Terahertz Generation by Optical Rectification of 780 nm Laser Pulses in Pure and Sc-Doped ZnGeP₂ Crystals

Abstract

Terahertz wave generation through the optical rectification of 780 nm femtosecond laser pulses in ZnGeP₂ crystals has been studied. All of the possible interactions of types I and II were analyzed by modeling and experimentally. We demonstrate the possibility of broadband “low-frequency” terahertz generation by an ee–e interaction (with two pumping waves and a generated terahertz wave; all of these had extraordinary polarization in the crystal) and “high-frequency” terahertz generation by an oe–e interaction. The arising possibility of achieving the narrowing of the terahertz generation bandwidth at the oe–e interaction using thicker ZnGeP₂ crystals is experimentally confirmed. It has been found that the thermal annealing of as-grown ZnGeP₂ crystals and their doping with a 0.01 mass % of Sc reduces the absorption in the “anomalous absorption” region (λ = 0.62–3 μm). The terahertz generation by the oo–e interaction in (110) ZnGeP₂:Sc and the as-grown ZnGeP₂ crystals of equal thicknesses was compared. It has been found that ZnGeP₂:Sc is more efficient for 780 nm femtosecond laser pulses optical rectification.

1. Introduction

ZnGeP₂ crystals with the chalcopyrite structure have been grown and used in nonlinear optics for 50 years [1,2,3]. It is known that this crystal has a high nonlinear susceptibility d₁₄ ≈ d₃₆ = 75 pm/V, a thermal conductivity of 0.35 W/(cm·K), a maximum transparency range of 3–8 µm (with α < 0.05 cm⁻¹ for the best samples), positive birefringence in the IR range n_e-n_o≈0.04, and high damage thresholds (up to 2–3 J/cm² for 30 ns pulses at λ = 2.05 μm for the best samples) [4,5]. To date, the development of the methods of synthesis [4,5,6] and the crystallization by the vertical Bridgman method [4,6] and the horizontal method of directed cooling [5] has led to the possibility of obtaining ZnGeP₂ ingots up to 50 mm in diameter and up to 140–200 mm in length.

Nevertheless, the development of growth technology for obtaining more perfect crystals with an enhanced damage threshold and a lower level of absorption in the wavelength range of 0.62–3 μm and in the terahertz range remains relevant. The crystals that are grown using modern technology have an anomalous absorption in the region of 0.62–3 μm with an absorption maximum about wavelength λ = 1 μm. This absorption is associated with the presence of point defects in the as-grown material [7]. Singly ionized zinc vacancies can act as such defects [4,5,7]. The use of thermal annealing or irradiation with high-energy electrons reduces the absorption in the ZnGeP₂ crystals [4]. Irradiation with high-energy electrons leads to the formation of radiation defects and the pinning of the Fermi level near the local electroneutrality level, which leads to the recharging of the acceptor levels and a decrease in their optical activity [7]. It is assumed [4] that irradiation leads to the motion of interstitial atoms and the formation of Frenkel complexes with acceptor defects. It is also supposed that ZnGeP₂ ingots of a large size contain fewer zinc vacancies because fewer volatile components, in particular zinc, are deposited on the walls of the ampoules during synthesis and crystallization [4,5]. To prevent the decomposition of the material, synthesis, as well as thermal annealing, is often carried out with the addition of ZnP₂, P, or ZnGeP₂ powders to the ampoule [8,9]. It is noted that optical damage occurs more often on the surface [4,5,10]. The value of the damage threshold strongly depends on the quality of the grown crystals and the polishing technology.

Currently, ZnGeP₂ crystals are mainly used to generate the harmonics of CO and CO₂ lasers and in optical parametric oscillators (OPO) with pumping at wavelengths of 2.05–2.94 μm and for the generation of radiation in the region of 3–10 μm. Such applications require crystals with a high damage threshold, large working aperture and low absorption in the 2–10 µm wavelength range. Another possible application of ZnGeP₂ crystals is the generation of terahertz radiation [11]. This requires crystals with a low absorption capacity in the given spectral range, and in the case of their generation by the optical rectification of femtosecond laser pulses, with a low dispersion of absorption coefficients [12,13]. To calculate the phase-matching conditions, it is important to know the wavelength dependences of the refractive indices for the ordinary and extraordinary waves. In this case, in contrast to the IR range, in which there are sufficiently reliable data for the spectral dependences of the refractive indices of ZnGeP₂ crystals [14], there are some contradictions in the published data in the terahertz frequency range [15,16]. In particular, it was found [8,15,16] that in the terahertz frequency range, the positive birefringence of ZnGeP₂ in the IR range is replaced by a negative one. Due to their optical properties, the ZnGeP₂ crystals are less advantageous for their application in the optical rectification of Ti:Sapphire laser radiation with λ = 750–850 nm. The majority of these studies have been devoted to the optical rectification of laser pulses with wavelengths of 1.1–2.4 μm. Additionally, a low birefringence capacity and a rather high difference between the optical group and terahertz refractive indices hampers the realization of phase-matching and high conversion efficiency expected for the material with high values for the components of the second-order nonlinear susceptibility tensor. To solve this problem in [17], a noncollinear scheme for optical rectification was proposed to maximize the θ (the angle between the laser wavevector and c-axis inside the crystal), and therefore, the effective nonlinearity for the oe–o and oe–e interactions. The optical rectification of laser pulses at wavelengths that were from 800 to 1550 nm was studied [18], and it was found that ZnGeP₂, having a rather high adsorption rate (17.88 cm⁻¹ @ 800 nm, 17.01 cm⁻¹ @ 1300 nm and 15.87 cm⁻¹ @ 1550 nm) is less efficient than the CdSiP₂ and CdGeP₂ crystals. One of the very few works where an 800 nm femtosecond pulse optical rectification in ZnGeP₂ was studied is [19], where also the electro-optical sampling of the terahertz transients in ZnGeP₂ was studied.

In the majority of cases for the 800 nm laser pulses, the optical rectification ZnGeP₂ crystals definitely lose to analogues such as GaSe, with the latter having a high transparency at both the terahertz and optical pump wavelengths, a high birefringence capacity and a large damage threshold for terahertz radiation [13,14]. Thus, the GaSe crystals are widely used in various terahertz and IR experiments, such as pump-probe schemes, terahertz and IR nanoscopy and spectroscopy [20]. The possible advantage of using ZnGeP₂ crystals could be the possibility to cut at phase-matching angles, their higher mechanical hardness and the availability of antireflection coatings. On the other hand, some experimental realizations of optical antireflection coatings on GaSe have been performed during the last few years [21,22]. High terahertz refractive indices for both GaSe and ZnGeP₂ and difficulties in producing the antireflection coatings for terahertz radiation using standard methods because of the required large thickness of the deposited films leads to high losses in the generated terahertz pulses.

The doping of nonlinear crystals is one of the ways to modify their transparency, mechanical properties, dispersion and nonlinearity [13,14]. The doping of ZnGeP₂ crystals for optical applications has not been studied intensively.

In the present work, we study the effect of thermal annealing and Sc doping on the optical transmission and refractive indices of ZnGeP₂ crystals in the optical and terahertz frequency range. Then terahertz generation through the optical rectification of 780 nm femtosecond laser pulses in these crystals is studied. All of the possible interactions of types I and II of nonlinear optical rectification have been studied both by modeling and by experiments. We find the advantageous interactions and phase-matching angles for (100) and (110) ZnGeP₂ crystals, taking into account the angular dependence of reflection, effective nonlinearity and the required terahertz frequency range.

2. Experimental Methods

2.1. Sample Preparation

To grow the ZnGeP₂ crystals, high-purity initial components (Zn, Ge and P of 6N grade) were taken. The crystals were grown using the vertical Bridgman method [6,8]. Two growth cycles were performed. The thermal annealing of the samples grown in the experiment N1 was carried out in sealed ampoules with the addition of ZnGeP₂ powder to create a vapor phase pressure in the ampule which prevented the decomposition of the material. The annealings were carried out at temperatures of 575–700 °C for 300–400 h. In experiment N2, for the synthesis Zn, Ge and P of 5N grade were used. The synthesized material was divided in to two parts. To one part (50% of mass of synthesized material) scandium was added in an amount of 0.01 mass % of the total charge. Then, two ingots were crystallized using the same setup and experimental growth conditions.

The slabs of annealed ZnGeP₂ with thicknesses of 200, 500 and 800 μm were prepared by cutting them along the (001) plane and polishing them. The slabs with thicknesses of 400 μm cut along the (110) plane were prepared from pure and scandium-doped ZnGeP₂. The samples did not have antireflection coatings.

2.2. Optical Absorption Measurement

The optical transmission spectra were measured using a UV-3600i-Plus (Shimadzu, Kyoto, Japan) spectrometer in 0.6–2.5 μm range. From the measured transmission spectra T(λ), the absorption coefficients α(λ) were calculated by solving, numerically, a system of two equations (which are below), taking into account the multiple reflections in the thin samples and reflection R(λ) from an absorbing medium:

$$\alpha (\lambda )=-\frac{1}{d}\ln (\frac{\sqrt[]{{(1-R(\lambda ))}^4+4T^2(\lambda )R^2(\lambda )}-{(1-R(\lambda ))}^2}{2T(\lambda )R^2(\lambda )})$$

(1)

and

$$R(\lambda )=\frac{{(n(\lambda )-1)}^2+{(\frac{\lambda \alpha (\lambda )}{4\pi })}^2}{{(n(\lambda )+1)}^2+{(\frac{\lambda \alpha (\lambda )}{4\pi })}^2}$$

(2)

where the refractive indices were calculated as n(λ) = n_o(λ) + 0.03, and n_o(λ) was taken from [23]. In Equations (1) and (2), R(λ) is intensity reflection coefficient for the ZnGeP₂/air interface, and T(λ) is the transmission coefficient which is influenced by multiple reflections. The measurements were carried out on (100) oriented samples in unpolarized light at a normal incidence.

2.3. THz-TDS Measurements

The experiments were conducted using the conventional terahertz time-domain spectroscopy (THz-TDS) setup [24] that is in Figure 1a. To obtain the terahertz pulses for the terahertz transmission measurements and tests of the nonlinear crystals, the laser pulses of Mai Tai SP (Spectra-Physics, Milpitas, CA, USA; λ = 780 nm, τ~100 fs) with a horizontal polarization (parallel to the optical table’s surface) were used. For the detection step, an electro-optical (110)-cut ZnTe crystal with a zinc blende structureand d = 1100 μm was used. The Teflon filter (Figure 1a) was used to block the residual 780 nm laser radiation and transmit the emitted terahertz pulse. The delay line (Figure 1a) was a motorized linear stage Model IMS600CCHA (Newport, Milpitas, CA, USA) with an XPS C4 controller (Newport, Milpitas, CA, USA), and this was used to scan the terahertz waveforms by changing the optical path of the laser probe pulse with a step of 5 or 10 μm. The difference in the intensity of the horizontally and vertically polarized components of the probing laser pulse separated by the Wollaston prism (Figure 1a) was measured using the Model 2007 Nirvana balanced detector (New Focus, Milpitas, CA, USA).

To measure the terahertz dielectric properties, the ZnGeP₂ crystals were placed just after the teflon filter (“Sample 1” in Figure 1a), normally, to the terahertz beam (SI-GaAs photoconductive dipole antenna was used as a terahertz emitter in this case), and the terahertz spectra were recorded.

The measurements of the group refractive indices at a 780 nm wavelength in the ZnGeP₂ crystals were made in the following way. The (100)- or the (110)-oriented sample was introduced to the laser beam which was travelling to the PDA (“Sample 2” in Figure 1a). Then, the terahertz waveform was recorded. By comparing the waveforms that were recorded with and without the sample, the time shift Δt related to the pump beam delay in the sample was measured. This delay was determined by the sample group refractive index and its thickness. The ordinary group refractive index was measured with the sample orientation when the optical axis c was oriented vertically (perpendicular to laser beam polarization), and the extraordinary group refractive index was measured for the sample when the optical axis c was oriented horizontally (parallel to laser beam polarization). Then, the group refractive index was calculated as:

$$n_{gr}=\Delta t\cdot c/d+1$$

(3)

where c is speed of light and d is sample thickness.

When we were performing the optical rectification experiments, the (001)-cut ZnGeP₂ crystals (“Sample 3” in Figure 1a) with the optical axis c that was perpendicular to the optical surface were tilted around a vertical direction to set the required external phase-matching (θ_ext) angles, and these were optimized by the azimuth angle φ (the angle between the projection of extraordinary polarization component of a beam to xy-plane and the x-axis) for a maximum signal to be obtained (see Figure 1b). To realize the eo (type II) phase matching, a λ/2 plate (Figure 1a) was placed onto the laser beam before the nonlinear crystal with its optical axis tilted by 22.5 degrees with respect to the horizontal direction to rotate the laser polarization direction by 45 degrees. The output terahertz polarization was controlled by a wire-grid polarizer.

The (110) ZnGeP₂ crystals (“Sample 3” in Figure 1) with an optical axis c which was lying within the optical surface and x axis that was oriented at 45° to the optical surface were placed normally to the incident laser beam with the optical axis c being oriented vertically and the x axis being oriented in horizontal plane, thus, setting the external phase-matching (θ = 90°) and azimuth angle φ = 45° and promoting the oo–e interaction (see Figure 1c).

3. Results and Discussion

In our experiments, the ordinary group refractive index that was measured was 3.95, and extraordinary group refractive index was 4.06 at λ = 780 nm for the annealed ZnGeP₂ crystals, while their values which were calculated using n_o(λ) and n_e(λ) from [23] were 3.919 and 4.034, respectively. Taking into account that for the majority of the samples the measured terahertz refractive indices (Figure 2a) were also about 0.03 higher than it follows from n_o(λ) and n_e(λ) in [23], in the further calculations we used dispersion relations from [23] but they were shifted 0.03 upwards in both of the optical and terahertz ranges, i.e., n_o(λ) = n_o(λ) + 0.03 and n_e(λ) = n_e(λ) + 0.03. From our measurements (in particular, the data in Figure 2a), it follows that refractive indices in ZnGeP₂ can be slightly different depending on the growth technology and the chemical impurity content. Additionally, the absorption (Figure 2b) differs; it is 1 cm⁻¹ at ν = 1 THz for the Sc-doped samples and 3 cm⁻¹ for the as-grown and annealed samples.

It was found that the thermal annealing of the as-grown ZnGeP₂ crystals and their doping with only a 0.01 mass % Sc reduces the absorption in the “anomalous absorption” region (Figure 3). Both annealing and Sc doping can lead to the formation and redistribution of point defects, leading to the Fermi level being pinned, as proposed in [7]. It is also seen that at λ = 780 nm, the level of absorption is still high, and it equals 7.5 cm⁻¹ for the annealed crystals, 11.5 cm⁻¹ for the Sc-doped crystals and 21 cm⁻¹ for the as-grown (N2) ZnGeP_2.

To investigate the influence of the crystal thickness, the polarization of the interacting waves and the phase-matching angles, a series of experimental measurements and model calculations were carried out. Firstly, we calculated the phase-matching conditions by taking into account the following. The phase-matching condition for a crystal of thickness d can be expressed as:

$$N\pi \le \left|\Delta k\right|\cdot d\le (N+1)\pi$$

(4)

where N = 0,2,4. When we were analyzing the phase-matching conditions, we considered the case of N = 0 for simplicity. For the ee–o, ee–e, oo–o and oo–e interactions of type I (when both incident laser beams have the same polarization), the phase mismatch can be written as [12,13,25]:

$$\Delta k(\nu ,\lambda ,\theta )=[n_{gr}(\lambda ,\theta )-n_{THz}(\nu ,\theta )]\cdot 2\pi \nu /c.$$

(5)

Here, ν is terahertz frequency, n_gr is the group refractive index and λ is the laser central wavelength. The group refractive index is calculated as:

$$n_{gr}(\lambda )=n(\lambda )-\lambda \frac{dn(\lambda )}{d\lambda }{|}_{\lambda }$$

(6)

In the case of the different polarizations of the laser pulse components participating in the nonlinear process (eo–o, eo–e, oe–o, oe–e interactions of type II), the phase mismatch (5) can be written the same way, but the group refractive index must be substituted by the effective function [12,13]:

$$n_{vis}=(n({\nu }_{opt})\cdot {\nu }_{opt}-n({\nu }_{opt}-\nu )\cdot ({\nu }_{opt}-\nu ))/\nu$$

(7)

According to the expressions (5–7), the calculated phase-matching conditions for all of the possible interactions are provided in Figure 4.

In the plots (Figure 4a–c), the semi-transparent magenta (dark grey)-filled area indicates where curves n_THz (θ) or n_vis(θ) at θ = 90° (θ = 0 °) should lie to fulfill the condition (4) (N = 0) for a crystal of a thickness d = 200 μm. For the intermediate angles of 0° < θ < 90°, the position of the filled areas would be in between those of the shown ones for these two critical angles (it is seen that their positions do not change significantly). Obviously for the thicker crystals, the phase-matching areas would be narrower than that which is illustrated by the boundaries for a crystal of a thickness d = 800 μm (the dashed lines of the same magenta and dark grey colors). Clearly, for the ordinary participating waves, the color-filled areas, n_THz(θ) or n_vis(θ) for θ = 0° at any θ values should be considered since for the ordinary waves there is no refractive index angular dependence.

As it can be seen, the angular dependence of the phase matching for all of the type I interactions is weak for the ZnGeP₂ crystals because of their low birefringence capacity and the large differences in the n_gr(λ = 780 nm)-n_THz(θ) (about 0.6, (Figure 4a). The condition (4) is fulfilled up to the frequencies about 1.3 THz for d = 200 μm or up to 0.3 THz for d = 800 μm. The best phase-matching is for the oo–e interaction. However, as is shown below, the effective nonlinearity and reflection angular dependencies make the ee–e interaction the most efficient one. The type II oe–e and oe–o interactions are the only ones for which there is a narrow frequency range with ideal phase matching (Δk = 0) (Figure 4b). The phase-matching angles θ of more than 20 degrees are not reasonable as the phase matching shifts to overly high frequencies. Increasing the θ angle increases the terahertz frequencies for which the phase matching is fulfilled. As it can be seen, the thicker crystal is taken, and the lower phase mismatch is required to yield the condition (4). Thus, for the thick crystals, the spectral range of phase matching at a given angle becomes narrower. This can be used to obtain narrowband terahertz generation. Finally, the eo–e and eo–o interactions are less interesting ones for practical realization. Only small θ angles that are below 10° provide phase matching (Figure 4c). As the internal θ angles are used in Figure 4a–c, we also show the internal θ angle dependence on the external angle of incidence for the (001) ZnGeP₂ crystals in Figure 4d.

Besides the phase-matching the terahertz generation by the optical rectification in a nonlinear crystal depends on the crystal’s thickness, absorption coefficient at the pump and generated terahertz wavelengths, Fresnel’s reflection and effective nonlinearity. In the case of terahertz generation by optical rectification of a femtosecond laser pulse, the widely used slowly varying amplitude approximation is not applicable. In order to model the terahertz generation spectra, we used the approach proposed in [25,26] where the amplitude of the generated terahertz wave is written as:

$$E_{THz}(\nu )~d_{eff}^{}{A}_{1g}^2{F}_0(\nu ,\tau )G(\nu ,\lambda ,d)$$

(8)

Here, d_eff is the effective nonlinearity of the second order (for ZnGeP₂ is given in

Table 1. Effective nonlinearities in ZnGeP₂ for all of the possible three-wave interactions.

Interaction	deff
oo–o	0
oo–e	$-d_{36}\sin (\theta )\sin (2\varphi )$
ee–o	$d_{14}\sin (2\theta )\cos (2\varphi )$
ee–e	$-(2d_{14}+d_{36}){\cos }^2(\theta )\sin (\theta )\sin (2\varphi )$
oe–e (eo–e)	$\frac{1}{2}(d_{14}+d_{36})\sin (2\theta )\cos (2\varphi )$
eo–o (oe–o)	$-d_{14}\sin (\theta )\sin (2\varphi )$

for all of the possible interactions), A_1g is the pump pulse electric field amplitude, and $F_0(\omega ,\tau )~{\omega }^2\exp (-{(\omega \tau )}^2/2)$ describes the effect of the spectral width and duration of the laser pulse. In the calculations, τ = 120 fs was used. The influence of the phase-matching conditions Δk(λ, ν, θ), the absorption coefficients in the visible and terahertz ranges ${\alpha }_{opt},{\alpha }_{THz}$ and the crystal thickness d on the emitted spectral waveform are gathered in the function:

$$G(\nu ,\lambda ,d,\theta )=\frac{e^{id[\Delta k(\nu ,\lambda ,\theta )+i{\alpha }_{THz}(\nu )]}-1}{i[\Delta k(\nu ,\lambda ,\theta )+i{\alpha }_{THz}(\nu )]}{e}^{-i{\alpha }_{opt}d}$$

(9)

The pump pulse electric field amplitudes A_1g and E_THz (ν) will definitely depend also on the Fresnel’s reflection losses. We have plotted the dependencies on the external incidence angle of the product of all of the reflection losses and effective nonlinearity for the (001) and (110) ZnGeP₂ crystals without antireflection coatings in Figure 5a,b. In both of the cases, the ee–e interaction at the θ angle close to the Brewster angle (about 74°) seems to be optimal. For the (110) ZnGeP₂ slabs also, the oo–e interaction at a normal incidence is advantageous.

The measured and calculated terahertz spectra which were generated in the annealed ZnGeP₂ crystals of thicknesses 200, 500 and 800 μm by ee–e and oe–e optical rectification are presented in Figure 6. For each interaction, all of the spectra are normalized to the maximal spectral amplitude of the most efficient conversion (θ = 55° d = 200 μm for ee–e and θ = 55° d = 800 μm for oe–e type model and θ = 45° d = 800 μm for oe–e type experiment). It is seen that the model reproduces the main features of the experimental spectra; the discrepancies are, first of all, due to the spectral dependence of the detection efficiency (which was not included in the model). The detection efficiency is lower for the frequencies that are above 2 THz. Additionally, the walk-off (arising for e-waves) was not accounted for. The walk-off probably explains the fact that while θ = 74° at ee–e is the optimal angle according to the calculations, experimentally, the highest signal was measured at θ = 55–60°.

In the next step, we experimentally checked the possibility to achieve the narrowing of the terahertz generation bandwidth at the oe–e interaction in the thicker ZnGeP₂ (d = 2015 μm) crystal. The modeled and measured terahertz generation spectra are shown in Figure 7a in comparison with those which were obtained in the d = 200 μm crystal. Finally, the terahertz generation in the ZnGeP₂:Sc crystals was tested. The prepared slabs had a (110) orientation. For these samples, the oo–e interaction at a normal incidence was deduced to be efficient. The obtained experimental and modeled spectra are given in Figure 7b. Taking into account the lower ${\alpha }_{opt},{\alpha }_{THz}$ of the Sc-doped crystal, the higher efficiency was expected. The experimentally measured efficiency is even higher when it is compared to that for reference crystal (pure ZnGeP₂ N2) than it was predicted to be by the models.

4. Conclusions

Terahertz wave generation through the optical rectification of 780 nm femtosecond laser pulses in ZnGeP₂ crystals has been studied. All of the possible interactions of types I and II were studied by modeling and in experiments. The possibility of broadband “low-frequency” terahertz generation by ee–e interaction and “high-frequency” terahertz generation by oe–e interaction was demonstrated. The possibility to achieve the narrowing of the terahertz generation bandwidth at the oe–e interaction using thicker ZnGeP₂ crystals was experimentally confirmed for a 2-mm-thick crystal. It was found that the thermal annealing of the as-grown ZnGeP₂ crystals and their doping with a 0.01 mass % of Sc reduces the absorption in the “anomalous absorption” region (λ = 0.62–3 μm). The terahertz generation by the oo–e optical rectification in (110) ZnGeP₂:Sc and the as-grown ZnGeP₂ crystals of equal thickness has been compared. It has been found that ZnGeP₂:Sc is more efficient for 780 nm femtosecond laser pulses optical rectification.