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Abstract
We demonstrate a high dynamic range (DR) Fourier-transform-based terahertz (THz) spectrometer by combining a THz photomultiplier tube (PMT) with a metasurface and a conventional Michelson interferometer. Because the THz-PMT response depends on the incident electric-field strength following the Fowler–Nordheim equation, we can directly obtain an electric field interferogram without any synchronized optical probe pulse in contrast to conventional THz-time-domain-spectroscopy (THz-TDS). The DR of the corresponding power spectrum using the proposed method was 4.6 × 105 without the use of a lock-in amplifier. The complex refractive index of a quartz glass plate obtained using the proposed method was in good agreement with the results of conventional THz-TDS.
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1. Introduction
Terahertz (THz) spectroscopy is an attractive tool because several molecules [1] and pharmaceuticals [2] exhibit a unique spectral fingerprint in this frequency range. Typically, THz spectroscopy is implemented using THz-time-domain spectroscopy (THz-TDS) [3,4] and Fourier-transform infrared spectroscopy (FTIR) [5]. THz-TDS has been widely used because it can obtain the temporal waveform of the THz electric field. Thus, the complex refractive index of a sample can be obtained directly without the Kramers–Kronig relation; however, THz-TDS requires a complex femtosecond laser-based optical sampling system [3]. Therefore, the system requires a level of complexity regarding spatial and temporal alignment. Moreover, a lock-in amplifier (LIA) is often required to remove the large noise on top of the typically weak signals from electro-optic sampling. Although dual-THz comb spectroscopy with two synchronized femtosecond laser systems [6] and single-shot THz-TDS [7] can be used to obtain the temporal waveform of a THz electric field in less than a few seconds without an LIA, a complex and expensive system, including two femtosecond lasers, is still required [8]. These THz-TDS systems are difficult to apply in industry owing to their complexity and high cost. Here, we focus on THz-FTIR, which is composed of only a simple interferometer, including a detector with broadband spectral responsivity, such as a pyroelectric [9] or micro-bolometer [10]. The THz interferometer provides a more simple and less complex setup due to its THz-only beamlines. Unfortunately, THz-FTIR also requires an LIA to obtain a significant signal output. Moreover, the detectors can only measure the average intensity of the THz waves. Thus, conventional THz-FTIR techniques cannot obtain the temporal waveform of the electric field of the THz waves. Consequently, THz-FTIR cannot evaluate the complex refractive index of a sample without any assumptions. Therefore, a THz-FTIR based on the THz electric field with a high dynamic range (DR) with a simple setup is desirable for real-world applications.
Recently, a THz-photomultiplier tube (THz-PMT) that can directly detect the electric field of an input THz pulse through THz-electron conversion using a metasurface based on field-emission theory has been developed [11–14]. Owing to electron multiplication in the well-established PMT, the response time of the THz-PMT is on the order of a few nanoseconds with a high signal gain and low noise [15]. Moreover, owing to electric field-driven electron emission, THz-PMTs show a nonlinear response to the input electric field based on the Fowler–Nordheim (FN) relation [11–14]. Thus, THz-FTIR with THz-PMT can be expected to have a high DR owing to the nonlinear response of the input THz electric field and high PMT gain, especially compared to conventional linear-response detectors, such as pyroelectrics and bolometers. THz-PMT-based THz-FTIR with a simple setup can be obtained using an interferometric trace of an electric field, yielding a corresponding complex refractive index, similar to THz-TDS, but crucially without any synchronized optical probe pulses.
Here, we introduce THz-FTIR based on a nonlinear interferometric technique using a THz-PMT (THz-PMT-FTIR) and a conventional Michelson interferometer (Section 2). With the THz-PMT, we can obtain the temporal waveform of the electric field of an interferogram with a high DR without the use of an LIA. We compare the interferogram and the corresponding spectrum obtained using the THz-PMT-FTIR with those obtained using conventional THz-TDS and pyroelectric-based THz-FTIR (Section 3). Finally, we evaluate the complex refractive indices and transmittances of the samples as obtained through the THz-PMT-FTIR method.
2. Experimental setup
The experimental setup is shown in Fig. 1(a). THz pulses were emitted by optical rectification in a ZnTe (110) crystal (thickness t = 1 mm) pumped by a regenerative-amplified Ti-sapphire femtosecond laser (Legend, Coherent, pulse duration 50 fs, pulse energy 2 mJ, repetition rate 1 kHz, center wavelength 800 nm). A black polyethylene sheet (t = 0.3 mm) was inserted behind the ZnTe crystal to remove residual NIR light. The temporal waveforms of the THz pulses were evaluated in advance using a conventional electro-optic-sampling-based THz-TDS system (not shown) with another ZnTe crystal (t = 1 mm) for detection. The generated THz pulses were guided using a conventional Michelson-type interferometer. High-resistivity silicon wafers (t = 0.525 mm) were used as THz beam splitters. The split THz beam in a fixed arm was retroreflected using an Ag mirror. The second split THz beam in a variable arm was retro-reflected using another Ag mirror on a programmable delay stage (OSMS20-85(X), SigmaKoki, resolution = 1 µm). Moving the delay stage by 1 mm made the THz-beam move by 2 mm. A spatially combined THz beam from the fixed and variable arms through the Si beam splitter was coaxially focused on the THz-PMT using a Tsurupica lens (f = 50 mm). The focused THz beam diameter at the THz-PMT interface was estimated to be 1 mm and the peak electric-field strength of the THz pulse at the same position was estimated to be 11 kV/cm (Fig. 1(b)). The output signal from the THz-PMT was recorded using a voltmeter (7351A, ADCMT) with a current amplifier (gain of 106 V/A, LI-76, NF) as an integrator [11]. The temporal waveform of the interferogram was obtained by varying the position of the delay stage.
Fig. 1. (a) Experimental setup. A THz beam is generated through optical rectification in ZnTe and split into two arms, forming a Michelson interferometer. The sample is placed in one arm, and the signal is detected by focusing the combined beam into the THz-PMT (b) Typical temporal waveform of a THz pulse emitted from a ZnTe crystal pumped by a NIR-fs pulse. The temporal waveform of the THz pulse was obtained by a conventional electro-optic sampling system. (c) Corresponding THz spectrum from (b) via Fourier transformation. THz-PMT: THz-photomultiplier tube.
The THz-PMT detects the THz electric field directly, owing to the THz-electron conversion approach based on a metasurface. Compared to a conventional PMT, the difference with the THz-PMT relates to the replacement of the conventional photocathode with the metasurface, while the remaining structure (i.e. the electron multiplication) remains unchanged. The metasurface consists of gold antenna arrays in a double-split-ring resonator configuration (DSRR, Fig. 1(a) inset), designed for an optimal response within the THz bandwidth of 0.3–1.1 THz [11]. In particular, the peak resonance frequencies of the DSRR were calculated as 0.45 and 0.76 THz from CST simulations. To increase the sensitivity of the THz-PMT, the metasurface was coated with a thin layer of cesium (Cs). Alkali metals like Cs decrease the effective work function of the combined metal stack [11]. A bias of -1500 V was applied to the THz-PMT, corresponding to an electron gain factor of the PMT dynodes of G∼1 × 105. The room temperature was maintained at 297 K.
3. Results and discussions
We evaluated the THz PMT response as a function of the THz electric field strength. A typical nonlinear THz PMT response regarding the input peak THz electric field strength of a single-cycle THz transient is shown in Fig. 2(a). We evaluated the voltage V of the output signal from the THz-PMT, controlled by the peak electric field of the input THz pulse modified by two wire-grid polarizers. The wire-grid polarizers allow for accurate attenuation of the polarized THz field while maintaining polarization—important for the polarization and polarity-sensitive THz-PMT [11]. According to Ohm's law, voltage V is proportional to current J. In this case, the measurable range of V was 1 mV to 0.6 V, limited by the current amplifier, meaning that at higher field strengths the PMT would saturate, and the gain needed to be reduced, lowering measurement consistency. The output was saturated when V was more than 0.3 V. When the peak electric field of the input THz pulse increased, J increased according to the FN relation [11–14]:
Fig. 2. (a) Nonlinear THz-PMT response with respect to the input THz electric field strength as calibrated in front of the PMT entrance window. The black dotted line represents a FN-fit [11–14] from the experimental data. (b) Interferogram after calibration with respect to (a). Corresponding amplitude (c) and phase (d) spectrum via Fourier transformation of the blue line from (b). The green dotted line is the normalized frequency-domain simulation of the field enhancement factor β at the antenna tip from [11].
As a proof-of-concept, we measured the interferogram using the THz-PMT-FTIR. After calibration using the fitting function in Fig. 2(a), we obtained the temporal waveform of the interferogram electric field (Fig. 2(b)), which linearizes the signal on the Y-axis. Due to the passes through the silicon beam-splitter as well as the silicon-substrate of the metasurface, the residual near-IR pump pulse was sufficiently attenuated to not affect the obtained interferometric signal. In particular, we can directly observe the electric field of the interfered THz pulse using the THz-PMT-FTIR method because the output signal from the THz PMT depends on the peak electric field of the THz pulse rather than the average intensity. The time origin was defined as the point where both THz-pulses overlap. Five peaks were observed in the interferogram. Reflected pulses, attributed to the Si-beam splitter and PMT internal metasurface Si-substrate were observed at ±17 and ±12 ps, respectively. Furthermore, multiple-reflected THz pulses of the Si components were observed at ±24 ps. Echoes from the PMT quartz entrance window are comparatively weak and appear at 13.3 ps. The dark noise of the system, mainly resulting from stray-light interacting with the alkali coating, as well as electronically induced noise from the LIA and voltmeter (black), effectively set the lower limit of the system, though we estimate this noise variation at less than 3 V/cm when evaluating the THz electric field strength, far below the operating regime of kV/cm field strengths. Owing to PMT saturation at a signal intensity of more than 0.3 V (see Fig. 2(a)), the peak signal at 0 s in the linear Y-axis interferogram is not equal to the sum of the signals from the fixed and delayed arms (see Fig. 2(b)). Using a fast Fourier transform (FFT), we derived the corresponding amplitude (Fig. 2(c)) and phase (Fig. 2(d)) spectrum from the obtained interferogram. The obtained spectrum is different from the output spectrum of the EO sampling system using the ZnTe crystal (Fig. 1(c)) because the THz-PMT imprints the frequency response from its metasurface onto the signal, which is highlighted by the two distinct spectral peaks observed at 0.50 and 0.76 THz. These two peaks agree with the resonance of the DSRR calculated from the simulation (green dotted line in Fig. 2(c)) [11]. The spectral sensitivity of the THz-PMT is thus determined by the resonance frequency of the metasurface, enabling the development of metasurfaces that are resonant at specifically desired frequency windows for spectroscopy.
We compared the DR of the power spectrum obtained using the THz-PMT method with those obtained using pyroelectric-based FTIR (THZ-2I-BNC, Gentec) and stage-based conventional THz-TDS. For pyroelectric-based FTIR, interferograms were measured by replacing the THz-PMT with a pyroelectric detector. An LIA was employed for all methods other than the proposed THz-PMT setup. The LIA integration times for the pyroelectric-based FTIR and THz-TDS were 300 ms and 30 ms, respectively. It was noted that pyroelectric-based FTIR cannot be obtained from the electric field because the pyroelectric detector can only measure the average interferogram intensity. Figure 3 shows the corresponding power spectra of the interferograms. The spectral power DR was defined as DR = (mean FT power)/(noise floor), where mean FT power and noise floor are the intensity of the obtained spectrum and the averaged intensity of the noise-floor between 5.0 to 7.0 THz, respectively [4]. The THz-TDS and THz-PMT-FTIR produce an amplitude spectrum because their methods obtain an electric-field profile. In contrast, pyroelectric-based FTIR provides a power spectrum because the method can only obtain an intensity profile. For clear comparison, we show the power spectrum from each method by squaring the amplitude profiles. The power DRs using the THz-PMT and pyroelectrics were more than 4.6 × 105 and 7.1 × 102, respectively. Thus, the DR of the proposed method can be increased by more than 600 times using the THz-PMT without a LIA compared to that using a pyroelectric detector. Further improvement could be obtained when operating the THz-PMT with a box-car integrator and a LIA. In addition, the DR from THz-TDS was more than 9.7 × 104 with a LIA. Consequently, our method boasts the highest DR and allows direct acquisition through electric-field tracing and its associated amplitude spectrum, all without a need of a LIA.
Fig. 3. Power DR spectrum corresponding to the interferogram in Fig. 2(b) (blue), interferogram with pyro and LIA (black), and conventional THz-TDS using ZnTe-based EO sampling technique with an LIA (red).
Last, we demonstrate the spectroscopy of two samples, a quartz glass plate (t = 0.5 mm) and a bandpass filter for 0.5 THz (BPF0.5, TYDEX), using the proposed method, with the THz beam passing through the sample twice. Figure 4(a) shows the calibrated electric field interferograms with and without a quartz glass plate. Although there were multiple reflected pulses, the transmitted THz pulses with and without the sample were observed at 0 and 8 ps, respectively (the region of interest is indicated by the dashed-line box in Fig. 4(a)). Using FFT, the refractive index n and extinction coefficient k were obtained as follows:
Fig. 4. (a) Interferogram with and without a quartz glass plate (t = 0.5 mm). The black box highlights the region of interest for FFT. (b) Complex refractive index of the sample using the proposed method (blue) and conventional THz-TDS (red). (c) Interferogram with and without a THz bandpass filter (0.5 THz). (d) Transmittance-amplitude profile of the bandpass filter (BPF0.5, TYDEX) using the THz-PMT-FTIR method (blue) and conventional THz-TDS (red).
The temporal measurement range (∼15 ps) was limited by the multiple reflections originating from the Si beam splitter, THz-PMT quartz-window, and Si-substrate of the THz-PMT metasurface. These reflections can be suppressed beneath the required field-strength threshold of the THz-PMT using antireflection (AR) coatings, such as parylene [16] or Si nanoparticles [17]. Consequently, the spectral resolution of the THz-PMT-FTIR can be improved with sufficient reflected THz pulse suppression.
The inversion of the interferograms, as described here, is not mathematically stringent. However, the spectroscopic approach is strictly valid in the situation where the THz-PMT is driven at high field strengths so that its response becomes quadratic (see Eq. (1) for high field strengths). In this situation, the interferogram resembles that of a first-order interferometric autocorrelation with a quadratic detector, where the Fourier transform of the interferogram represents the spectral amplitude and phase of the THz pulse. Hence, the spectroscopic approach demonstrated here works well under the conditions of strong THz fields and low dispersion of the sample.
In this study, the scanning time was limited by the delay stage and communication with devices, such as the voltmeter, resulting in a measurement time of approximately 70 ms per plot. To overcome this limitation, a rotation-mirror-based delay stage [18] with a high-speed digitizer can be used, potentially reducing the scanning time for each trace to less than a few hundred ms [19] because of the high response speed of the THz-PMT. Furthermore, the measurement time was limited by the repetition rate of the pump laser (repetition frequency =1 kHz). Future improvements to the detection threshold of the THz-PMT will enable a fiber-based THz source with a repetition rate exceeding 100 MHz [20]. Alternatively, photo-conductive antennas operated using Er-fs fiber lasers are being improved upon, leading to almost 1 mW output THz power [21, 22], reaching output field strengths of approximately 1 kV/cm. Thus, we estimate that the THz-PMT can soon be combined with oscillator-based THz light sources, especially when considering improvements to the sensitivity of the THz-PMT to less than 1 kV/cm, e.g., with nanoslit-geometries for the metasurface [11]. Moreover, fiber-based femtosecond lasers are less expensive and more robust than Ti:Sapphire lasers and the spectral resolution can be improved above 100 MHz [6,20]. Ultimately, the measurement limit is a few nanoseconds owing to the electron transit time in the dynode of the THz-PMT [15]. However, this would also require high-power THz CW or quasi-CW sources that are not yet available.
The DR of the obtained THz spectrum was limited by the charged amplifier. To improve the DR, an appropriate high-DR amplifier should be used. Due to the minimum required field to drive electron tunneling in the PMT metasurface, fields below this threshold cannot be detected. (see Fig. 2). Thus, the proposed method cannot perfectly detect the destructive interference signals. As a result, the THz spectrum obtained using the proposed method is slightly distorted. A solution to this is to expand the input dynamic range of the THz-PMT by engineering more favorable values for β and Φ in Eq. (1). However, this may decrease the sensitivity of the THz-PMT in certain cases, leading to a trade-off between the input dynamic range and THz-PMT sensitivity.
The spectral sensitivity of the THz-PMT can be tuned by changing the metasurface design, leading to more pronounced resonances, or a more flat-top response with generally reduced sensitivity. In addition, the general resonance of the metasurface can be tuned by scaling the dimensions of the structures. Lange et al. reported that an electric field of 40 THz could be detected using a mid-infrared (MIR)-PMT [11] based on the same principle as the THz-PMT. Therefore, the spectral bandwidth of the THz-PMT-FTIR method can be expanded to any frequency within the low-THz to MIR range.
4. Conclusions
We demonstrated a novel method for high DR Fourier-transform-based THz spectroscopy using a conventional Michelson interferometer and a THz-PMT. As the THz-PMT depends on the peak electric field of the input THz pulse, the proposed method obtains an interferogram that is directly dependent on the electric field, rather than an average intensity as with conventional THz detectors. Owing to the nonlinear response based on the FN relation and the fast response of the well-established-PMT technique with low noise, we obtained a high DR of 4.6 × 105 without an LIA. The required scanning time was limited by the employed voltmeter and laser repetition rate. It can be improved by replacing these devices, especially with future generations of more sensitive THz-PMTs allowing higher-repetition-rate THz sources. We confirmed that the THz-PMT-FTIR method can obtain the complex refractive index of a quartz glass plate. Furthermore, the frequency transmittance-amplitude profiles of a THz bandpass filter were presented with high accuracy. The obtained results are in good agreement with those of conventional THz-TDS. The retrieval of the optical properties of materials with our technique is nontrivial, and further investigations are needed to document the parameter space (field strengths, dispersion of the material) under which the technique works best. To the best of our knowledge, this is the first study that THz-PMT and interferometer, without any synchronized optical probe pulse, were combined and applied for spectroscopy, as compared to established THz-TDS. We believe that the proposed method has the potential to be a feasible and cost-efficient alternative to conventional THz-TDS, maintaining the DR without the need for an LIA. The proposed THz-PMT-FTIR method with a simple and cost-efficient setup should be useful for real-world THz applications such as spectroscopy and non-destructive testing.
Acknowledgment
We thank G. Sugiura (Hamamatsu), Y. Takida, and H. Minamide (Riken) for the fruitful discussions and K. Hirano and S. Shirai from Hamamatsu for creating the measurement programs. We would like to thank Editage for English language editing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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