Demonstration of high-stable self-mode-locking pulses based on self-focusing in fiber lasers

•Both the fundamental frequency operation, 3rd harmonic, and 81st harmonic are observed.•The self-mode-locking operation has excellent stability, since the SNR of the 81st harmonic is as high as 80 dB.•The 81st harmonic has a narrow 3-dB optical spectrum bandwidth of 0.29 nm.•The maximum output power in our work is 27.63 mW.•The self-focusing caused by the Kerr-lens effect of SMF is the major mechanism of self-mode-locking.