1. Introduction

Terahertz time-domain spectroscopy (THz-TDS) and imaging have emerged as powerful, non-destructive techniques for scientific investigation and testing of various materials [1–5]. In THz-TDS, the fast-Fourier transform of experimentally measured time-domain waveforms of the electric field (E) unveils the THz frequency characteristics of the transmitted or reflected E-field amplitude and its phase. This allows for the quantitative study of a material’s dielectric, conductivity, or optical anisotropy (birefringence and dichroism) characteristics [6–10]. In addition, THz radiation features a non-ionizing nature, and typical output power of THz-TDS emitters is limited to the harmless µW range. However, similar to x-ray imaging, THz radiation has high penetration depths in different materials such as ceramics, minerals, plastics, pharmaceuticals, and other natural products, which are otherwise opaque to visible light [11–14]. In combination with a high signal-to-noise (S/N) ratio at ambient conditions and with submillimeter spatial optical resolution, THz-TDS is a promising tool that has received great interest in the last two decades.

The typical THz-TDS scheme to study optical anisotropy in the THz range involves a pair of THz photoconductive antennas operating as a dipole emitter (DE) and a dipole detector (DD) with linear polarization properties and at least two wire-grid polarizers. The first polarizer (P) before the sample removes any parasitic angular components from a predominantly linearly polarized output of the photoconductive DE and THz optics. The second rotating polarizer/analyzer (A) is placed after the sample. Its role is to probe the DD’s response on sample-induced changes in the polarization state of a transmitted or reflected THz beam. However, it is desirable to simplify this scheme by employing a THz detector that is sensitive to arbitrary polarization component, i.e., by eliminating the use of $A$. In principle, this will improve data acquisition times and will simplify the optical setup.

In particular, such a detector could be useful for stress-induced THz anisotropy, magneto-optical phenomena (Kerr and Faraday rotations), as well as ellipsometric studies in the THz range [15–19]. Moreover, it could be advantageous even for ordinary THz-TDS, since images obtained with a DE/DD pair are sometimes difficult to interpret due to complex absorption, scattering, anisotropy, and sample reflectivity contrasts. With a DE/DD pair, only one component of the E vector is measured. As such, polarization-sensitive THz detectors with high angular accuracy and straightforward data acquisition/analysis are of great importance in improving THz-TDS optical systems.

Polarization-sensitive THz photoconductive detectors have been previously reviewed [15,16]. In this work, a similar, two-orthogonal bow-tie antenna flare design [20] is investigated. However, its actual geometry has been significantly modified to be in resonance with the its paired DE’s THz spectral output. In addition, frequency domain analysis below 5 THz is provided, which is also different from earlier reported data in the time domain [20]. Numerical simulation results are used to design the corresponding optical setup capable of delivering a linear angular response to the incident light polarization angle. The effect of the lead lines on the detector’s spectral signature is considered as well. Understanding the effect of such factors is important for polarization-sensitive detectors, and it could lead to the development of better designs in the future.

2. Experimental

The 4-contact detector (4-CD) shown in Fig. 1(a) was microfabricated on a low-temperature-grown gallium arsenide (LT-GaAs) surface by liquid photolithography and substrate metallization with successive vacuum electron beam depositions of Ti (5nm) and Au (150 nm) layers [see Figs. 1(b)-1(d)] [21]. The double-sided polished GaAs (BATOP GmbH) wafer had a thickness of 625 µm, a 3 µm-thick LT-GaAs top layer on one side, and a 132 nm-thick buffer layer between the GaAs substrate and the LT-GaAs. The LT-GaAs had nominal carrier lifetimes of 250 fs. An 80 fs mode-locked Ti:sapphire laser (Tsunami, Spectra-Physics), DE, and two wire-grid polarizers were employed in measuring the 4-CD characteristics. The details of the THz-TDS setup is described in an earlier work [22]. The bias voltage on the DE was modulated at 20 kHz with a peak-to-peak voltage of 40 V. Figure 1(e) shows the schematic of the optical setup.

 

Fig. 1 Microfabricated 4-CD (a)-(d) and scheme of its testing. (a) Photomask geometry in mm; (b) total view of the microfabricated detector chip (6 × 6 mm) with bowie-tie electrodes, lead lines, and 1 × 1 mm contact pads; (c) enlarged view of the ~70 µm bowie-tie flares and lead lines; (d) the magnified detector center; (e) schematic diagram of the optical setup with wire-grid polarizers. Note that (c) and (d) show the electrode structure at the center of (b) with different magnifications. See text for more details and abbreviations.

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The finite-difference time-domain (FDTD) simulations of the 4-CD response were conducted via Lumerical FDTD Solutions 8.6.0 Solver. The detector electrodes were modeled as a perfect electric conductor (PEC) according to its nominal photomask geometry and microfabrication thickness. The PEC approximation is valid owing to the high Au conductivity in the THz range [23]. The PEC electrodes were placed on top of the 200 µm dielectric half-space in air with $n_{LT}{}_{-GaAs}$ = 3.6 [6] and $n_{air}$ = 1. The broadband (0.01-5 THz) Gaussian source having a waist radius of 500 µm was made to originate inside the LT-GaAs slab at a 100 µm distance beneath the LT-GaAs/PEC interface. It had the direction of THz wave propagation towards the PEC surface. The perfectly matched layer (PML) boundaries and non-uniform meshes were employed in the simulations.

3. Results and discussion

3.1. FDTD modeling

To understand the spectral and angular responses of the 4-CD on incident THz polarization and various optical alignments, three-dimensional FDTD simulations were conducted. Figure 2 shows the E field intensity enhancements with respect to the source intensity (${\left|E_0\right|}^2$) on the LT-GaAs/PEC interface plane at 0.72 THz. The diagram may be alternatively described as the source-normalized map of ${\left|E_{xy}\right|}^2=\left({\left|E_x\right|}^2+{\left|E_y\right|}^2\right)/{\left|E_0\right|}^2$. It also displays the corresponding vector ($\overrightarrow{E_{xy}}$) plot at the 4-CD center and schematically depicts the $E_x$- and $E_y$-channel circuits for these orthogonal polarization components. The origin of the $xyz$-coordinate system in the diagram is at the center of the 4-CD on the LT-GaAs/air interface plane.

 

Fig. 2 FDTD simulation results of electric field intensity and vector distributions at the center of the 4-CD. The THz source with linearly polarized output is behind the picture plane. The schematic instantaneous charges on bowie-tie antenna tips (in blue color), which are generated by incident electric field (red arrows), are also shown to explain the detection principle with two electric circuits.

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The FDTD simulations demonstrate that the laser probe beam should be tightly focused at the detector center to avoid any parasitic currents between the neighboring electrodes. The results in Fig. 2 also show that the experimental spot size of the fs-laser probe beam is tight enough to have $\overrightarrow{E_{xy}}$ component currents only between the opposite electrode tips. From Fig. 2, a spot size of between 1 and 2 µm in diameter is safe to use, which is also achievable experimentally. Within this spot, the enhanced electric field intensity values (${\left|E_{xy}\right|}^2$) of up to two orders of magnitude are predicted, suggesting high detector sensitivity. Even so, the current design of the lead lines does not eliminate a measurable $E_y$ component for the $\overrightarrow{E_0}$ vector parallel to the x-axis (the incident THz-wave polarization angle α = 0°, where α is measured from the horizontal x-axis).

Figure 3(a) shows the ${\left|E_{xy}\right|}^2$ maps for $\alpha$ = 0° and 45° at smaller magnification. In this case, the polarizability of the lead lines, which are parallel to $\overrightarrow{E_0}$ and that lead to the orthogonal bowie-tie flares, is clearly observed. Nevertheless, the spectral responses for the ${\left|E_x\right|}^2$ and ${\left|E_y\right|}^2$ components measured at the detector center are very different, as in Fig. 3(b). For example, the ${\left|E_x\right|}^2$ component of the 4-CD with 70 µm bowie-tie flare length ($l$) has a broad spectral band (~0.3-1.2 THz range) having a maximum at ~0.6 THz. The corresponding resonance wavelength normalized to $n_{LT}{}_{-GaAs}$ is ~139 µm, i.e., it is ≅2$l$. As expected, this band is very sensitive to $l$ variations. This can be seen by comparing the ${\left|E_x\right|}^2$ spectra for different $l$ on Fig. 3(b) as well as experimental ones for the bowie-tie emitters [24]. As a result, this band was ascribed to a bowie-tie flare resonance. In contrast to ${\left|E_x\right|}^2$, the ${\left|E_y\right|}^2$ component has a strong band at a much lower frequency of ~0.1 THz and a weak broad shoulder at ~0.55 THz. In the case of the ${\left|E_y\right|}^2$ component, the intense peak at ~0.1 THz and the shoulder at ~0.55 THz were attributed to the effect of the lead lines since the spectral positions of these bands were almost independent from $l$ [compare ${\left|E_y\right|}^2$ spectra for $l$ = 70 and 50 µm in Fig. 3(b)]. In other words, the parasitic ${\left|E_y\right|}^2$ component frequencies at $\alpha$ = 0° were governed by the lead line dimensions.

 

Fig. 3 The FDTD simulation results for intensity and spectral responses of 4-CD, which are observed for different incident THz illumination angles, antenna geometries, and observation positions between antenna electrodes: (a) the $\log \left({\left|E_{xy}\right|}^2\right)$ map plots at α = 0° and 45°; the legends for plots on (b) and (c) correspond to the $l,\alpha ,E$ component (see actual values on scale labels), and $xyz$ coordinate of observation point on (a) and Fig. 2. For example, the label “70, 0, Ex, x=y=z=0” corresponds to $l$ = 70 µm, $\alpha$ = 0°, $E$ component along the $x$-axis, and observation point at the coordinate origin. See text for used abbreviations.

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It must be stressed, that the bowie-tie flare spectral response was found to be almost independent on $\alpha$ only at the detector center [the reader is directed to the corresponding ${\left|E_x\right|}^2$ and ${\left|E_y\right|}^2$ on Fig. 3(b) for0° and 45°]. However, large spectral and intensity variations were predicted at other spatial positions [see Fig. 3(c)], i.e., the crosstalk was expected between ${\left|E_x\right|}^2$ and ${\left|E_y\right|}^2$ components for the laser spot position between neighboring electrode tips. These results demonstrate the necessity for alignment of the probe-laser spot at the very center of the 4-CD. Moreover, Fig. 3(b) shows the calculated $\left|E_x\right|/\left|E_y\right|$ ratio at the detector center for $\alpha$ = 0°. This ratio is frequency dependent and it has a maximum value of 3 between 0.7 and 0.8 THz. Note that for an ideal detector, the $\left|E_x\right|/\left|E_y\right|$ value is infinitely large at $\alpha$ = 0°. However, the finite maximum value for a real detector should not affect the linearity of its angular response as long as its spectral responses for ${\left|E_x\right|}^2$ and ${\left|E_y\right|}^2$ components are angularly independent. As discussed above, this condition holds at the center position of the structure in the simulations. In practice, higher $\left|E_x\right|/\left|E_y\right|$ values are beneficial for measurements with low signal-to-noise (S/N) ratios. Therefore, the 4-CD should have a linear angular response to the incident polarization angle, provided the appropriate optical alignment requirements and sufficient S/N conditions are satisfied in the experiments.

3.2. THz-TDS experiments

Prior to the experimental investigation of the characteristics of the microfabricated 4-CD with $l$ ≅70 µm [see Figs. 1(b)-1(d), and 1(e)], the wire-grid $P/A$ pair were oriented to get maximum transmission intensity for the DE/DD-pair combination. The resulting setup corresponds to $\alpha$ = 0° for $\overrightarrow{E_0}$ on the DD surface. The DD was then replaced with the 4-CD and measurements were conducted by changing $\alpha$ via $A$ rotation [see Fig. 1(e)]. Figure 4 exhibits the experimentally measured waveforms collected from $E_x$- and $E_y$-channel circuits of the 4-CD for $\alpha$ = −10°. The three-dimensional plot of the reconstructed total $E$ waveform is shown in Fig. 4(a). Due to an installation/positioning offset $\varphi$, the results shown for angle $\alpha$ = −10° actually correspond to the $\overrightarrow{E_0}$ closely aligned along the 4-CD $x$-axis (discussed below), i.e. −10°-$\varphi \approx$0°.

 

Fig. 4 The (a) time-domain and (b) frequency-domain responses of 4-CD for DE radiation. The spectral signature of DE/DD pair is also shown for comparison in (b).

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From Fig. 4, two orthogonal but almost equally intense $E_x$- and $E_y$-components were observed in the time-domain data. However, their frequency spectral signatures were different [see Fig. 4(b)]. The ${\left|E_x\right|}^2$-component had two major peaks at ~0.4 and ~0.7 THz, but ${\left|E_y\right|}^2$ exhibited an intense peak at 0.1 THz and a weak shoulder at frequencies above 0.2 THz. Note that DE/4-CD spectra are the convolutions of the individual DE and 4-CD spectral responses. The DE spectral signature was measured with the DE/DD setup as shown in Fig. 4(b), while the 4-CD spectral response was FDTD modeled as shown in Fig. 3(b). By comparison, it can be inferred that the 0.1, 0.4, and 0.7 THz peaks correspond to the 4-CD lead line, main DE, and 4-CD bowie-tie resonances, respectively. The peak at ~0.7 THz in the DE/4-CD setup was also the most sensitive to $\alpha$-value variations. These results agree well with the frequency characteristics of the ${\left|E_x\right|}^2/{\left|E_y\right|}^2$ maximum from FDTD simulations.

As a further study, the plot in Fig. 5(a) shows the experimentally determined $\left|E_x\right|/\left|E_y\right|$ ratio at ~0.7 THz as a function of $\alpha$. For comparison, the angular response for an ideal detector is also shown. A nonlinear curve fitting (Levenberg-Marquardt algorithm) of experimental data points to the $\left|E_x\right|/\left|E_y\right|=\tan (C+B\left|\alpha -\varphi \right|)$ function was applied. The good quality fit strongly suggests that the angular 4-CD response is close to linear. In the fitting function, $B$ and $C$ constants are the slope and intercept, respectively, with $\varphi$ = 0°, $C$ = 90°, and with $B$ = 1 for an ideal detector. For the real detector, $C\ne$90° was due to the finite value of the $\left|E_x\right|/\left|E_y\right|$ ratio, while $B\ne$1 depicts the case of a misaligned laser probe beam with respect to detector center. Finally, $\varphi \ne$0° is due to the offset between the DD and 4-CD installation and positioning in our experiments. The accuracy of the nonlinear curve fitting for the current experimental data was ± 0.7° (~1 mrad) in terms of $C$ and $\varphi$ detections and may be further improved with better alignment and device fabrication. Previously, the accuracy of $\alpha$ detection in the µrad range was predicted or reported for polarization-sensitive detectors [20,22,25], improved measurements with DE/DD pair [26], and a polarization modulation technique [27]. More so, the maximum value of 9 for the $\left|E_x\right|/\left|E_y\right|$ ratio is even higher than what was predicted by the FDTD simulations [see Fig. 3(b)].

 

Fig. 5 Comparison between ideal linear angular response and real experimental one with (a) nonlinear and (b) linear curve fittings on the same data.

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The quality of the linear response can be observed in more detail in Fig. 5(b), where $\mathrm{arc}\tan \left(\left|E_x\right|/\left|E_y\right|\right)$ versus $\alpha$ is plotted and analyzed using a least squares linear fit. The good quality fits were obtained for $-60°\le \alpha \le -10°$ and $-5°\le \alpha \le -60°$ ranges, wherein the data points with low S/N ratios (nearly crossed $P$ and $A$ wire-grids) were ignored. Differences in the $C$ and $B$ values for these ranges indicate a certain degree of asymmetry in the negative and positive slopes.

This may be attributed to the slight, off-center alignment of the laser probe beam. With larger misalignments, the asymmetry in the angular detector response will become larger due to crosstalk. Such crosstalk was predicted by the FDTD simulations shown in Fig. 3(c). The lower S/N ratio in the experimental waveforms will result in more scattered data points. The best fit linear response similar to one in Fig. 5 was observed between 0.6 and 0.8 THz. This frequency range corresponds to the minimum spectral overlapping between the bow tie and lead line resonances.

4. Conclusion

The reported 4-CD design could be used in any THz-TDS system by properly switching the addressable contact pads or by acquiring the $E_x$- and $E_y$-channels simultaneously. With proper design and alignment in order to yield a linear angular response, sufficient sensitivity to the incident THz light polarization-angle, and intensity, this antenna structure could become a useful tool in measurements involving THz anisotropy. The spectral range having a linear response could be widened by redesigning the lead line structure. This could also increase the $\left|E_x\right|/\left|E_y\right|$ maximum value and improve the quality of the detector performance.