We have demonstrated the realization of the nearly transform-limited conventional solitons (CSs) with narrow spectral bandwidth in an Er-doped linear-cavity fiber laser, which is mode-locked by the graded index multimode fiber (GIMF)-based saturable absorber (SA). To our knowledge, this is the first report of the GIMF-based SA in the narrow bandwidth soliton generation. Simultaneously, the wavelength tunability of 0.48 nm and controllable Kelly sidebands for the narrow bandwidth solitons can be realized by the polarization controller (PC). Thereby, the minimum spectral bandwidth of the CSs reaches to be 0.1 nm, accompanied by the pulse duration of 20.8 ps and pulse energy of 1.07 nJ. Our work provides a compact and low-cost alternative for the narrow bandwidth solitons and offers a promising platform in the fields such as spectroscopy, quantum optics and other fields.
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