## 1 Introduction  
Single-mode fiber resonators of different architectures such as linear [1], Fox-Smith [2], ring [3; 4; 5], and compound fiber ring [6; 7; 8; 9] cavities have been theoretically and experimentally explored in designing and building various kinds of fiber laser sources with single-longitudinal mode operation for low and high optical power applications such as optical communication systems, and for scientific, medical, material processing and military purposes [10]. Adjustable, scalable output optical power and wavelength tunability properties of a fiber laser source are of a great interest in the aforementioned applications that require high optical power. Complex and expensive in-line variable optical attenuators (VOAs) with adjustable insertion losses are usually used to control the output optical power level of laser sources. Mechanical, micro-electromechanical [11; 12; 13], acousto-optic [14], and electro-wetting [15] methods as well as optical fiber tapers [16] and hybrid microstructure fiber-based techniques [17] are widely used to adjust the insertion losses of the in-line fiber-based VOAs. However, all-fiber-based low power variable reflectors or mirrors such as Sagnac loop mirrors (SLMs) can also be used to control the amount of optical power from low and high power fiber laser sources. All-single-mode fiber-based Sagnac loop mirrors have been widely used in temperature [18], strain [19], and pressure [20] high sensitivity sensors as well as in wavelength optical switches [21]. Moreover,SLMs with adjustable reflectivity have been used to form Fabry-Perot linear resonators [22; 23; 24; 25] where the amount of the output optical power from the resonators depends on the reflectivity of the SLMs [26; 27]. In this work, two SLMs were used to control the amount of optical power delivered from two output ports of the proposed fiber compound-ring laser. In addition, two inexpensive low power semiconductor optical amplifiers (SOAs) were placed in two parallel nested ring cavities to demonstrate the possibility of achieving a highly power scalable, adjustable and switchable fiber laser structure based on multiple nested compound-ring cavities formed by \(\mathrm{N}\times\mathrm{N}\) fiber couplers with two SLM-output couplers. Different methods have been utilized to scale up optical power of laser sources where beam combining has shown to be a promising alternative technique of achieving high power by scaling up multiple combined laser elements. High power laser sources with high beam quality have been demonstrated by using complex coherent and spectral beam-combining techniques in external cavities [28; 29; 30; 31; 32; 33; 34; 35]. In addition, incoherent beam-combining method [36; 37] has been used to scale up the optical power by combining individual laser elements as well. Michelson and Mach-Zehnder resonators were mostly used in coherent beam combining in order to achieve high combining efficiency and almost diffraction-limited beam quality [38; 39; 40]. More importantly, ring resonators have proven to be efficient and stable [41] for a passive coherent beam-combining method. In order to achieve high power laser sources with high combining efficiency, all the aforementioned methods require sophisticated high power external optical components such as micro-lenses, isolators, circulators, photonic crystal fibers and master oscillator pre-amplifiers that are usually complex and very expensive. In addition, rare-earth, ytterbium doped fiber amplifiers (YDFAs) [41] or erbium doped fiber amplifiers (EDFAs) [42] that are usually used as gain media for beam combining to achieve high power laser systems with different types of cavity structures such as Y-shaped linear cavities also need to be pumped with other types of laser sources, which makes them very inefficient.