## 1 Introduction
However, by using nested compound-ring cavities where circulating beams are equally split in N-number of low power beams that can be amplified by N-number of low power SOAs, one can achieve a highly efficient high power laser system that does not require the extra pump lasers, master oscillator pre-amplifiers or other expensive external high power optical components. Semiconductor optical amplifiers (SOAs) [43], stimulated Raman scattering (SRS) amplifiers [44; 45] and stimulated Brillouin scattering (SBS) amplifiers [46; 47] have also been used as gain media in different fiber laser systems. However, the SOAs are more advantageous than their above-mentioned counterparts because they are compact, light, less expensive, efficient, and available for different operational regions from a wide range of wavelength spectra. In particular, SOAs have the capability to be integrated with other InP (Indium phosphide)-based optical components, which makes it more attractive to implement very high compact optical systems. Extensive theoretical studies and analysis of SOA-based optical systems have shown that they can be used for several applications, such as compact SOA-based laser rangefinders [48], optical pulse delay discriminators [49; 50], and optical and logic gates [51] for high-speed optical communications by exploiting four-wave mixing [52; 53]. In addition, note that when the SOAs are used in a bidirectional fiber ring resonator structure, such as the proposed one, they do not require extra optical components, for instance, optical isolators and optical circulators; as a result, they are easy to integrate with other optical components for compact fiber laser systems. Semiconductor optical amplifiers have also been used along with erbium doped fiber amplifiers in order to suppress optical power fluctuation in a pulsed lightwave frequency sweeper where the suppression of power fluctuation is attributed to the gain saturation and fast response of the SOA [54; 55]. In this work, we demonstrate a novel technique for a coherent beam-combining method based on the passive phase-locking mechanism [56; 57; 58] of two C-band low power SOAs-based all-single-mode fiber compound-ring resonators by exploiting beam combining (i.e., interference) at 3-dB fiber couplers that connect two parallel merged ring cavities. This is unlike previous work [59] where non-adjustable multimode fiber laser output formed by a high power and expensive power combiner with a multimodeoutput fiber (i.e., low brightness) was replaced by two low power Sagnac loop mirrors to create a dual-output port all-single-mode fiber laser structure with switchable and adjustable output power. In addition, the single-mode performance is maintained in order to improve the brightness at the proposed fiber compound-ring laser output port. The output power of the proposed combined fiber compound-ring resonators with two low power SOAs was almost twice as large as the output power obtained from a single SOA-based fiber ring or the Fabry-Perot linear resonator [25]. More than 98% beam combining efficiency of two parallel nested fiber ring resonators is demonstrated over the C-band tuning range of 30 nm. Optical signal-to-noise ratio (OSNR) +45 dB, and optical power fluctuation of less than \(\pm\)0.02 dB are measured over three hours at room temperature. The main characteristics of the proposed fiber compound-ring laser, power tunability, and switchable output port can find applications in long-distance remote sensing [60]. Moreover, its wide range wavelength tunability can benefit several applications in fiber sensors [61; 62; 63; 64; 65] and wavelength division multiplexer (WDM) optical communications [66] as well as biomedical imaging systems [67] working in the third near infrared biological window [68]. Finally, we discuss on how to achieve a highly power-scalable fiber compound-ring laser system using low power and inexpensive optical components such as tunable filter and low power SOAs.