 3.5 THz as FNIR increases from 1.5 mJ/cm2 to 4.4 mJ/cm2. Similar THz spectral changes at high FNIR have also been observed previously [67], but further investigation is still required to fully understand this effect. Considering our saturation model and the fact that FNIR can be significantly increased without inducing damage to the crystal, we can anticipate that a NIR peak fluence of 124 mJ/cm2, corresponding to a NIR pulse energy of 5 mJ with the same beam size, will produce a THz peak field of 866 kV/cm with a spectrum also centered at 2.6 THz.
Fig. 3. (a) Measured THz peak electric field $E_{THz}^{Peak}$ strength versus NIR peak fluence FNIR. The red dashed line is a linear fit while the blue dashed line corresponds to a saturation model: aFNIR /(1 + bFNIR), where both a and b are fitting parameters. (b) Corresponding THz spectra measured with NIR generation pulses with different NIR peak fluence. We normalize these measurements to the maximum amplitude obtained with a 14.2 mJ/cm2 NIR peak fluence.
4. Conclusion
We demonstrate a high-field THz system using collimated NIR pulses impinging on a GaP crystal with a surface phase grating to generate pulses with 303 kV/cm peak field centered at 2.6 THz. This peak field is confirmed by measurements performed with a calibrated Golay cell. We also show that our system operates significantly below the GaP damage threshold and close to a linear regime, allowing more powerful NIR sources to produce even higher peak fields approaching 1 MV/cm. Note that increasing the NIR beam size on the generation crystal allows the use of higher pulse energies without damaging the crystal, hence resulting in larger THz powers. A laser source at a longer wavelength could also be used to reduce the multi-photon absorption processes in GaP, which may help to reduce saturation effects observed in the THz generation process as well as increase the crystal damage threshold. Considering a tilted-pulse-front configuration with an optimal grating design, this latter approach could, according to numerical models, produce peak fields reaching up to 17 MV/cm at a central frequency of 3 THz [47]. Finally, although our experiment focuses exclusively on GaP as the THz generation crystal, the same optical configuration could be used to generate high-field THz in other materials with a surface phase grating to gain access to different spectral ranges or to increase THz generation efficiencies. This work will pave the way towards a new class of high-field THz sources able to access a spectral range departing from the conventional region below 2 THz and will enable novel nonlinear and coherent control experiments in condensed matter systems.
Funding
Ontario Ministry of Colleges and Universities (ER21-16-206); National Research Council Canada (HTSN-702, JCEP); Natural Sciences and Engineering Research Council of Canada (RGPIN-2016-04797, RGPIN-2023-05365); Canada Foundation for Innovation (Project Number 35269).
Acknowledgments
We thank R. Huber for helpful discussions. This work was supported by the High Throughput and Secure Networks Challenge Program at the National Research Council of Canada (HTSN-702), the NSERC Discovery funding program (RGPIN-2016-04797, RGPIN-2023-05365), the Canada Foundation for Innovation (CFI) (Project Number 35269), the Ontario Ministry of Colleges and Universities’ Early Researcher Award (ER21-16-206) and the National Research Council of Canada via the Joint Centre for Extreme Photonics (JCEP).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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