Objective   Ultrashort pulse laser technology develops rapidly, it has been applied in various fields, such as industrial materials processing, biomedical diagnostics, and terahertz generation. The passive mode-locked fiber lasers have the advantages of high efficiency and low cost, which are usually used to generate ultrashort pulses. The passive mode-locking technology includes many kinds of technologies, among which the nonlinear polarization rotation technology has the advantages of high damage threshold, large modulation depth and short response time, etc. However, the mode-locked fiber laser based on the nonlinear polarization rotation technology is sensitive to the polarization state of laser pulses. The K-means algorithm is a classic algorithm based on distance segmentation and clustering. It is terse and has fast convergence speed when analyzing large data sets. This paper realizes a passive mode-locked erbium-doped fiber laser with nonlinear polarization rotation technology and K-means algorithm, which can automatically find the fundamental frequency mode-locked pulse state.

  Methods   An electric polarization controller with programmable motion is used to adjust the polarization state of the pulse in a passive mode-locked erbium-doped fiber laser. First, all angles of the electric polarization controller are traversed and the output pulse data at different angles are collected simultaneously. The fundamental frequency mode-locked pulse points are obtained through the pulse decision algorithm. Then, the fundamental frequency mode-locked points are clustered and analyzed using K-means algorithm. When the pulse is out of lock or in other states, a set of rotating paddle angles is fed back to the electric polarization controller through the K-means algorithm. At last, the fundamental frequency mode-locked pulse are exported from the laser.

  Results and Discussions  By properly adjusting the manual polarization controller and the electric polarization controller, a traditional fundamental frequency mode-locked pulse (Fig.3) is obtained, when the pump current is about 230 mA. The central wavelength of the spectrum is 1 531 nm with the pulse duration and fundamental repetition frequency of 0.96 ps and 9.847 MHz, respectively. 1102 mode-locked points are obtained with the pulse decision algorithm and displayed in the three-dimensional coordinate space (Fig.4). The classification result is optimum when the K value is set as 6 using the Silhouette Coefficient method (Fig.5). Therefore, the mode-locked points are divided into 6 categories using the K-means clustering algorithm (Fig.6). After 100 tests, the fastest, slowest and average time for finding the fundamental frequency mode-locked point is 0.11 s, 0.92 s, and 0.25 s, respectively (Fig.7). A comparative test is conducted by randomly changing manual polarization controller state, in order to test the applicability of the algorithm (Fig.8).

  Conclusions   The proposed method can quickly find the fundamental frequency mode-locked pulse points in a mode-locked fiber laser based on nonlinear polarization rotation technology and K-means algorithm. The average time required to adjust from other states to the fundamental mode-locked point is 0.25 s in 100 tests. This method can rapidly realize the output of fundamental frequency mode-locked pulse, and provides a new scheme for realizing efficient and convenient automatic mode-locking of fiber laser.