Optical Parameters of Deuterated Triglycine Sulfate in Terahertz Range

Abstract

In this work, the optical parameters of a 550 μm thick deuterated triglycine sulfate (DTGS) crystal in the range of 0.3–1.5 THz were investigated in low and high fields by time-domain spectroscopy. The X and Z axes of the refractive index ellipsoid were identified, and the refractive indices and extinction coefficients were determined. In addition, it was shown that, in strong THz fields, a phonon A-mode with a frequency of about 40 cm⁻¹ can be excited in the DTGS crystal when the THz wave vector coincides with the polar axis of the crystal and the polarization of the THz radiation coincides with the X-axis of the crystal. The use of the observed effect and the determination of the mode excitation parameters can be twofold. First, they show the limits of the THz field for non-invasive action on the crystal. Second, they present the mode excitation conditions that can be used, for example, in controllable absorbers.

1. Introduction

Ferroelectric materials are widely used in nano- and optoelectronic applications due to their radiation resistance, energy efficiency, short switching times, stability over a wide temperature range, and low dielectric losses [1,2]. In traditional electro-optical devices, optical properties of the ferroelectrics are controlled by an external electric field, which limits their switching speed to nanoseconds, which corresponds to gigahertz frequencies. The search for conceptually new methods and mechanisms to control the state of ferroelectrics in significantly shorter times, down to picoseconds, is critical for the development of new, efficient, and ultrafast optoelectronic devices. One promising approach is the use of powerful sub-picosecond electromagnetic pulses in the terahertz range [3,4,5,6].

Another promising application of ferroelectric materials in the THz range is the development of highly efficient THz radiation modulators. The ability to achieve high modulation depth in these devices has already been demonstrated [7,8,9]. The implementation of these modulators will significantly enhance the speed of information transfer. To develop efficient optoelectronic devices in the THz range, precise knowledge of the optical properties of the materials used in this frequency range is required.

To date, optical constants in the THz range are determined for such materials as silicon, sapphire, crystalline quartz, silica, and pyrex glass [10,11,12] etc., which are typical substrate and window materials. Some ferroelectrics materials, including LiNbO₃ (Lithium Niobate) [13], SrTiO₃ (Strontium Titanate) [14], and PZT (Lead Zirconate Titanate) [15], have also been characterized in the THz and sub-THz ranges. However, the optical constants of triglycine sulfate in the THz range have not been reported previously.

Triglycine sulfate (NH₂CH₂COOH)₃ ∗ H₂SO₄ (TGS) is a widely studied ferroelectric material. It has monoclinic symmetry with a C₂ polar axis. It is commonly used in IR detectors, nonlinear capacitors, temperature sensors, and other nano- and optoelectronic devices [16,17,18]. Research into its properties and possible applications is still ongoing [19,20,21]. For instance, in Ref. [22], the phase switching of order to disorder states of TGS by the impact of acoustical shock waves was demonstrated. In [23], the method for the fabrication of a thin TGS film consisting of ordered nanocrystals inside the nanopores of the anodic aluminum oxide template and along the polar axis of the crystal was proposed. This structure has a potential for the creation of thermal energy harvesting devices. Therefore, investigation into TGS’s optical properties in the THz range is also important task.

Modification of TGS crystals (deuteration and doping) leads to the stabilization of the domain structure and an increase in spontaneous polarization. These crystals have one of the highest values in terms of their pyroelectric coefficient and are widely used as the main functional element of pyroelectric detectors. Although in recent years the range of pyroelectric detector materials has significantly expanded, pyroelectric and IR detectors based on TGS find their niche and show high efficiency [24,25,26].

Here, we present the results of the deuterated TGS (DTGS) optical parameters investigation in the THz range using a time-domain spectroscopy (TDS) technique. These results will expand the scope of TGS applications and accelerate the creation of new-generation optoelectronic devices operating in the THz range.

2. Materials and Methods

A 550 μm thick DTGS crystal was made by a slow cooling method from solution at Shubnikov Institute of Crystallography RAS. The XRD pattern of the crystal (Figure 1) confirmed that the DTGS is a single crystal with the surface oriented perpendicular to its polar axis.

The transmission spectra of the DTGS crystal in the THz range were investigated by time domain spectroscopy (TDS) technique on three different facilities (see Figure 2).

The optical anisotropy of the sample in the THz range was investigated using a terahertz time-resolved spectroscopy facility (Facility 1). The facility is based on a femtosecond laser system consisting of a Ti:sapphire laser with a regenerative amplifier with a wavelength of 800 nm, a pulse duration of 50 fs, and a repetition rate of 3 kHz. The THz radiation source was a CoFeB/Pt spintronic emitter (SE) placed in an external magnetic field to generate THz radiation polarized along the X-axis in the laboratory frame (X-component). A wire grid polarizer transmitting only the X-component of the THz radiation was placed in front of the DTGS crystal for additional polarization control. Detection was performed by a 1 mm thick ZnTe crystal. To register the X-component of the THz field after passing through the DTGS crystal, the ZnTe [−110] axis was aligned along the X-axis in the laboratory frame. To register the Y-component, the polarization of the probe radiation and the ZnTe crystal were rotated by 90 degrees.

To reveal the anisotropy, the DTGS crystal was rotated around the Z axis of the laboratory frame (blue axes in Figure 3a) in 20-degree increments for a full 360 degrees. For each step, temporal forms of the X-and Y-components of the THz pulse were measured, and the peak-to-peak signals were taken (see Figure 4, top left panel) [28]. These values were plotted on the graph (Figure 3), which allowed us to determine the principal axes of the index ellipsoid (red axes in Figure 3a).

After determining the principal axes, and, therefore, the polarization directions of two linearly polarized waves propagating in the crystal, the transmission spectra of these waves in the THz range were studied in both weak and strong THz fields.

Studies in weak THz fields were carried out using a commercial THz spectrometer Tera K15 (Menlo System) in the range of 0.25–1.5 THz (Facility 2).

To study the THz transmission spectra in high fields using the TDS technique, Facility 3 was used, based on a Cr:forsterite laser with a wavelength of 1240 nm and a repetition rate of 10 Hz.Due to a low repetition rate, this facility has a low signal-to-noise ratio. The THz radiation source was an organic crystal OH1 [29]. The THz field strength reached 4 MV/cm, and the spectral range was 0.5–3 THz. The strong terahertz field made it possible to carry out measurements at different field strengths, achieved by adjusting the optical pump energy. A 200 µm thick GaP crystal was used for detection. The wider spectral range and intense THz radiation allowed for detailed study of the THz-induced effects in the DTGS crystal, which was not possible with the commercial Tera K15 device. All experiments were performed in dry air (humidity ≤ 5%). The comparison of the three facilities is presented in

Table 1. Comparison of the three facilities.

	Facility 1	Facility 2	Facility 3
THz source	SE CoFeB/Pt	Photoconductive antenna	OH1 organic crystal
Repetition rate	3 kHz	100 MHz	10 Hz
Possibility of sample rotation	Yes	No	No
Possibility of X and Y THz component measurements	Yes	No	No
THz field	<50 kV/cm	<50 kV/cm	Up to 3.6 MV/cm
Possibility of THz field changing	No	No	Yes
Evaluate of the error	4%	<1%	12%

.

3. Results

Figure 3 shows the azimuthal dependences of the X and Y components of the peak-to-peak signal of the THz pulse transmitted through the DTGS crystal. This signal changes depending on the azimuthal orientation of the DTGS crystal and allows us to distinguish two characteristic directions in the crystal (marked with thin red lines). For these crystal positions (120 and 30 degrees), higher and lower maxima of the X-component of the terahertz field azimuthal dependence are observed (Figure 3a). In our case, these are the directions along the X and Z main axes of the refractive index ellipsoid (see Section 4).

Figure 4 presents the temporal and spectral forms of the input THz pulse (reference) and of the pulse transmitted through the sample with polarizations along the X and Z directions in the refractive index ellipsoid frame. The right panels show the spectral forms for different facilities with different THz field strengths (Facility 2 and Facility 3). The spectral range of the reference pulse at Facility 2 is about 0.5–1.5 THz. For Facility 3, the spectral range of the reference pulse is about 0.5–2.7 THz. In the frequency range above 1.5 THz, strong absorption of THz radiation by the DTGS crystal is observed at both facilities. Since most of the reference pulse spectrum at Facility 2 falls into the low absorption region, the maxima of the temporal forms of the pulses transmitted through the crystal relative to the input pulse in this case are higher than at Facility 3.

4. Discussion

A standard theoretical approach was applied to determine the refractive index and extinction coefficient of the DTGS crystal in the terahertz range [30,31]. Denoting the complex spectral amplitudes of the reference and sample pulses as $E_{ref}\left(\omega \right)$ and $E_{samp}\left(\omega \right)$, respectively, the spectral transmittance $H\left(\omega \right)$ can be expressed as

$$H\left(\omega \right)={\displaystyle \frac{E_{samp}\left(\omega \right)}{E_{ref}\left(\omega \right)}}=T\left(\omega \right)e^{i\phi \left(\omega \right)}={\tilde{t}}_{12}{\tilde{t}}_{23}{e}^{-{\displaystyle \frac{\alpha d}{2}}}{e}^{i\left(n-1\right)\omega {\displaystyle \frac{d}{c}}},$$

(1)

where $T\left(\omega \right)$ is the real part of the spectral transmittance, $\phi \left(\omega \right)$ is the phase, ${\tilde{t}}_{12}$ and ${\tilde{t}}_{23}$ are the Fresnel coefficients for transmission on the front and back sides of the sample, respectively, and $d$ is the sample thickness. The complex refractive index of the sample is $\tilde{n}=n+ik$, where $k$ is the extinction coefficient, which is related to the absorption coefficient $\alpha$ by the expression $k\left(\omega \right)={\displaystyle \frac{\alpha \left(\omega \right)c}{2\omega }}$.

Generally, the Fresnel coefficients ${\tilde{t}}_{12}$ and ${\tilde{t}}_{23}$ are complex, which leads to additional phase shifts relative to the reference pulse. However, for materials with a low absorption coefficient, where $k\ll n$, the Fresnel coefficients become real. As we will see below, the extinction coefficient of the studied material within our spectral range actually turns out to be more than an order of magnitude lower than the refractive index. In this approximation, it is possible to express $n\left(\omega \right)$ and $k\left(\omega \right)$ as

$$n\left(\omega \right)=1+{\displaystyle \frac{\phi \left(\omega \right)c}{\omega d}},$$

(2)

$$k\left(\omega \right)=-{\displaystyle \frac{c}{\omega d}}ln\left({\displaystyle \frac{{\left(n+1\right)}^2}{4n}}T\left(\omega \right)\right).$$

(3)

These equations allow for the direct calculation of the refractive index $n\left(\omega \right)$ and absorption coefficient $\alpha \left(\omega \right)$ from the phase $\varphi \left(\omega \right)$ and transmittance $T\left(\omega \right)$ in the low-absorption limit.

The graphs in Figure 5 show the $n\left(\omega \right)$ and $k\left(\omega \right)$, calculated using the described method. The values are presented in the spectral range from 0.3 to 1.5 THz in accordance with the spectrum of the reference pulse. In the low-frequency region, the values of $n\left(\omega \right)$ are underestimated, since phase shifts at the interface between the sample and air are not taken into account in the low-absorption approximation [30].

The most exciting result of our work was found for the extinction coefficient k_x. This is a strong absorption peak at 40 cm⁻¹ (1.2 THz), which is absent on the k_x dispersion curves at the low-field facilities. It is clear that the spectral amplitude of this peak solely increases with increasing field strength from 0.46 to 3.6 MV/cm, while the other spectra (for k_z within the whole spectral range, measured as well as for k_x everywhere excluding the range of the peak itself) coincide for both facilities and do not depend on the power applied.

As is known [32], all modes in the TGS crystal at frequencies below 170 cm⁻¹ correspond to phonon modes. The mode we observed corresponds to the lowest phonon mode (A-mode) of the TGS crystal, which is both Raman and IR active [33]. Its appearance can be explained by the excitation of this mode by the strong electric field of the THz pulse.

According to the literature, this mode is also observed in TGS crystals by Raman scattering [34,35]. This mode appears in the case of the propagation of incident radiation along the polar axis C₂, with mutually perpendicular orientations of the polarization of the incident radiation and the radiation transmitted through the sample. Thus, experimental conditions for the case of Figure 3b) correspond to the A-mode appearance.

This mode was also observed in experiments on terahertz transmission in TGS crystals. This type of mode corresponds to the propagation direction of the incident electromagnetic wave along the C₂ symmetry axis of the DTGS crystal. In this case, when the vector $\overrightarrow{E}$ is polarized along the X axis in the generally accepted notation [33], in accordance with the literature, a phonon mode occurs at a frequency of about 40 cm⁻¹. With a perpendicular orientation of the vector $\overrightarrow{E}$ (along the Z axis), this mode does not appear. This fact also confirms that the crystal position for maximum of the THz pulse X-component in Figure 3a corresponds to the case of $\overrightarrow{E}\upuparrows \mathrm{X}$ and $\overrightarrow{k}\upuparrows C_2$, where $\overrightarrow{k}$ is the wave vector of the incident electromagnetic wave. The crystal position for the lower maximum of the THz pulse X-component in Figure 3a corresponds to the case $\overrightarrow{E}\upuparrows \mathrm{Z}$ and $\overrightarrow{k}\upuparrows C_2$. The experimental results in this work correspond to the data in previous works for the TGS crystal. The spectral dependences of the optical constants of the crystal in this work correspond to the values along the main axes of the refractive indices’ ellipsoid, that is, the values of n_x and n_z.

The possibility of resonant and non-resonant excitation of IR-active and Raman-active phonon modes by THz radiation has been demonstrated previously in other materials. In [36], the possibility of the coherent excitation of the large-amplitude lattice displacements associated with non-fully symmetric phonon modes in single-crystal SrCu₂(BO₃)₂ by the narrow-band THz source was demonstrated. In [37], it was demonstrated that narrow-band THz radiation can resonantly excite the soft mode in BST films for different crystallographic orientations. In [38], the mechanism for a coherent parametric excitation of a low-energy Raman-active phonon in the LaAlO₃ by broad-band THz pulse was present. This mechanism is based on the absorption of photons through an optical transition involving a pair of acoustic vibrational modes.

The results for Facility 2 show a monotonic increase in the refractive indices $n_x$ and $n_z$ with increasing frequency, except for areas at the edges of the reference pulse spectrum, where the signal-to-noise ratio is high. Oscillations of refractive index and extinction coefficient in the range below 20 cm⁻¹ (including absorption peak at 18 cm⁻¹) can be attributed to interference effects similar to that described in Ref. [39]. $k_x$ and $k_z$ also increase monotonically, except for the areas at the edges of the spectral range.

As determined as a result of calculations, in the DTGS in the frequency range of 20–55 cm⁻¹, the values of the refractive indices $n_x$ and $n_z$ lie in the range of 2.8–3.0 and 2.1–2.3, respectively. The extinction coefficients $k_x$ and $k_z$ lie in the range of 0.05–0.25.

The dependences of the DTGS optical constants on the applied THz field magnitude are also presented in Figure 5 (for Facility 3). Figure 5 shows that, for the $k_x$ extinction coefficient, an absorption increase on THz field near 1.2 THz is observed. It may indicate an increase in terahertz radiation influence on the excitation of the phonon mode at 40 cm⁻¹. As mentioned above, modes in the TGS crystal at frequencies below 170 cm⁻¹ correspond to optical phonon modes. Thus, as the field strength of the incident radiation increases, the forced electric dipole oscillations increase, which leads to an increase in the electromagnetic wave absorption.

5. Conclusions

In conclusion, by measuring the transmission anisotropy of the X- and Y-components of the THz radiation in the DTGS crystal, the orientations of the X and Z axes of the refractive index ellipsoid were identified, and the optical constants in the range of 0.3–1.5 THz were determined. The refractive indices $n_x$ and $n_z$ are in the range of 2.8–3.0 and 2.1–2.3, respectively, while the extinction coefficients $k_x$ and $k_x$ are in the range of 0.05–0.25. This knowledge is in demand for the development of optoelectronic devices based on DTGS, operating in the THz range.

The key finding is that the phonon A-mode with a frequency of about 40 cm⁻¹ can be excited in the DTGS crystal by a strong THz field of several MV/cm, when $\overrightarrow{k}\upuparrows C_2$, and the THz radiation polarization is aligned with the X axis of the crystal. These results allow us to determine the boundary between invasive and non-invasive action of the THz pulse on the DTGS crystal. The former determines the THz field range in which nonlinear THz modulation of optical properties occurs. This range can be used in devices based on phonon excitations and resonances [40,41,42]. In the latter, no excitation of nonlinear processes takes place, and the material can be used for passive elements and sample substrates. These insights are valuable for the development of sensor and device technologies in the terahertz range and contribute to the emerging field of terahertz phononics.