Terahertz balanced self-heterodyne spectrometer with SNR-limited phase-measurement sensitivity

Terahertz balanced self-heterodyne spectrometer with SNR-limited phase-measurement sensitivity Shintaro Hisatake, 1, Yuki Koda, 1 Ryosuke Nakamura, 2 Norio Hamada, 2 and Tadao Nagatsuma 1 1 Advanced Electronics and Optical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan 2 Science & Technology Entrepreneurship Laboratory, Osaka University, Suita 565-0871, Japan hisatake@ee.es.osaka-u.ac.jp Abstract: Photonics-based frequency-domain terahertz (THz) wave measurement systems have received significant attention in both scientific and industrial fields due to their high-frequency resolution. Highly sensitive phase-measurement systems have been desired in the chemical, material, and biomedical sciences to facilitate microanalysis of materials. Here, we demonstrate a balanced self-heterodyne technique that, for the first time, simultaneously offers wide frequency tunability of more than 2.5 THz and high phase sensitivity, which is limited only by the signal-to-noise ratio (SNR) of the amplitude measurement. Using free-running lasers for THz wave generation and detection, the experimentally achieved minimum detectable optical path length change was 400±50 nm at 2 THz for a SNR of 37.7 ± 0.7 db, even though the theoretically expected SNR-limited value was 310 ± 20 nm. The phase measurement sensitivity of our system is almost one order of magnitude better than that of the conventional systems in which limitations arise from phase instabilities in the optical components and/or laser linewidth. 2015 Optical Society of America OCIS codes: (300.6495) Spectroscopy, terahertz. References and links 1. I. Amenabar, F. Lopez, and A. Mendikute, In introductory review to THz non-destructive testing of composite mater, J. Inf. Millimeter Terahertz Waves 34, 152 169 (2013). 2. T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, N. Yoshimoto, J. Terada, and H. Takahashi, Terahertz wireless communications based on photonics technologies, Opt. Express 21(20), 23736 23747 (2013). 3. G. Mouret, S. Matton, R. Bocquet, D. Bigourd, F. Hindle, and A. Cuisset, Anomalous dispersion measurement in terahertz frequency region by photomixing, Appl. Phys. Lett. 88, 181105 (2006). 4. L. Rong, T. Latychevskaia, C. Chen, D. Wang, Z. Yu, X. Zhou, Z. Li, H. Huang, Y. Wang, and Z. Zhou, Terahertz in-line digital holography of human hepatocellular carcinoma tissue, Sci. Rep. 5, 8445 (2015). 5. J.-Y. Kim, H.-J. Song, M. Yaita, A. Hirata, and K. Ajito, CW-THz vector spectroscopy and imaging system based on 1.55-µm fiber-optics, Opt. Express 22(2), 1735 1741 (2014). 6. R. Rahman, T. R. Ohno, P. C. Taylor, and J. A. Scales, Optically activated sub-millimeter dielectric relaxation in amorphous thin film silicon at room temperature, Appl. Phys. Lett. 104, 182104 (2014). 7. T. Y. Wu, High dynamic range terahertz-wave transmission loss measurement at 330 500 GHz, Sci. Technol. 23, 085904 (2012). 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26689

8. T. Gobel, D. Stanze, B. Globisch, R. J. B. Dietz, H. Roehle, and M. Schell, Telecom technology based continuous wave terahertz photomixing system with 105 decibel signal-to-noise ratio and 3.5 terahertz bandwidth, Opt. Lett. 38(20), 4197 4199 (2013). 9. S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, Phase-sensitive terahertz selfheterodyne system based on photodiode and low-temperature-grown GaAs Photoconductor at 1.55 µm, IEEE Sens. J. 13(1), 31 36 (2013). 10. J.-Y. Kim, H. Nishi, H.-J. Song, H. Fukuda, M. Yaita, A. Hirata, and K. Ajito, Compact and stable THz vector spectroscopy using silicon photonics technology, Opt. Express 22(6), 7178 7185 (2014). 11. K. Thirunavukkuarasu, M. Langenbach, A. Roggenbuck, E. Vidal, H. Schmitz, J. Hemberger, and M. Grüninger, Self-normalizing phase measurement in multimode terahertz spectroscopy based on photomixing of three lasers, Appl. Phys. Lett. 106, 031111 (2015). 12. S. Hisatake and T. Nagatsuma, Precise terahertz-wave phase measurement based on photonics technology, in 39th International Conference on Infrared, Millimeter, and Terahertz Waves (IEEE, 2014), pp. 1 2. 13. S. Hisatake, H. H. Nguyen Pham, and T. Nagatsuma, Visualization of the spatial-temporal evolution of continuous electromagnetic waves in the terahertz range based on photonics technology, Optica 1(6), 365 371 (2014). 14. S. Hisatake, J.-Y. Kim, K. Ajito, and T. Nagatsuma, Self-heterodyne spectrometer using uni-traveling-carrier photodiodes for terahertz-wave generators and optoelectronic mixers, J. Lightwave Technol. 32(20), 3683 3689 (2014). 15. M. Naftaly and R. Dudley, Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers, Opt. Lett. 34(8), 1213 1215 (2009). 16. S. L. Zabell, On Student s 1908 article The probable error of a mean, J. Am. Stat. Assoc. 103(481), 1 7 (2008). 1. Introduction Terahertz waves (THz waves: 0.1 THz 10 THz) have received increasing interest not only in industrial applications, such as non-destructive spectroscopic imaging [1] and ultrafast wireless communications [2], but also in the chemical, material, and biomedical sciences. In particular, THz frequency-domain measurement systems based on continuous wave (CW) technology have been extensively studied [3] because they provide a higher signal-to-noise ratio (SNR), higher linearity of measurement, and higher frequency resolution compared to the well-established THz time-domain spectrometers (THz-TDS). Using the CW-system at the point frequency of 2.5 THz, THz phase imaging has been shown to be critical for cancer diagnosis because the absorption properties of a cancerous sample are influenced by two opposing factors in the THz range [4]. Moreover, the absorbance and relative permittivity can serve as complementary markers for material specifications using THz fingerprint spectra [5]. For these applications, precise and wide-bandwidth measurements of the complex dielectric constant in the samples has been highly desired to facilitate microanalysis of materials. The operation frequency of vector network analyzers (electronics-based CW systems) has been extended to the THz range. Rahman et al. demonstrated the measurement of the frequencydependent photo-induced complex conductivity of thin silicon films (1 µm) at a limited frequency band in the 100 350 GHz range for improved photovoltaics and other semi-conductor devices [6]. A loss measurement system at 330 500 GHz has also been demonstrated with an expanded standard phase-measurement uncertainty of 0.58 [7]. Due to phase locking and frequency multiplexing, electronics-based CW-systems offer a precise phase measurement. However, the bandwidth or the frequency tunability of electronics-based systems still limits applications to THz spectroscopic applications where the fingerprint spectra of materials, which typically lies above 1 THz, has been investigated. Using 1.55-µm telecom technology, photonics-based CW systems have been demonstrated with a maximum SNR of 105 db and a 3.5-THz bandwidth due to state-of-the-art photoconductive antennas (PCAs)[8]. In photonics-based systems, a self-heterodyne technique [9] offers simultaneous measurement of THz amplitude and phase while canceling the phase noise originating from the free-running lasers, which are key components for the wide frequency tunability of the system. However, fiber-based THz CW systems, which contain a fiber section (40 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26690

cm) in an insulated box for thermal stability, have a large phase drift of 1.5 /min [5], which ultimately limits the sensitivity of the phase measurement or the contrast of phase imaging. Although the root-mean-square (RMS) phase variation is expected to decrease to about 1 at the dynamic range (DR) of 65 db by replacing fiber components with a thermally stabilized silicon-photonics circuit [10], the reported phase variation in ref [10] is still 10 times larger than theoretical expectation, which is limited by the SNR of the amplitude measurement. Using frequency-stabilized lasers with one laser frequency locked to a Doppler-free Rb absorption line, Thirunavukkuarasu et al. proposed a homodyne-type self-normalizing phase-measurement system and demonstrated a minimum detectable optical path length change of 1 2 µm, which was limited by the laser frequency instability [11]. Thus, conventional photonics-based techniques have required temperature-stabilized optical components and/or highly stabilized lasers for precise THz wave phase measurements. In this letter, we demonstrate a photonics-based CW system with a SNR-limited phasemeasurement sensitivity. We show that the experimentally obtained relation between the SNR of the amplitude measurement and the standard deviation of the phase measurement fits the theoretically predicted curve. This result indicates that the development of high-power THz generators and/or highly sensitive THz mixers will improve the sensitivity in not only the absorbance measurement but also the optical path length (reflective index and/or displacement) measurement. 2. System configuration Figures 1(a) and (b) show the system configuration of the conventional self-heterodyne system and the proposed balanced self-heterodyne system [12], respectively. In both systems, a continuous THz wave is generated by optical-to-electrical (O/E) conversion and detected via mixing with an optical beat signal (optical local oscillator (LO) signal). For the radio-frequency (RF) signal, the frequency of the first laser (laser1) is shifted with an optical frequency shifter (FS) to realize self-heterodyne detection. Note that PCAs, electrooptic (EO) crystals [13], and photodiodes [14] can be used as mixers. In the conventional self-heterodyne system, the relative phase change between the THz wave and the optical LO signal are measured. The excess phase noise originates from the relative phase fluctuation between the optical beat signals in the RF arm and the optical LO signal. The phase noise of the optical beat signal in the RF arm can be expressed as φ RF = (φ LD2 φ LD1 ) + (φ 32 φ 12 ) + (φ 2g2 φ 2g1 ), Laser1 FS 1 2 RF O/E THz wave 2 Mixer_r O/E Laser2 3 4 LO Mixer_s Sample IF 4 5 Mixer_s Sample Conventional Balanced (a) (b) Fig. 1. Configurations of the (a) conventional and (b) balanced self-heterodyne system. FS: optical frequency shifter and O/E: optical-to-electrical converter. 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26691

where φ LD1 and φ LD2 are the laser phase noises, φ i j are the phase fluctuations imposed on the optical signals in the fiber between nodes i and j, φ 2g2 and φ 2g1 are the optical phase fluctuations imposed on the laser2 and laser1 components, respectively, in the fiber between node 2 and the RF generator (O/E converter). The phase noise of the optical LO signal can be expressed as φ LOa = (φ LD2 φ LD1 ) + (φ 34 φ 14 ) + (φ 4m2 φ 4m1 ), where φ 4m2 and φ 4m1 are the optical phase fluctuations imposed on the laser2 and laser1 components, respectively, in the fiber between node 4 and the mixer. We assumed that no time delay exists between the RF and LO arms. Therefore, excess phase noise in the THz phase measurement can be expressed as φ na = (φ 32 φ 12 ) (φ 34 φ 14 ) + (φ 2g2 φ 2g1 ) (φ 4m2 φ 4m1 ). (1) The components (φ 2g2 φ 2g1 ) and (φ 4m2 φ 4m1 ) are the phase noises imposed on the optical beat signals, whereas the components φ 32, φ 12, φ 34, and φ 14 are the phase noises independently imposed on the optical carriers in the fiber within the dashed box in Fig. 1. In this experiment, the shortest RF beat signal wavelength is 120 µm (2.5 THz), whereas that of the optical signal is 1.55 µm in vacuum. Therefore, the influence of the ambient thermal and vibrational noise to the optical signal phase is about 100 times greater than that to the optical beat signal. The primary components of excess phase noise (φ 32,φ 12,φ 34,φ 14,φ 2g2,φ 2g1, and part of (φ 4m2 φ 4m1 )) can be eliminated in the proposed balanced self-heterodyne system, where the phase change of the THz wave relative to the reference phase are measured as shown in Fig. 1(b). The remaining phase noises originate from the difference between the phase noise imposed to the optical LO signals (optical beat signals) in the optical fibers between node 5 and each mixer (Mixer s for the signal and Mixer r for the reference in Fig. 1). Figure 2 shows the experimental setup. Two frequency-detuned 1.55-µm laser diodes (LDs) are combined to produce a beat signal. The THz wave is generated by photomixing at the uni-traveling-carrier photodiode (UTC-PD) and is detected by PCAs. The frequency of LD1 is shifted by 500 khz with the EO frequency shifter. Each amplitude and phase detected by PCA1 and PCA2 are measured by a two-channel dual-phase lock-in amplifier. After the detection, the common phase noises are subtracted (θ = θ 2 θ 1 ). In the experiments, we have not actively stabilized the temperature of the optical fibers. LD1 EDFA FS UTC-PD LD2 EDFA 500 khz PCA1 PCA2 Sample θ 2 -θ 1 A 1 A 2 2-ch. Lock-in amp. TIA Fig. 2. Experimental setup. LD: laser diode, EDFA: erbium-doped fiber amplifier, FS: EO frequency shifter, UTC-PD: uni-traveling-carrier photodiode, and PCA: photoconductive antenna. 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26692

Dynamic range HdBL 80 60 40 20 0 0.5 1.0 1.5 2.0 Frequency HTHzL 2.5 3.0 Fig. 3. Frequency response of the system. Figure 3 shows the frequency response of the system. The power of the THz wave at 0.2 THz was about -10 dbm. The DR is defined by the ratio of the measured signal to the noise floor measured without the RF signal. The frequency was tuned from 0.1 to 3 THz. The frequency tuning speed was 125 GHz/s, and the time constant of the lock-in detection was 2.3 ms. Therefore, the frequency resolution, which is limited by the lock-in time constant, was about 0.3 GHz. A higher frequency resolution can be achieved with a slower frequency tuning speed, although the maximum resolution will be limited by the frequency fluctuation of the lasers (on the order of several tens of megahertz). 3. System evaluation The SNR (db) of the amplitude measurement can be expressed as SNR = 20 log10 A/σA, where A is the amplitude of the detected THz wave and σa is the standard deviation of the amplitude measurement. Note that the DR describes the maximum quantifiable signal change, while the SNR indicates the minimum detectable signal change [15]. If no excess phase noise exists, the standard deviation of the phase measurement is limited by the SNR of the amplitude measurement. The theoretical relationship between the phase standard deviation σθ (rad) and the SNR (db) of the amplitude measurement can be derived as σθ = 10 SNR/20. (2) Figure 4 shows the relationship between the phase standard deviation σθ and the SNR. In the experiment, we measured the THz amplitude and phase for 1 min and calculated the SNR and σθ. The measurement was performed five times to evaluate the standard errors (error bars in Fig. 4) of the SNR and σθ using the Student s t-distribution (90% confidence) [16]. The SNR was changed by changing the power of the THz wave and the lock-in time constant. The SNRs obtained with PCA1 and PCA2 were almost the same. The fiber length between node 5 in Fig. 1 and each mixer was 2.5 m. The traveling length of the THz wave from the UTC-PD to each mixer was set to be 0.5 m. The closed and open circles in Fig. 4 are the results obtained with our #240994 2015 OSA Received 26 May 2015; revised 4 Sep 2015; accepted 29 Sep 2015; published 2 Oct 2015 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26693

Phase standard deviation (deg.) 20 15 10 5 : Conventional (0.2 THz) : Balanced (0.2 THz) : Balanced (2.0 THz) : Theory 0 10 20 30 40 50 SNR (db) Fig. 4. Relation between the phase standard deviation and the SNR of the amplitude measurement. proposed system at 0.2 THz and 2.0 THz, respectively, while the crosses are the results obtained with the conventional self-heterodyne system at 0.2 THz. The solid curve is the theoretical relation calculated by Eq. (2). The phase standard deviation in the conventional system was limited to about 2, which is primarily due to the phase noise independently imposed on the optical carriers in the fiber within the dashed box in Fig. 1. On the other hand, the phase standard deviation in the balanced self-heterodyne system was well fitted to the theoretical curve of Eq. (2), regardless of the frequency. The phase standard deviation in the balanced self-heterodyne system was σ θ = 0.18±0.02 and σ θ = 0.95±0.13 for SNR of 50.6±1.5 db at 200 GHz and for 37.7 ± 0.7 db at 2 THz, respectively. At 200 GHz, the phase measurement sensitivity of the proposed system was about 10 times better than that of the conventional self-heterodyne system. The minimum detectable optical path length change δ x limits the sensitivity of refractiveindex contrast imaging. The value of δx can be calculated by δx = cσ θ 2π f, (3) where c is the speed of light and f is the THz frequency. Note that δx is inversely proportional to the THz frequency. However, the SNR, and therefore σ θ, generally decreases when the THz frequency increases. In our system, the experimentally achieved minimum detectable optical path length at 2 THz was δx=400±50 nm for the SNR of 37.7 ± 0.7 db, while the theoretically expected SNR-limited value is 310 ± 20 nm. If we assume 10-µm-thick frozen tissue sections with a refractive index of 1.5, which are typical values for biomedical samples, our system will resolve 2.6% of the refractive index change. In real applications, a path length difference δl must exist between the reference and sample paths due to the sample insertion, optical fiber instability, and so on. This path length difference leads imperfect phase noise cancellation. To evaluate system robustness, we measured the relationship between the phase standard deviation σ θe and δl, as shown in Fig. 5. Each measurement was performed five times to evaluate the standard errors of the standard deviation using the Student s t-distribution (90% confidence). We changed δ l by changing fiber length between node 5 and the Mixer s in Fig. 1(b). Note that δl is measured in the free-space length 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26694

Phase standard deviation deg. 25 20 15 10 5 Excess phase noise 0 0 5 10 δl (m) 15 Fig. 5. Relation between the phase standard deviation and the path length difference. in Fig. 5. The measurements were conducted at 2 THz, and the SNR was about 23 db. As pass length difference increases, the phase noise increases. We assumed a phase standard deviation of σ θe = σθ0 2 + (αδl)2, (4) and fitted it to data using σ θ0 and α as fitting parameters. The fitted curve (the solid curve in Fig. 5) with σ θ0 = 4.3 and α = 1.3 agrees well with data. The fitted σ θ0 parameter coincides with measured σ θe results at δl = 0, which was σ θe = 4.21 ± 0.12. Note that we performed the experiments at the SNR of 35 db, 25 db, and 23 db and achieved the similar results for the fitting parameters of α and σ θ0. Using the fitted α parameter, we can calculate that a path length difference δl of about 25 cm leads to excess phase noise of 0.012, which corresponds to onetenth of the standard error of our phase measurement with δl = 0 at SNR=23 db. Maintaining the path length difference within a few centimeters is not difficult; thus, our proposed system is robust and practical for performing precise phase measurements in THz spectroscopy. 4. Conclusion We demonstrated a balanced self-heterodyne technique for performing precise phase measurements in photonics-based frequency-domain THz spectrometry. Although our system is based on free-running lasers and optical fiber components, we confirmed that the experimentally achieved standard deviation of THz phase measurements agrees well with the theoretically derived SNR-limited standard deviation. The experimentally derived relation between the standard deviation of the phase measurement and the path length difference between the reference and the sample paths revealed that our system is robust and practical. Acknowledgments The authors would like to thank Dr. K. Ajito and Dr. A. Hirata of NTT Corporation for their encouragement. This work was supported in part by JSPS KAKENHI Grant Number 25709028. 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI:10.1364/OE.23.026689 OPTICS EXPRESS 26695