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Abstract
Optical rectification is experimentally investigated in a biaxial BaGa4Se7 crystal by considering various combinations of near-infrared excitation polarizations and crystal orientations. The highest terahertz radiation is produced along the Z crystallo-physical direction of the BaGa4Se7 crystal. Despite the optical complexity of the BaGa4Se7 crystal in the terahertz spectral regime, this systematic experimental investigation determines the optimal excitation polarization and crystal orientation for the optical rectification process.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radiation generation via optical rectification has been demonstrated in crystals having various point group symmetries, such as $3m$ crystals (e.g. LiNbO3, LiTaO3 [1,2]), $\bar{4}3m$ crystals (e.g. ZnTe, GaAs [3,4]), and $\bar{4}2m$ crystals (e.g. CdSiP2, ZnGeP2, AgGaSe2 [5,6]). However, crystals having m point group symmetry, consisting of three principal axes and two optic axes, have received less attention simply because of their complex crystal structure. Such inherent biaxial anisotropy makes the optical rectification process highly complex by influencing both the excitation [i.e. near-infrared (IR)] frequency components and the generated THz frequency components. Herein, the near-IR frequency components propagate as linearly-polarized eigenmodes in these biaxial crystal, and the generated THz frequency components propagate as elliptically-polarized eigenmodes [7]. Clearly, an accurate mathematical model involving the decomposition into elliptically-polarized eigenmodes is a challenging task, such that a systematic experimental analysis provides the most direct and informative procedure for investigating this frequency-conversion process.
It is crucial to consider the interaction between the excitation pulse and the BaGa4Se7 crystal. The wide transparency range of this crystal (i.e. 0.776-14.7 µm [8]) allows for excitation pulses produced using various laser sources. Additionally, the crystal’s wide bandgap of 2.64 eV results in a laser induced damage threshold that is higher than that of other nonlinear crystals (e.g. AgGaS2, AgGaSe2, etc. [8]). In regard to nonlinear characteristics, the m point group BaGa4Se7 crystal has recently been introduced as a mid-IR radiation source, exhibiting the high conversion efficiency of ∼19% [9]. This is largely due to the BaG4Se7 crystal’s high second order nonlinear coefficient, ${d^{(2 )}}({\Omega } )$ [9], which depends on the generation frequency, ${\Omega }$ [10]. Despite its frequency-dependent nature, a high ${d^{(2 )}}({\Omega } )$ in the mid-IR region indicates the potential for a high ${d^{(2 )}}({\Omega } )$ in the THz frequency regime. Advantageously, ${d^{(2 )}}({\Omega } )$ is often higher in the THz frequency regime in comparison to the mid-IR regime, due to enhancement from phonon resonances [10]. In certain frequency bands, phonon mode absorption loss dominates ${d^{(2 )}}({\Omega } )$ enhancement, thus suppressing THz radiation generation. However, in other frequency bands, ${d^{(2 )}}({\Omega } )$ enhancement dominates phonon mode absorption loss, thus improving THz radiation generation. Although numerous phonon modes are located within the low THz frequency range (i.e. >20 phonon modes located at frequencies <4 THz [11]), narrow transmission bands exist at ∼2 and 2.3 THz [7]. At these frequencies, absorption losses are low and ${d^{(2 )}}({\Omega } )$ is expected to be high, thus potentially permitting narrowband THz radiation generation via the process of optical rectification. Interestingly, narrowband THz radiation is essential for nonlinear spectroscopy, where the spectral resolution is improved by the narrow linewidth [12], and narrowband THz radiation is used to accelerate or decelerate free space electron beams [13].
Here, we investigate optical rectification in the biaxial BaGa4Se7 crystal for various combinations of near-IR excitation polarizations and crystal orientations. Optimal THz radiation generation is observed having a polarization oriented along the Z crystallo-physical direction of the BaGa4Se7 crystal, independent of the near-IR excitation polarization. Therefore, although the biaxial BaGa4Se7 crystal is optically complex in the THz frequency regime, the performed systematic experimental investigation determines the optimal near-IR excitation polarizations and crystal orientations for optical rectification THz radiation generation.
2. Optical properties of the BaGa4Se7 crystal and experimental arrangement
Optical rectification experiments are performed using a 500 µm thick <010>-cut BaGa4Se7 crystal grown using the horizontal gradient freeze method [14]. Due to the numerous low-frequency phonon modes inherent to this crystal [11], natural THz transmission bands having the central frequencies of ∼2 and 2.3 THz are present [7]. Therefore, for optical rectification, narrowband THz radiation generation is expected to occur centered at these frequencies, provided that the phase-matching condition is satisfied. For the BaGa4Se7 crystal, the second-order nonlinear polarization tensor is [15],
Figure 1(a) shows a schematic of the experimental arrangement used to excite the BaGa4Se7 crystal defined with respect to the reference coordinates xr, yr, and zr. Here, the near-IR excitation electric field, ${\vec{E}_{exc}}$, has a linear-polarization defined by the angle θ and the BaGa4Se7 crystal angular orientation is denoted by the angle α. A THz wire grid polarizer, used to select the polarization component of the generated THz radiation, is set up to have its transmission axis fixed along the zr-direction. This arrangement ensures that well-defined linearly-polarized THz radiation, ${\vec{E}_{THz}}$, is incident on a fixed-orientation 500 µm-thick ZnTe electro-optic (EO) crystal. The unit cell of the BaGa4Se7 crystal is illustrated in Fig. 1(b), which shows ${\vec{E}_{exc}}$ and ${\vec{E}_{THz}}$ relative to the crystal orientation, as represented by its crystallo-graphic coordinates [16,17].
Fig. 1. (a) Schematic showing the setup implemented to perform optical rectification THz radiation generation experiments using the BaGa4Se7 crystal. xr, yr, and zr define the reference coordinates. (b) An illustration of a BaGa4Se7 crystal unit cell. The near-IR excitation electric field, ${\vec{E}_{exc}}$, and the generated terahertz radiation electric field, ${\vec{E}_{THz}}$, polarizations are shown with respect to the crystal orientation.
3. Experimental results
Optical rectification experiments are conducted by focusing a 5.1 MHz Ti:sapphire laser pulse onto the BaGa4Se7 crystal, where the excitation pulse has a duration of 50 fs, a central wavelength of 800 nm, and an average power of 24 mW. The laser beam spot size is 590 µm, corresponding to a peak intensity of 34 MW/cm2, at the input face of the BaGa4Se7 crystal. Since the optical rectification process strongly depends on the polarization of ${\vec{E}_{exc}}$ and the crystal orientation, this nonlinear phenomenon is investigated for various angles of θ and α [see Fig. 1(a)]. Optical rectification measurements are performed for an ${\vec{E}_{exc}}$ oriented along the X-direction of the BaGa4Se7 crystal (i.e. α=θ). As displayed in Fig. 2(a), the maximum ${\vec{E}_{THz}}$ is measured when the crystal’s Z-direction is aligned with the transmission axis of the wire grid polarizer (i.e. θ=0°) and ${\vec{E}_{THz}}$ is nearly zero when the crystal’s X-direction is aligned along the transmission axis (i.e. θ=90°). A close examination of the ${\vec{E}_{THz}}$ time-domain signals indicates evidence of frequency beating. As shown from the power spectra in Fig. 2(b), this is as a result of frequency beating between two narrowband (i.e. 50 GHz linewidth) ${\vec{E}_{THz}}$ fields generated at 1.97 and 2.34 THz. Notably, these generation frequencies can be used to calculate the beating period of the time domain signal as |2.34 THz-1.97 THz|-1=2.7 ps, which agrees with the beating period seen in Fig. 2(a). Additionally, the spectral power generated along the Z crystallo-physical direction (i.e. θ=0°) is ∼14 times higher than the spectral power generated along the X crystallo-physical direction (i.e. θ=90°), such that the generated THz radiation has a polarization ratio of 14:1. The peak spectral powers at 1.97 and 2.34 THz are displayed in Fig. 2(c) for the various excitation angles. When θ≈90°, THz radiation generation is influenced by the combination of the d11 nonlinear coefficient [see Eq. (2)] and phase-matching between the X-polarized ${\vec{E}_{exc}}$ pulse and the X-polarized ${\vec{E}_{THz}}$ pulse. However, when θ≈0°, THz radiation generation is influenced by the combination of the d31 nonlinear coefficient [see Eq. (3)] and phase-matching between the X-polarized ${\vec{E}_{exc}}$ pulse and the Z-polarized ${\vec{E}_{THz}}$ pulse. Clearly, the latter combination proves to be optimal, since the highest spectral powers are measured at θ=0° and 22.5°. At these angles, generation at 2.34 THz is >20% higher than generation at 1.97 THz.
Fig. 2. (a) Time-domain THz signals generated by exciting the BaGa4Se7 crystal along its X-direction (i.e. α=θ) and (b) the corresponding spectral power. (c) Spectral powers at the frequencies of 1.97 and 2.34 THz as a function of θ. The inset shows an illustrative representation of the orientations of ${\vec{E}_{exc}}$ and ${\vec{E}_{THz}}$ with respect to the X, Z, xr, and zr axes. Here, the excitation polarization and crystal orientation are fixed using the relationship of α=θ.
Optical rectification is investigated for ${\vec{E}_{exc}}$ polarized along the Z-direction of the BaGa4Se7 crystal (i.e. α=θ+90°), as illustrated in the inset in Fig. 3(c). The generated THz radiation time-domain signals are shown in Fig. 3(a), whereas the associated power spectra are presented in Fig. 3(b). The THz time-domain pulses exhibit a nearly monotonic decay with a characteristic time of approximately 10 ps. The peak spectral powers at various angles show a strong narrowband (i.e. 50 GHz linewidth) frequency component at 1.97 THz and a weak one at 2.34 THz, such that narrowband generation occurs mainly at the frequency of 1.97 THz. As expected, the measured decay time agrees with the measured linewidth via the theoretical relationship [i.e. (2×10 ps)-1≈50 GHz]. Additionally, the spectral power generated along the Z crystallo-physical direction (i.e. θ=90°) is ∼15 times higher than the spectral power generated along the X crystallo-physical direction (i.e. θ=0°), such that the generated THz radiation has a polarization ratio of 15:1. The peak spectral powers at the frequencies of 1.97 and 2.34 THz are shown in Fig. 3(c) for the various excitation angles. When θ≈0°, THz radiation generation is influenced by the combination of the d13 nonlinear coefficient [see Eq. (2)] and phase-matching between the Z-polarized ${\vec{E}_{exc}}$ pulse and the X-polarized ${\vec{E}_{THz}}$ pulse. However, when θ≈90°, THz radiation generation is influenced by the combination of the d33 nonlinear coefficient [see Eq. (3)] and phase-matching between the Z-polarized ${\vec{E}_{exc}}$ pulse and the Z-polarized ${\vec{E}_{THz}}$ pulse. The latter of these is the optimal combination, since the highest spectral powers are measured at θ=67.5° and 90°. For these angles, the generated 1.97 THz radiation is 13 times greater than that at 2.34 THz.
Fig. 3. (a) Time-domain THz signals generated by exciting the BaGa4Se7 crystal along its Z-direction (i.e. α=θ+90°) and (b) the corresponding power spectra. (c) Spectral powers at the frequencies of 1.97 and 2.34 THz as a function of θ. The inset shows the illustrative representation of the orientations of ${\vec{E}_{exc}}$ and ${\vec{E}_{THz}}$ with respect to the X, Z, xr, and zr axes. Here, the excitation polarization and crystal orientation are fixed using the relationship of α=θ+90°.
Optical rectification experiments are performed to investigate THz radiation generation when the crystal’s X-direction is oriented along the wire grid polarizer’s transmission axis (i.e. α=90°), as shown in the inset of Fig. 4(c). The time-domain signals, power spectra, and peak spectral powers at 1.97 and 2.34 THz are displayed in Figs. 4(a), 4(b), and 4(c), respectively. Clearly, THz radiation generation is weak, where the highest spectral power in Fig. 4(c) is 0.17 and 0.04 times the highest spectral power in Figs. 2(c) and 3(c), respectively.
Fig. 4. (a) Time-domain THz signals when the X-direction of the BaGa4Se7 crystal is oriented along the transmission axis of the wire grid polarizer (i.e. α=90°) and (b) the corresponding power spectra. (c) Spectral powers at the frequencies of 1.97 and 2.34 THz as a function of θ. The inset shows the illustrative representation of the orientations of ${\vec{E}_{exc}}$ and ${\vec{E}_{THz}}$ with respect to the X, Z, xr, and zr axes for α=90°.
Optical rectification is investigated when the crystal’s Z-direction is oriented along the wire grid polarizer’s transmission axis (i.e. α=0°), as depicted in the inset of Fig. 5(c). The generated THz time-domain signals are shown in Fig. 5(a) and the associated power spectra are presented in Fig. 5(b). Interestingly, ${\vec{E}_{exc}}$ can be used as a means to control the relative strength between the narrowband peaks at 1.97 and 2.34 THz. Here, when ${\vec{E}_{exc}}$ is oriented along the crystal’s Z-direction (i.e. θ=90°), narrowband generation occurs primarily at 1.97 THz, since the spectral power at this frequency is 15 times higher than that at 2.34 THz. By altering θ, the peak spectral power at 2.34 THz increases at the expense of the peak spectral power observed at 1.97 THz. When ${\vec{E}_{exc}}$ is oriented along the X-direction of the crystal (i.e. θ=0°), the peak spectral power at 2.34 THz is 1.5 times larger than the peak spectral power at 1.97 THz. Figure 5(c) shows the peak spectral powers at 1.97 and 2.34 THz, depicting this dependence on the polarization angle.
Fig. 5. (a) Time-domain THz signals when the Z-direction of the BaGa4Se7 crystal is oriented along the transmission axis of the wire grid polarizer (i.e. α=0°) and (b) the corresponding power spectra. (c) Spectral powers at the frequencies of 1.97 and 2.34 THz as a function of θ. The inset shows the illustrative representation of the orientations of ${\vec{E}_{exc}}$ and ${\vec{E}_{THz}}$ with respect to the X, Z, xr, and zr axes for α=0°.
4. Summary
Optical rectification experiments are conducted to investigate THz radiation generation in a BaGa4Se7 crystal at various near-IR excitation polarizations and crystal orientations. The strongest THz radiation generation is observed having a polarization along the Z crystallo-physical direction of the BaGa4Se7 crystal. As such, by systematically considering various combinations of near-IR excitation polarizations and crystal orientations, the optimal experimental arrangements are determined for THz radiation generation via optical rectification in the BaGa4Se7 crystal. Other BaGa4Se7 crystal thicknesses and cut orientations could be investigated, which would allow for a detailed analysis pertaining to optical rectification phase-matching. Future studies could also focus on thermal cooling of the BaGa4Se7 crystal, which has the potential to reduce the phonon mode absorption losses and allow for a controlled shift of the narrowband THz radiation generation frequencies. Additionally, the ∼4-5 THz frequency region of the BaGa4Se7 crystal does not support phonon modes but may still exhibit high second-order nonlinear coefficient magnitudes [11], such that a high-frequency detection arrangement should be implemented to investigate the crystal for THz radiation generation in this spectral band.
Funding
Natural Sciences and Engineering Research Council of Canada.
Disclosures
The authors declare no conflicts of interest.
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