## 1 Introduction  
Switchable and tunable multi-wavelength fiber lasers have generated significant interest for their potential in telecommunications [1, 2]. They are typically constructed from erbium-doped fiber and configured in either ring- or linear-type optical cavities [3, 4, 5, 6, 7]. In recent years, methods have been reported that can generate a stable tunable multi-wavelength and tunable range laser emission [8, 9, 10, 11, 12, 13, 14, 15, 16, 17], such as polarization controllers (PCs) [18] and wavelength-selective filters (WSFs), which balance the wavelength depending on their cavity losses [8]. WSFs can be fabricated with different structures, such as fiber Bragg grating (FBG) [9] or Mach-Zehnder interferometers (MZIs) [8, 10, 11], and with different compounded fiber filters [12; 18]. The MZI filter is fabricated by using SMF [13; 14], photonic crystal fiber (PCF) [8], and thin-core fiber [10; 11]. In a laser cavity, filters are used, which, by increasing curvature [8; 12], temperature [9], or strain [12; 15], can make a laser tunable and switchable. By utilizing three PCs, [PERSON], [PERSON] et al. [16] reported achieving a switchable erbium-doped fiber laser with a dual-wavelength tuning range of 3.42 nm and a side mode suppression ratio (SMSR) above 64 dB. The maximum power fluctuation and wavelength shift were 0.50 dB and 0.01 nm, respectively. [PERSON] et al. [18] reported a wide tuning range of 153 nm; this proposal uses a filtering mechanism in conjunction with four PCs and lasing lines with high power (57.3 dB) across single-, dual-, triple-, quadruple-, and quintuple-wavelength lines, which were adjusted using different pumping power outputs and PCs. [PERSON], [PERSON] et al. [12] reported that using fiber Bragg grating together with an MZI in a laser cavity produced an emission of laser lines that can be smoothly switched from single to quadruple wavelengths from 1527.68 nm to 1550.22 nm, with an optical signal/noise ratio (OSNR) greater than 50 dB, by applying up to 258 \(\upmu\)e of voltage to the filter. [PERSON] et al. [9] present a multi-wavelength 12- and 8-line emission laser, with an OSNR of 45 dB and 47 dB, respectively, which is generated by using a Fabry-Perot interferometer (FPI) and FBG dual cavity; the tunable 8-line emission laser is obtained by using temperature increments in a span of 1 nm. Thin-core fibers (TCFs) are very efficient because they have almost no loss, as shown in the work of [PERSON], [PERSON] et al. [11], where they used one TCF to create an MZI loop and a Sagnac interferometer (SI) working in conjunction with a single-emission line tuned at 40 nm, with a 32.68 dB SMSR and a dual and triple loop with an SMSR of over 34.51 dB. A modal analysis of MZIs based on SMF and thin-core fiber was developed by [PERSON] et al., and high sensitivity was found in the interferometers [19]. Interferometers based on thin-core fibers have been studied in relation to curvature [20], temperature [21], and refracometers [22], among many others, with advantages in terms of low cost, simple fabrication, and relatively high sensitivity. In this work, a multi-wavelength tunable and switchable erbium-doped fiber laser based on a thin-core erbium-doped fiber (TCEDF) filter is proposed and experimentally demonstrated. By incrementing the curvature in the filter, the laser can operate as tunable for single-, dual-narrow, and dual-wavelength emissions, and it can switch between triple- and quadruple-emission wavelengths. The analysis of the stability tests for the power and wavelength fluctuation determined that the lowest were 0.67 dB and 0.10 nm; the highest were 2.86 dB and 2.57 nm, respectively. The best SMSR was 49.80 dB for a single-emission line.