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, !"# = ( !"! - !"! ) + ( !" - !" ) + ( !!! - !!! ), (1) where !"! and !"! are the laser phase noises, !" are the phase fluctuations imposed on the optical signals in the fiber between the node i and j, !!! and !!! 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, !"# = ( !"! - !"! ) + ( !" - !" ) + ( !!! - !!! ), (2) where !!! and !!! 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, !" = ( !" - !" ) − ( !" - !" ) +( !!! - !!! ) − ( !!! - !!! ). (3) The components ( !!! - !!! ) and ( !!! - !!! ) are the phase noises imposed on the optical beat signals, whereas the components !" , !" , !" , and !" 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 F )6 /DVHU /DVHU 5) /2 7+] ZDYH 2( ,) 6DPSOH D 0L[HU 2( 5HI 6DPSOH E &RQYHQWLRQDO %DODQFHG