Abstract—We demonstrate that the photonics-based balanced self-heterodyne system enables us to measure the phase change of the continuous terahertz-wave with the theoretical uncertainties limited by the signal-to-noise ratio (SNR) of the amplitude measurement. Although our system is based on free-running lasers and fiber components, excess phase noise can be cancelled out. When the SNR was 44 dB, the standard deviation of the phase measurement was 0.37 degree, which is 10 times better than the previous method.

I. INTRODUCTION REQUENCY-DOMAIN terahertz (THz) spectrometers based on a continuous wave (CW) technology have been

extensively studied recently, because they provide a higher signal-to-noise ratio (SNR), and higher frequency resolution [1]. Photonics-based system is superior to the electronics-based system in terms of the bandwidth [2]. Conversely, sensitivity of the phase measurement is significantly low compared with the electronics-based system because of the laser phase noise and the optical phase fluctuations imposed in the optical fiber cable. Recently, we proposed and demonstrated self-heterodyne technique [3, 4] in which two 1.55-µm free-running lasers are used both for the generation and the detection of the continuous THz-wave. Although the laser phase noise is canceled out in the self-heterodyne detection process, the optical phase fluctuation imposed in the fiber limits the sensitivity of the THz-wave phase measurement.

In this paper, we demonstrate a balanced self-heterodyne technique, which enables us to measure the phase change of the continuous THz-wave without the excess phase noise originated from the optical system. We show that the experimentally obtained relation between the SNR of the amplitude measurement and the standard deviation of the phase measurement fit the theoretical curve well.

II. PRINCIPLE Figure 1 (a) and (b) show the system configuration of the

conventional self-heterodyne system and the balanced self-heterodyne system, respectively. In both systems, continuous THz-wave is generated by optical-to-electrical (O/E) conversion and detected by mixing with an optical beat signal (optical LO signal). For the RF signal, the frequency of the laser1 is shifted with a frequency shifter (FS) to realize the self-heterodyne detection. Note that the photoconductive antenna (PCA) [3], the electrooptic (EO) crystal [4], and the photodiode [5] can be used as the mixer.

In the conventional self-heterodyne system, the relative phase changes between the THz wave and the optical LO signal are measured. The origin of the excess phase noise comes from the relative phase noise between the optical sub-carriers (optical beat signals) in the RF arm and the

Fig. 1. Configurations of the (a) conventional and (b) balanced self-heterodyne system. FS: frequency shifter, O/E: optical-to-electrical converter.

optical LO signal. The phase noise of the optical beat signal in the RF arm can be expressed as,

𝜙!"# = (𝜙!"!-𝜙!"!) + (𝜙!"-𝜙!") + (𝜙!!!-𝜙!!!), (1)

where 𝜙!"! and 𝜙!"! are the laser phase noises, 𝜙!" are the phase fluctuations imposed on the optical signals in the fiber between the node i and j, 𝜙!!! and 𝜙!!! are the optical phase fluctuations imposed on the laser2 and laser1 components, respectively, in the fiber between the node 2 and the RF generator (O/E converter). The phase noise of the optical LO signal can be expressed as,

𝜙!"# = (𝜙!"!-𝜙!"!) + (𝜙!"-𝜙!") + (𝜙!!!-𝜙!!!), (2)

where 𝜙!!! and 𝜙!!! are the optical phase fluctuations imposed on the laser2 and laser1 components, respectively, in the fiber between the node 4 and the mixer. We assumed that there is no time delay difference between the RF and LO arms. Therefore, excess phase noise in the THz phase measurement can be expressed as,                                                      𝜙!" = (𝜙!"-𝜙!") − (𝜙!"-𝜙!")                                                                        +(𝜙!!!-𝜙!!!) − (𝜙!!!-𝜙!!!). (3) The components (𝜙!!!-𝜙!!!) and (𝜙!!!-𝜙!!!) are the phase noises imposed on the optical beat signals, whereas the components 𝜙!" , 𝜙!" , 𝜙!" , and 𝜙!"   are the phase noises imposed on the optical carriers independently in the fiber within the dashed box in Fig. 1. In this experiment, the wavelength of the RF beat signal is 1 mm (300 GHz) whereas that of the optical signal is 1.55 µm in the vacuum. Therefore, the influence of the ambient thermal and vibrational noise to the phase of the optical signal is 1000/1.55 ≈650 times greater than that to the optical beat signal.

The main components of the excess phase noise can be eliminated in the balanced self-heterodyne system, where the phase changes of the THz wave relative to the reference phase of the THz wave are measured, as shown in Fig. 1(b). The remaining phase noises are the difference between the phase

Shintaro Hisatake and Tadao Nagatsuma Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

Precise Terahertz-wave Phase Measurement Based on Photonics Technology

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noises imposed to the optical LO signals in the fiber between the node 5 and each mixer.

III. EXPERIMENT AND RESULT Figure 2 shows experimental setup. Two frequency-detuned

1.55 µm laser diodes (LDs) are combined to produce a beat signal (300 GHz). A THz wave is generated by photomixing at uni-traveling-carrier photodiode (UTC-PD) and detected by PCAs. The frequency of the LD1 is shifted by 500 kHz with the EO frequency shifter. The amplitude and the phase are measured by two-channel lock-in amplifier. The common phase noises are subtracted (𝜃 = 𝜃! − 𝜃!).

The detected IF signal is not an ideal sinusoidal wave, as it has the amplitude noise and the phase noise. The SNR of the amplitude measurement can be expressed as

                                                                 𝑆𝑁𝑅 = 20 log!" 𝐴/𝜎!,                                                       (4)

where 𝐴  is the amplitude of the detected THz wave,  𝜎! is the standard deviation of the amplitude measurement. If there is no excess phase noise, the standard deviation of the phase measurement is finally limited by the SNR of the amplitude measurement. The theoretical relationship of the phase standard deviation,  𝜎! , and the SNR of the amplitude measurement can be expressed as                                                                                  𝜎! = 10!!"#/!" . (5)

Figure 3 shows the relation between the phase standard deviation and the SNR. The SNR was changed by changing the power of the THz wave. The SNRs obtained with the PCA1 and PCA2 were almost same. The closed red circles are the results obtained with our new system. The open circles are the data obtained without subtracting (conventional self-heterodyne detection). The solid line is the theoretical relation calculated by equation (5). In the experiment, we measured the THz phase for 1 minute at the time constant of 81.8 ms and calculated the standard deviation of the phase measurement. The measurement was performed 5 times to

Fig. 2. Experimental setup. LD: laser diode, EDFA: erbium-doped fiber amplifier, UTC-PD: uni-traveling-carrier photodiode, FS: optical frequency shifter, PCA: photoconductive antenna. TIA: transimpedance amplifier. θ1 and θ2 are the phase detected by the PCA1 and PCA2, respectively.

Fig. 3. Relation between the standard deviation of the detected phase and the SNR of the detected amplitude.

evaluate the uncertainty of the phase standard deviation obtained in the experiment. The data obtained with our new system fit the theoretical curve well. On the other hand, the phase standard deviation in the conventional self-heterodyne detection was limited to 3.5 degrees. This is mainly due to the phase fluctuations imposed in the fiber within the dashed box in Fig. 1. The phase standard deviation in the balanced self-heterodyne system was 0.37 degree at the SNR of 44 dB. The sensitivity of the phase measurement improved about 10 times compared with the conventional system.

IV. CONCLUSION We demonstrated a balanced self-heterodyne technique

showing the precise THz phase measurement at 300 GHz. The standard deviation of the phase measurements was improved to theoretical limit. We achieved a sensitivity 10 times better than the previous one at SNR of 44 dB. This technique is applicable to other self-heterodyne measurements such as spectroscopy [5] and EO field visualization [4].

ACKNOWLEDGMENTS The authors would like to thank Dr. A. Hirata, Dr. K. Ajito,

and Dr. J.-Y. Kim of the NTT Microsystem Integration Laboratories, NTT Corporation for their supports. We would also like to thank Mr. Y. Koda of Osaka University for his help in the experiments. This research was partially supported by a Grant-in-Aid for Young Scientists (A) (25709028) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

REFERENCES [1] 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., vol. 88, 181105, 2006. [2] T. Göbel, 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., vol. 38, pp. 4197-4199, 2013. [3] S. Hisatake, G. Kitahara, N. Kukutsu, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-sensitive terahertz self-heterodyne system based on photodiode and low-temperature-grown GaAs Photoconductor at 1.55 µm,'' IEEE Sensors Journal, vol. 13, pp. 31-36, 2013. [4] S. Hisatake and T. Nagatsuma, “Continuous-wave terahertz field imaging based on photonics-based self-heterodyne electrooptic detection,'' Opt. Lett., vol. 38, pp. 2307-2310, 2013. [5] S. Hisatake, J.-Y. Kim, K. Ajito, T. Nagatsuma, “Self-heterodyne spectrometer using uni-traveling-carrier photodiodes for terahertz-wave generators and optoelectronic mixers,” J. Lightwave Technol., to be published.

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