# Fast Frequency Acquisition and Phase Locking of Nonplanar Ring Oscillators
## 1 Introduction  
An optical phase locking loop (OPLL) plays an important role in space homodyne coherent optical communication systems, which have a significant advantage in receiving sensitivity. Gbps-level LEO-LEO [1], LEO-GEO [2], LEO-GS [3], and GEO-GS [4] communication links were verified, where LEO, GEO and GS denoted low earth orbit satellites, geostationary earth orbit satellite, and ground station, respectively. Compared to electrical wave sources in an electrical PLL, laser sources have a wider line width and a faster frequency drift [5], which result in difficult frequency acquisition and poor tracking performance. Early OPLLs were based on gas laser sources. [PERSON] et al. achieved phase locking of CO\({}_{2}\) lasers and 100 Mbps homodyne communication [6]. However, limited by certain disadvantages in lifespan, volume, and efficiency, it is hard for gas lasers to meet certain requirements in space applications. The development of optical communication has greatly promoted the progress of semiconductor laser technology. [PERSON] et al. achieved phase locking of an external cavity semiconductor laser with a residual phase error of 7.4\({}^{\circ}\)[7]. Although semiconductor lasers have a small size and low cost, the linewidth of these devices is relatively wide, or the phase noise is large, which leads to losing lock or large residual phase error. Recently, integrated OPLLs based on semiconductor lasers have been studied intensively. Such loops have potential applications in optical frequency synthesis [8] and microwave photonics [9]. Integration of OPLLs reduces the loopdelay, broadens the loop bandwidth, and improves the loop stability [10]. Thanks to the intensive study of diode-pumped solid-state lasers (DPSSL) over the last three decades, their performance has greatly improved in coherence, service life, and reliability. Among DPSSLs, nonplanar ring oscillators (NPROs) have a narrow linewidth (<1 kHz), low intensity noise (relative intensity noise <\(-\)140 dB/Hz), and good frequency stability. Due to the merit of a narrow linewidth, in OPLL applications, small residual phase error can be obtained. In homodyne coherent optical communication systems, small residual phase error is conducive to an improvement in the receiving sensitivity, which is important for space communication systems. Until now, NPRO is the only laser source that has been verified in orbit for applications of homodyne coherent optical communication, to the best of our knowledge. We believe that NPRO is, up to now, the first-choice laser source in space homodyne coherent optical communication systems. For OPLLs based on NPRO, [PERSON] presented the scheme and performance of a dither loop, which did not require residual carrier transmission [11]. [PERSON] et al. studied phase locking stability of OPLLs based on NPRO [12]. The authors analyzed the effect of response bandwidth of frequency tuning on phase locking precision [13]. Frequency acquisition performance is also quite important for phase locking loops. Frequency acquisition schemes based on a bang-bang phase detector [14] and a Hogge phase detector [15] have been reported in electrical PLLs. The range of initial frequency difference (or offset) between signal laser and local laser is larger in OPLLs, compared with electrical PLLs, and this is mainly due to laser frequency drift. Even under the condition of precise temperature control, the initial frequency offset can still be around 100 MHz. In addition, for OPLLs based on NPROs, the response bandwidth of the frequency tuning of the laser source is narrower, and loop delay is much longer, compared to electrical PLLs. Therefore, the lock-in range and pull-in range of an OPLL are much narrower. The frequency acquisition range, for OPLLs based on NPROs, should start from tens of kHz to more than 100 MHz. Thus, a special acquisition scheme with a wide range, high speed, and good compatibility with loop filters should be proposed for OPLLs based on NPROs.