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High-resolution broadband terahertz spectroscopy via electronic heterodyne detection of photonically generated terahertz frequency comb D. G. Pavelyev, A. S. Skryl, and M. I. Bakunov* University of Nizhny Novgorod, Nizhny Novgorod, Russia *Corresponding author: [email protected] Received July 11, 2014; revised August 22, 2014; accepted August 22, 2014; posted August 22, 2014 (Doc. ID 216823); published September 25, 2014 We report an alternative approach to the terahertz frequency-comb spectroscopy (TFCS) based on nonlinear mixing of a photonically generated terahertz pulse train with a continuous wave signal from an electronic synthesizer. A superlattice is used as a nonlinear mixer. Unlike the standard TFCS technique, this approach does not require a complex double-laser system but retains the advantages of TFCS—high spectral resolution and wide bandwidth. © 2014 Optical Society of America OCIS codes: (120.6200) Spectrometers and spectroscopic instrumentation; (300.6495) Spectroscopy, terahertz. http://dx.doi.org/10.1364/OL.39.005669

Terahertz frequency-comb spectroscopy (TFCS) is a recent technique with a high potential for practical applications. TFCS is based on using photonically generated terahertz pulse trains whose Fourier spectrum is a series of harmonics of the pulse repetition frequency, i.e., a frequency comb. Due to a short duration of a single terahertz pulse, the frequency comb extends over a wide interval of terahertz frequencies, whereas the width of a discrete spectral line in the comb can be made very narrow by expanding the detection time window (i.e., increasing the number of acquired pulses). Thus, TFCS combines the merits of the two widely used spectroscopic techniques, namely, broadbandness of the terahertz time-domain spectroscopy (THz-TDS), which is based on measuring a single terahertz pulse, and high resolution of the frequency-domain spectroscopy with narrow tunable continuous-wave terahertz radiation (CW-THz spectroscopy). Furthermore, stabilizing the repetition rate of the driving femtosecond laser can calibrate the absolute frequencies of the terahertz comb components. This allows one to use a terahertz comb as a precise ruler of terahertz frequency. TFCS appeared [1] as an extension of similar techniques developed earlier for the visible and mid-infrared frequency ranges [2,3]. A typical TFCS spectrometer contains dual (pump and probe) femtosecond lasers with stabilized individual repetition rates and the frequency offset between them [1,4–6]. A photoconductive antenna (PCA) driven by the pump laser emits an electromagnetic terahertz comb, whereas the probe laser induces a photocarrier terahertz comb with different frequency spacing in another PCA used as a detector [7]. The photoconductive mixing of the two combs in the PCA-detector results in the generation of photocurrent pulses whose spectrum is a replica of the terahertz comb only downscaled to the RF frequency range. By measuring this spectrum with an RF spectrum analyzer, one can visualize the terahertz comb. This detection technique is often referred to as multi-frequency-heterodyning [1]. The current state-ofthe-art of TFCS is using the time-window-extended asynchronous-optical-sampling THz-TDS (ASOPS-THz-TDS) for the signal-to-noise-enhanced detection of the terahertz frequency comb [6]. 0146-9592/14/195669-04$15.00/0

In the present Letter, we propose and implement an alternative approach to realization of TFCS. In this approach, only an electromagnetic terahertz comb is generated photonically, with use of a single femtosecond laser and PCA (or an electro-optic emitter). The comb, transmitted through a sample, is heterodyned to the UHF frequency range via nonlinear mixing in a superlattice (SL) diode [8] with a sinusoidal EHF signal from a frequency synthesizer. The UHF replica of the terahertz comb is observed with an RF spectrum analyzer. Unlike the standard TFCS technique, this approach does not require the use of a complex dual laser system. At the same time, it retains all the advantages of TFCS, as we demonstrate below. Figure 1 shows a schematic diagram of the experimental setup. A mode-locked femtosecond Er-fiber laser (1.55 μm wavelength, 65 fs pulse duration, 30 mW average power, and 100 MHz repetition rate; Menlo Systems GmbH) was used to trigger PCA. PCA emits a terahertz pulse train with a comb spectrum nf r , where f r is the repetition rate and n is an integer number. The terahertz beam was collimated and focused onto the entrance aperture of a horn antenna by a pair of TPX lenses. The low-frequency components of the terahertz signal were filtered out by waveguide 1 whose cutoff frequency was set to 187.5 GHz. The higher frequency components were fed to a SL-mixer. Simultaneously the mixer was 9 kHz - 26.5 GHz Spectrum analyzer

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pumped (through waveguide 2) by a CW signal of frequency f s from a frequency synthesizer with a 78– 178 GHz tuning range and 20 mW output power. An attenuator regulated the power on SL. The pump signal causes high-harmonic currents to flow in SL, any one of which can be used as a local oscillator to downconvert the terahertz signal to low microwave frequency, as in a standard heterodyne scheme [9]. Detailed description of the mixer is given elsewhere [10]. Thus, the mixer produces multiple beat signals at the frequencies jnf r − mf s j, where m is an integer, which are amplified by 54 dB and observed with use of an RF spectrum analyzer of a 26.5 GHz bandwidth (Agilent Technologies E4407B). Figure 2(a) shows a temporal waveform of a single terahertz pulse from the train emitted by PCA. It was measured on a 460 ps time window [only 85.5 ps part

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of the window is shown in Fig. 2(a)] by the standard THz-TDS with Tera K15 spectrometer (Menlo Systems GmbH). Corresponding amplitude spectrum is continuous without comb structure [Fig. 2(b)]. The narrow dips in the spectrum are absorption lines of water vapor. The frequency resolution (the reciprocal of the time window) is 2.2 GHz. Figure 3(a) shows the output power spectrum measured with the TFCS setup (Fig. 1) for f s  85 GHz. The width and large-scale inhomogeneity of the spectrum are mainly determined by the frequency response of the amplifier, which is shown in Fig. 3(b). The spectrum in Fig. 3(a) contains many beat signals between a certain mth harmonic of the CW signal and the terahertz comb components with different n. The beat signals may be divided into two sets with nf r > mf s and nf r < mf s . In every set, the beat signals are separated by the repetition rate f r  100 MHz. To determine the harmonic number m in the output spectrum in Fig. 3(a), the following procedure was used. We retuned slightly (by several MHz) the operating frequency of the synthesizer. This caused shifting the spectral lines in the output spectrum. The shift of a specific spectral line divided by the change in the operating frequency of the synthesizer gives, evidently, the number m. By using this procedure, we obtained m  4 for the spectrum in Fig. 3(a). Physically, the predominance of the fourth harmonic can be

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explained by the following reasons. First, due to quadratic nonlinear conductivity of the SL, which was used in the experiment, only even harmonics of f s were generated in the mixer. Second, since the low-frequency part of the terahertz comb spectrum was filtered out by waveguide 1, the beat signals between the second harmonic (170 GHz) and the terahertz comb components (>187.5 GHz) did not fall into the bandwidth of the amplifier. Third, the sixth and higher harmonics were, evidently, too weak to be observed. To evaluate the spectroscopic potential of the proposed technique, we measured the absorption profile of the rotational manifold of transition J 0 − J  20 − 19 near 0.4136 THz of fluoroform (CF3 H) at a pressure of 50 Torr. At pressures more than ∼0.1 Torr, the twenty K-components of the manifold are completely overlapped and form a single collision-broadened spectral line. To measure the shape of the line, a quartz cell (a 30-mm diameter and 150-mm length) with CF3 H was placed between the TPX lenses (Fig. 1). The frequency f s of the synthesizer was increased from 103.40 to 104.15 GHz by 25-MHz steps, so that the frequency of the fourth harmonic 4f s changed in the interval 413.60–416.60 GHz by 100-MHz steps equal to the frequency spacing between the terahertz comb components. Measurement of the output power at a fixed frequency of 1.5 GHz (the center of the amplifier bandwidth) gave us the amplitudes of the terahertz comb components at nf r  4f s − 1.5 GHz from the interval 412.1– 415.1 GHz. The results are shown in Fig. 4. After fitting the spectral shape by a Lorentzian function, the spectral linewidth was determined to be 1.4 GHz. The center frequency of the absorption profile 413.6 GHz is in a good agreement with the result of our calculation based on Eqs. (3)–(55) in [11] for the frequency of a rotational transition with the rotational and centrifugal constants taken from [12–14]. The proposed technique has a broad spectral coverage. The spectral band is primarily determined by the nonlinear properties of the SL-mixer and can be as large

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as several hundreds gigahertz. To demonstrate the broadbandness of the technique, we measured the amplitudes of the terahertz comb components (without a sample) in a wide range ∼200–500 GHz using a single SL-mixer (the frequency range can be extended to the higher frequencies by using a higher frequency SL-mixer). In the experiment, we varied the frequency of the synthesizer by large steps and measured the output beat signal power at 1.5 GHz. The measurements in the interval ∼200– 300 GHz were performed by mixing the terahertz comb with the second harmonic of the synthesizer frequency, and in the interval ∼340–520 GHz—with the fourth harmonic. The results are shown in Fig. 5. The large-step structure of the terahertz spectrum (the oscillations at ∼200–300 GHz and maximum at ∼400 GHz) correlates with the spectrum shape of a single terahertz pulse [Fig. 2(b)]. In the vicinity of any frequency from the interval ∼200–500 GHz, where we obtained the beat signal, precise spectroscopic measurements with 100MHz spectral resolution can be performed using our experimental setup. To conclude, we experimentally demonstrated photonic–electronic TFCS, which does not require a complex dual laser system. The spectral resolution of the technique is determined by the repetition rate of the pump laser (100 MHz) and exceeds the resolution of THz-TDS by the order of magnitude. The spectral coverage is determined by the nonlinear properties of the mixer. For a mixer based on a superlattice diode, which generates high harmonics more efficiently than widely used Schottky barrier diodes [15], the coverage can be as large as several hundreds gigahertz. With our experimental setup, we have demonstrated the possibility to perform precise spectroscopic measurements in the frequency range ∼200–500 GHz. The spectral coverage can be extended to the higher frequencies by using a higher frequency superlattice mixer.

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This work was supported in part by the Ministry of Education and Science of the Russian Federation through Agreement Nos. 11.G34.31.0011 and 02.B.49.21.0003 and RFBR Grant No. 14-02-00581. We are grateful to M. Yu. Tretyakov for advising us about fluoroform. References 1. T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, Appl. Phys. Lett. 88, 241104 (2006). 2. Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002). 3. F. Keilmann, C. Gohle, and R. Holzwarth, Opt. Lett. 29, 1542 (2004). 4. T. Yasui, M. Nose, A. Ihara, K. Kawamoto, S. Yokoyama, H. Inaba, K. Minoshima, and T. Araki, Opt. Lett. 35, 1689 (2010). 5. Y. Kim, D.-S. Yee, M. Yi, and J. Ahn, J. Korean Phys. Soc. 56, 255 (2010). 6. Y.-D. Hsieh, Y. Iyonaga, Y. Sakaguchi, S. Yokoyama, H. Inaba, K. Minoshima, F. Hindle, Y. Takahashi, M. Yoshimura, Y. Mori, T. Araki, and T. Yasui, IEEE Trans. Terahertz Sci. Technol. 3, 322 (2013).

7. S. Yokoyama, R. Nakamura, M. Nose, T. Araki, and T. Yasui, Opt. Express 16, 13052 (2008). 8. D. G. Pavel’ev, N. V. Demarina, Yu. I. Koshurinov, A. P. Vasil’ev, E. S. Semenova, A. E. Zhukov, and V. M. Ustinov, Semiconductors 38, 1105 (2004). 9. A. Rogalski and F. Sizov, Opto-Electron. Rev. 19, 346 (2011). 10. D. G. Paveliev, Yu. I. Koschurinov, V. M. Ustinov, A. E. Zhukov, F. Lewen, C. Endres, A. M. Baryshev, P. Khosropanah, W. Zhang, K. F. Renk, B. I. Stahl, A. Semenov, and H.-W. Huebers, “Short GaAs/AlAs superlattices as THz radiation sources,” in Proceedings of the 19th International Symposium on Space Terahertz Technology, Groningen, The Netherlands, 28–30 April 2008, pp. 319–328. 11. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover, 2013). 12. R. Bocquet, D. Boucher, W. D. Chen, D. Papousek, G. Wlodarczak, and J. Demaison, J. Mol. Spectrosc. 163, 291 (1994). 13. M. A. Pashaev, O. I. Baskakov, B. I. Polevov, and S. F. Dyubko, J. Mol. Spectrosc. 131, 1 (1988). 14. Y. Kawashima and A. P. Cox, J. Mol. Spectrosc. 61, 435 (1976). 15. V. Vaks, J. Infrared Milli Terahz Waves 33, 43 (2012).