**1. Introduction**

Single-frequency narrow-linewidth lasers are fundamental to a vast array of applications in fields including metrology, optical frequency transfer, coherent optical communications, highresolution sensing, and light detection and ranging (LIDAR) [1–9]. In these applications, the phase and frequency noise is one of the key factors to affect the system performance. The characterization and measurement of the phase and frequency noise are very important for the applications, and thus have been one of the most attractive subjects of researches in laser

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and photonics field. The phase and frequency noise of such lasers can be conveniently described either in terms of linewidth or in terms of the power spectral density (PSD) of their phase or frequency noise. The linewidth gives a basic and concise parameter for characterizing laser coherence but lacks detailed information on frequency noise and its Fourier frequency spectrum, which is needed for understanding the noise origins and improving laser performances. Therefore, the measurement of frequency noise PSD is a focus of attention in the field, especially for lasers of very high coherence, whose linewidth is not easy to be measured.

To measure the phase and frequency noise, many methods have been proposed, such as beat note method [10], recirculating delayed self-heterodyne (DSH) method [11], DSH technique based on Mach-Zehnder interferometer with 2 × 2 coupler [12, 13], or Michelson interferometer (MI) with 2 × 2 coupler [14]. These methods can obtain good measurement results but need some strict conditions. The beat note method needs a high coherent source as a reference. The recirculating DSH method needs very long fiber delay lines. The DSH interferometers with 2 × 2 coupler need to control the quadrature point by some active feedback methods and accurate calibration.

To overcome these difficulties, we introduce a robust technique that can demodulate directly the laser differential phase accumulated in a delay time and then derive strict mathematical relations between the laser differential phase and the laser phase noise or frequency noise that can describe the complete information on laser phase and frequency noise. Because 3 × 3 optical fiber coupler acts as a 120° optical hybrid, it can demodulate the differential phase of the input light and has been used for DxPSK signal demodulation [15], optical sensors [16], optical field reconstruction, and dynamical spectrum measurement [17]. In this chapter, 120° phase difference interference technology based on an unbalanced Michelson interferometer, which is composed of a 3 × 3 optical fiber coupler and two Faraday rotator mirrors, is utilized to demodulate the differential phase of a laser. The structure has the advantage of being polarization insensitive and adjust-free. Especially, it does not need any active controlling operation that is used in the DSH methods with 2 × 2 coupler. Furthermore, based on the differential phase and strict physical and mathematical derivation, the PSD of the differential phase fluctuation and frequency fluctuation, the PSD of the instantaneous phase fluctuation and frequency fluctuation, laser phase noise, and linewidth are completely calculated and discussed.
