## 1 Introduction  
Solid-state lasers based on Er\({}^{3+}\) emitting around 3 \(\upmu\)m have attracted significant attention because of their potential for numerous applications, such as laser microsurgery, laser radar, plastic and polymer processing, and pumps for longer wavelength oscillations [1; 2; 3]. Lasing on the \({}^{4}\)I\({}_{11/2}\rightarrow{}^{4}\)I\({}_{13/2}\) transition of Er\({}^{3+}\) ions has been widely studied with a variety of host materials at the mentioned spectral region [4; 5; 6; 7; 8; 9; 10]. Conventionally, the lifetime of the upper level is lower than the terminated one. For preventing the self-terminating effect of the mentioned transition, high Er\({}^{3+}\)-ion doping concentration is typically required to depopulate the lower laser level by using the concentration dependent energy transfer up-conversion process. In view of the large quantum defect with the most spread \({}^{4}\)I\({}_{15/2}\rightarrow{}^{4}\)I\({}_{11/2}\rightarrow{}^{4}\)I\({}_{13/2}\) pump-laser scheme (~70%) and the shallow pump absorption result from the high doping level, a large amount of heat would concentrate near the surface of the gain media. The induced temperature gradient may lead to distortion of the laser mode and strong thermal lensing with pronounced spherical aberrations. In this regard, thermally advanced host materials, such as sesquioxides, are of great interest for high power Er 3-\(\upmu\)m laser operations [9; 10]. Lu\({}_{2}\)O\({}_{3}\) is an appealing sesquioxide, which exhibits low phonon energy (618 cm\({}^{-1}\)) and a wide spectral transparency range (0.225-8 \(\upmu\)m), which favors its applications as a mid-infrared laser gain medium [11]. In addition, its thermal conductivity stays high even at a high Er\({}^{3+}\)-ion doping level, because of the similar atomic mass of the Lu\({}^{3+}\) and Er\({}^{3+}\) ions [9]. Recently, Er:Lu\({}_{2}\)O\({}_{3}\) crystal was proven to be an excellent sesquioxide for power scaling, and efficient laser operation at 2.84 \(\upmu\)m has been demonstrated [9]. Due to the difficulty in growing high quality and large-volume sesquioxide crystals, which originates from their high melting point (>2400 \({}^{\circ}\)C), intense research efforts have been focused on the development of sesquioxide ceramic lasers [10; 11; 12; 13; 14; 15; 16]. Polycrystalline Er:Lu\({}_{2}\)O\({}_{3}\) ceramic has recently been fabricated successfully and spectroscopically characterized [13; 14]. In 2014, the first continuous-wave (CW) laser radiation of Er:Lu\({}_{2}\)O\({}_{3}\) ceramic around 3 \(\upmu\)m was reported [15], and very recently, efficient diode pumped CW operation was realized [16]. Q-switched mid-infrared (MIR) lasers capable of producing nanosecond pulses with a high peak power are of great interest for applications as a pump source of longer wavelength oscillations, and for using in laser microsurgery and materials processing. Passively Q-switched approaches offer advantages over the active ones in terms of simplicity, compactness and they have no need of extra electric devices. A variety of saturable absorbers (SAs), such as graphene, black phosphorus (BP), MoS\({}_{2}\), ReS\({}_{2}\), graphitic carbon nitride (g-C\({}_{3}\)N\({}_{4}\)), Bi\({}_{2}\)Te\({}_{3}\), have so far been used for Q-switching of \(\sim\)3-\(\upmu\)m lasers [17; 18; 19; 20; 21; 22; 23]. Up to watt-level outputs at 2.84 \(\upmu\)m have been demonstrated using Er:Lu\({}_{2}\)O\({}_{3}\) crystal, generating pulses of \(\sim\)350 ns durations and \(\sim\)100 kHz repetition rates [21; 22; 23]. Compared with the newly developed two-dimensional (2D) materials-based SAs, the semiconductor saturable absorber mirror (SESAM) has many advantages since the key parameters, e.g., the absorption recovery time and the modulation depth, can be tailored in a wide range [24]. Recently, the successful Q-switched and mode-locked operation of Er:ZBLAN fiber lasers has been demonstrated [25; 26]. In these systems, specifically structured metal-reflector-based SESAMs were utilized.