Linear optical properties of ZnGeP<sub>2</sub> in the terahertz range

Kai Zhong; Chu Liu; Maorong Wang; Jie Shi; Bin Kang; Zerui Yuan; Jining Li; Degang Xu; Wei Shi; Jianquan Yao

doi:10.1364/OME.7.003571

1. Introduction

The positive uniaxial chalcopyrite crystal zinc germanium phosphide (ZnGeP₂ or ZGP) is a tetragonal crystalline structure with $\bar{4} 2 m$ point group [1]. It has suitable birefringence for phase matching, excellent optical, mechanical and thermal properties as well as relatively high laser damage threshold. The nonlinear optical figure of merit d_eff²/n³ for ZGP is much higher than most of the other infrared (IR) crystals like GaSe, GaP and GaAs [2]. Besides the wide transparent range from 0.74 to 12 μm, ZGP has low absorption coefficient in the terahertz (THz) range, making it a popular material in generating and detecting THz radiation. Recently, continuously widely tunable monochromatic THz waves were obtained from phase-matched difference frequency generation (DFG) in ZGP [3,4], and the milestone maximum average output power reached 2 mW [5]. ZGP crystals were also utilized for broadband THz pulse generation pumped by near-IR femtosecond lasers based on collinear phase-matched optical rectification showing conspicuous advantages than the other nonlinear materials [6,7], like lower nonlinear absorption, larger second-order nonlinearity, smaller velocity mismatch in the near-IR and lower free-carrier absorption below 3 THz. The electro-optic detection capabilities of ZGP crystals was studied in the THz frequency regime demonstrating much larger PM bandwidths than the commonly used ZnTe, ZnSe and GaP crystals [8].

Direct THz applications of ZGP requires detailed knowledge of its properties in this range. However, the optical properties of ZGP in the THz range are still not well studied compared with that in the near- and mid-IR ranges [9,10]. There are few references that can be found to acquire or conclude the THz behavior of ZGP except a few reports on its Raman and IR spectra. With the development of THz technology, the THz time-domain spectroscopy (TDS) can provide us a powerful tool to measure the THz properties like refractive indices, absorption coefficients and study the low-frequency optical phonon resonances [11–13]. As an effective complement, the conventional Fourier transform infrared spectroscopy (FTIR) extends the measurement range to mid- and far-IR, covering the blind band of TDS beyond 3–4 THz.

In this paper, we investigate and make the first comparison on the optical properties in the THz range of ZGP crystals grown by two methods: the horizontal gradient freezing (HGF) and vertical gradient freezing (VGF) techniques. The birefringence and the absorption coefficients of the ZGP samples was measured in the frequency range of 0.2–3.4 THz based on TDS. The experimental results show that ZGP has a high transmittance and a moderate birefringence over a wide THz range, good for THz applications below 3 THz. The difference of birefringence and absorption coefficients for both HGF and VGF grown crystals was observed and discussed. A FTIR system was also adopted to measure the optical properties from 1 THz to 6 THz, uncovering the obvious absorption bands locating at the 3–6 THz region relating to different phonon modes in different polarizations.

2. Sample details and the experimental schemes

The ZGP single crystals were grown with both HGF and VGF techniques under the same conditions (the same synthesized polycrystalline and similar freezing gradient) by the coauthors (Affiliations 3 and 4). Earlier representative ZGP growth with both techniques were reported by Verozubova et al. and Zawilski et al. in [14] and [15], respectively. The detailed growth and optical properties of our crystals in the near- and mid-IR regions were demonstrated in [16] and [17], showing that the absorption coefficient of the HGF grown ZGP crystals was lower than 0.01 cm^–1 in a wide range of 3–8 μm and lower than 0.03 cm^–1 at 2 μm, while the two values were 0.02 cm⁻¹ and 0.04 cm⁻¹ for the VGF grown crystals. That is, the crystal quality of HGF grown ZGP crystal was better, which was also indicated in [15]. The optical-optical conversion efficiency from 2 μm to 3–5 μm for the HGF grown crystal reached 56.2% [17]. In this study, we focused on investigating the optical properties of ZGP in the THz range and compared their difference for both growing techniques. For this purpose, (100) and (001) ZGP samples were prepared, cut and polished into 10 mm × 10 mm apertures with 1.24–1.30 mm thickness. The polarization of the THz beam was designed to be consistent with the crystalline principal axes (o-polarized beam was along the x or y axes, and e-polarized beam was along the z axis in the following text).

A compact commercial THz TDS (TAS7500, Advantest Corp.) with high-speed optical sampling was employed to measure the samples in the low frequency range. The schematic diagram under transmission mode is shown in Fig. 1(a). It had two synchronously controlled femtosecond fiber lasers at 1550 nm with 50-mW average output power for THz generation and detection. Compared with mechanical delay line, the optical sampling technique enables a much higher sampling rate of 8 ms per scan at a frequency resolution of 7.6 GHz. The whole system including the sample chamber was integrated and purged by flowing dry air to eliminate the water vapor absorption. The maximum signal-to-noise ratio (SNR) reached over 40 dB averaged by 2048 times per measurement.

Fig. 1 Schematic diagrams of the measurement systems: (a) THz TDS with high-speed optical sampling; (b) FTIR in Michelson interferometer mode.

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Although TDS has a high SNR and is able to characterize the complete electric field of a THz pulse with full phase and amplitude information directly giving the complex dielectric function of a sample, the effective frequency range of TDS is usually below 3 THz. FTIR can be a good supplement to TDS as its strongest spectrum emitted by a mercury lamp or globar locates at the mid- to far-IR, or in other words, the high-frequency THz part. Here we used a roof-mirror FTIR (SPS-300, Sciencetech Inc [18].) working in Michelson interferometer mode with the schematic diagram shown in Fig. 1(b). The effective spectrum range was 0.5-7.5 THz in the THz region limited by the beam splitter. The resolution was set to be 0.4 cm⁻¹ considering a reasonable scanning time of the moveable mirror and the internal memory of the computer. A wire grid polarizer (Microtech Instruments Inc.) positioned before the sample assured polarized measurement. The SNR of the interferogram was over 30 dB after averaging 10 times with a 4.2-K Si bolometer detector. Although FTIR gave the intensity measurement only, we could obtain the refractive index of the plane parallel ZGP samples from the etalon interference fringes in simple transmission spectroscopy and then the absorption coefficients were straightforward from the Fresnel equations [19].

3. TDS measurement and discussion

The time-domain signal and the spectrum after Fourier transform for (100) samples grown by both techniques are shown in Fig. 2(a) and Fig. 2(b), where the corresponding references are also given. Clearly the time-domain THz signal after both samples in both polarizations demonstrated similar pulse waveforms to the reference with only decreased intensities, from which smooth absorption spectra could be expected in the effective range. However, the time delays were quite different: First, for each sample the e-polarized beam had a longer time delay thus the group refractive index should be higher than the o-wave, which was coincident with the properties of positive uniaxial crystals. Second, the time-delay difference between o- and e-polarized beams for the VGF grown crystal was obviously larger than the other one, which stood for a larger birefringence in this region. Considering the thickness was 1.240 mm and 1.290 mm for the HGF and VGF grown samples, the group birefringence for both samples with different growing methods were 0.019 and 0.033, respectively. There was almost no distinguishable difference in the frequency-domain spectra for both samples, so little useful information was available. The actual dispersion in the THz band for both polarizations should be given after a strict theoretical calculation.

Fig. 2 Time-domain signal and Fourier transformed frequency-domain spectra for (100) samples: (a) HGF grown crystal; (b) VGF grown crystal.

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As a great advantage of TDS, the complex refractive index of the sample $\hat{n} = n + i κ$ consisting of the refractive index n and the extinction coefficient κ can be obtained from the complex transmission coefficient, the ratio of the Fourier transforms of the THz time-domain signal with ( $E_{sam} (ω)$ ) and without ( $E_{ref} (ω)$ ) the sample [20]. If $\frac{E_{sam} (ω)}{E_{ref} (ω)} = A e^{i ϕ}$ , the refractive index is extracted from the phase $ϕ$ :

n = n (ω) = 1 + \frac{ϕ c}{ω d}

where c is the light speed in vacuum and d is the sample thickness. The complex index κ can be deduced from the complex amplitude A:

κ (ω) = - \frac{c}{ω d} l n [\frac{{(n (ω) + 1)}^{2}}{4 n (ω)} A]

Then the absorption coefficient α is expressed as:

α (ω) = 2 \frac{κ (ω) ω}{c} = - \frac{2}{d} l n [\frac{{(n (ω) + 1)}^{2}}{4 n (ω)} A]

Calculated with the theories above, the refractive indices and absorption coefficients of the o- and e-polarized beam for the (100) samples grown by HGF and VGF techniques are shown in Fig. 3 (a) and Fig. 3(b), respectively. As there were no obvious low-frequency phonons, the refractive indices demonstrated smooth curves. Just like what we had estimated from the time-domain signal, the birefringence of the VGF grown sample was obviously larger than the HGF grown one (e.g., at 1.5 THz the birefringence of the VGF grown crystal was 0.034 and it was 0.021 for the HFG grown one). This should be caused by the different crystalizing condition, which induced different strain in equivalent planes. To test the applicability of available empirical fitted IR Sellmeier equations of ZGP in the THz range, we also made comparisons between the experimental and theoretical results, one of which was calculated from the Sellmeier equations given in [21] and shown in Fig. 3(a). The calculated values were close but not exactly equal to the true values, thus phase-matching predictions in THz generation could only be a reference and couldn’t precisely reflect the real condition, which explained the discrepancy between experimental and theoretical results in [3]. Another reference gave good prediction of refractive indices from 2 μm to 9 μm [10], but it totally lost the validity in THz range because the refractive index of o-wave would be larger than that of e-wave.

Fig. 3 TDS measurements of the (100) samples grown by HGF and VGF techniques: (a) Refractive indices; (b) Absorption coefficients.

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In the case of absorption coefficient, slow increase was observed below 2.2 THz, which should be attributed to the low-frequency wings of phonons at higher frequencies. It’s obvious that the HGF grown crystal had lower absorption than the VGF grown one, inheriting the advantage of better quality in the near- and mid-IR range for HGF technique. It should also be noted that the o-polarized THz wave had slightly higher absorption compared with the e-wave. The random oscillations above 2.2 THz was caused by the low SNR of TDS, thus only the data below 2.2 THz were regarded to be accurate.

The (001) ZGP wafers grown by two techniques were also measured with TDS, giving the results that both the refractive indices and absorption coefficients were the same to those of the o-wave in Fig. 3. It was reasonable because however we rotated the azimuthal angle of the sample all the polarizations kept in the crystalline xoy plane (or o-wave) for a (001) sample, equivalent for uniaxial crystals.

4. FTIR measurement and discussion

With respect to the intensity-only measurement from FTIR, the refractive index of a plane parallel plate of thickness d can be determined from the etalon-type interference fringes observable in simple transmission spectroscopy, applicable to TDS as well [19,22]. A typical interferogram and the directly Fourier transformed spectrum of a ZGP sample is shown in Fig. 4 (a) and Fig. 4(b). The spectrum without interference fringes in Fig. 4(b) was acquired by cutting off the minor peak in Fig. 4(a) before performing Fourier transform, giving the actual transmittance curve.

Fig. 4 Typical interferogram (a) and the Fourier transformed spectrum (b) of a ZGP sample.

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In Fig. 4(a), the minor peak was caused by multiple reflection when the scanning mirror moved another round trip inside the ZGP wafer over the main peak. Usually this minor peak was cut from the interferogram to get a smooth transmission curve, while here we had to use it to derive the optical coefficients. At a certain wavelength λ, the interference intensity is determined by optical path difference (OPD) between successive reflected or transmitted beams, so for normally incident wave $OPD = 2 n d$ . The refractive index n is related to λ through dispersion. As the light source of the FTIR is broadband, interference fringes appear in the transmittance spectra after Fourier transform, shown in Fig. 4(b). Constructive interference occurs when the OPDs are multiple of the wavelength λ. Two neighboring interference peaks in the frequency domain fulfils

2 n d = m λ_{1} = (m + 1) λ_{2}

where m is the interference order and the refractive indices at

λ_{1}

and

λ_{2}

have been regarded as the same. m and n can be solved with the given thickness d and wavelengths

λ_{1}

and

λ_{2}

. Extending this calculation to the whole range of fringes can we get all the refractive indices. Then the absorption coefficient can be obtained from Eq. (3), where the amplitude transmittance

A = \sqrt{T}

(T is the intensity transmittance). The problem for this method is that only the optical coefficients away from the absorption peaks can be obtained, where clear interference fringes are distinguished.

The transmission curves for (100) ZGP samples grown by HGF and VGF techniques are shown in Fig. 5(a) for comparison. Quite different to the low-frequency range, ZGP crystal demonstrated obvious anisotropic absorption in the 3–6-THz range. The o-polarized beam had an absorption peak locating at 4.26 THz (142 cm⁻¹), while absorption peak for the e-polarized beam located at 3.6 THz (120 cm⁻¹). The two peaks corresponded to different polar phonon modes. According to the Raman and IR reflection spectroscopy analysis [23,24], the 3.6 THz phonon mode was a B₂ mode and had symmetric vibration of the Ge and Zn atoms, polarized along the z direction. Whereas, the 4.26 THz phonon mode was an E mode and had antisymmetric vibration of the Ge and Zn atoms, polarized along the x or y direction. The phonon frequency and polarization accorded well with the calculated results reported before [25]. A (001) ZGP sample was also measured with the transmittance shown in Fig. 5(b). No matter how the orientation of the crystal was rotated around the optical axis, the transmitted spectrum kept unchanged, which verified that the 4.26 THz phonon mode was polarized in the xoy plane.

Fig. 5 FTIR measurements of ZGP transmittance grown by HGF and VGF techniques: (a) (100) samples (b) (001) samples.

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Based on the raw data measured with FTIR, the refractive indices and absorption coefficients for the (100) samples grown by HGF and VGF techniques are calculated and shown in Fig. 6(a) and Fig. 6(b), respectively. Considering the refractive-index extraction depends on the interference fringes shown in Fig. 4(b), it was impossible to process the data near the phonon frequencies. As an exception, the 4–5-THz transparent range for e-polarized incident beam was wide and good enough for optical-constant extraction, and it was shown that the refractive index had an obvious leap after the phonon mode at 3.6 THz. As to the 0.6–3.5 THz range, the value, variation and birefringence for both samples and polarizations were in good accordance with TDS measurement, presented more clearly by the data in Table 1. Considering the SNR and repeatability of both systems, the TDS measurements should be closer to the true values. On the other hand, there existed a great discrepancy on absorption coefficient between two systems because of the weakness of FTIR, thus the FTIR absorption measurements were more qualitative than quantitative. The detailed frequency dependence of the refractive index and absorption coefficient beyond the reach of measurement facilities could be calculated with a damped multi-harmonic oscillator model

ε (v) = ε_{\infty} + \sum_{i = 1}^{n} \frac{s_{i} v_{i}^{2}}{v_{i}^{2} - v^{2} + i γ_{i} v}

ε^{2} (ν) = \hat{n} = n (ν) + i κ (ν)

if the high-frequency dielectric constant

ε_{\infty}

and all the parameters for the i-th transverse optical phonon mode including oscillating strength

s_{i}

, oscillating frequency

v_{i}

, and damping coefficient

γ_{i}

are given. Although data are not sufficient at present, we can conclude that obvious peaks should exist in the refractive index and absorption coefficient curves at the phonon frequencies, a common behavior for most of the nonlinear materials.

Fig. 6 Refractive index (a) and absorption coefficient (b) for (100) samples grown by HGF and VGF techniques measured by FTIR.

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Table 1. Comparison of measured refractive index and birefringence of HGF and VGF grown crystals by TDS and FTIR.

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It was noteworthy that the e-polarized THz wave had a wide low-absorption band around 4–5 THz, while the absorption coefficient of o-polarized THz wave went up through the phonon frequency at 4.26 THz and then a narrow transparent band emerged. Therefore, generating e-polarized THz beam should be more advantageous in tunability expanding. On the other hand, the anomalous dispersion from optical frequency to THz provided a large difference on refractive index, thus the relatively small THz birefringence had minor impact on phase-matching condition. Therefore, either o- or e-polarized THz beam can be generated, which was verified in [3]. On the basis of the TDS measurements on absorption coefficients, phase-matched e-polarized THz generation should be a much better option with lower absorption loss.

5. Conclusion

For the first time, we presented the experimental comparison of optical properties in the THz frequency band from 0.2 to 6 THz on ZGP crystals grown by two commonly used techniques: HGF and VGF. The refractive indices and the absorption coefficients were quantitatively measured with TDS and FTIR. It was shown that ZGP had no obvious phonon mode in the 0.2–3 THz band and had two strong polar phonon modes at 3.6 THz and 4.26 THz, respectively. The HGF grown ZGP crystals had smaller birefringence than the VGF grown ZGP crystals, and more importantly, the HGF grown crystals had smaller absorption due to its better temperature and stress control during crystallization, a good advantage in THz applications. It was also observed that the e-polarized THz wave along the z-axis had lower absorption and broader transparent range than the o-polarized wave, thus e-polarized THz wave was more favorable in THz generation. All the measurements had good consistency with previously reported theoretical, Raman/IR spectroscopic analysis and actual ZGP applications in the THz range.

Funding

National Basic Research Program of China (2014CB339802); National Natural Science Foundation of China (NSFC) (61675146); Science and Technology Support Program of Tianjin (14ZCZDGX00030); Open Fund of State Key Laboratory of Crystal Materials, Shandong University (KF1505).

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Frequency (THz)	HGF(TDS/FTIR)			VGF(TDS/FTIR)
Frequency (THz)	n _o	n _e	n_e–n_o	n _o	n _e	n_e–n_o
0.7	3.392/3.375	3.413/3.400	0.021/0.025	3.385/3.365	3.419/3.412	0.034/0.047
1.5	3.398/3.376	3.419/3.405	0.021/0.029	3.391/3.366	3.425/3.415	0.034/0.049
2.2	3.406/3.387	3.425/3.411	0.019/0.024	3.400/3.373	3.430/3.422	0.030/0.049
3.0	3.423/3.402	3.439/3.426	0.016/0.024	3.415/3.388	3.445/3.438	0.030/0.050

Linear optical properties of ZnGeP₂ in the terahertz range

Abstract

1. Introduction

2. Sample details and the experimental schemes

3. TDS measurement and discussion

4. FTIR measurement and discussion

5. Conclusion

Funding

References and links

Cited By

Figures (6)

Tables (1)

Equations (6)

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