Objective  Ultrafast mode-locked fiber lasers have gained increasing popularity in various fields due to their narrow pulse width, broad spectrum, and high peak power. In the field of laser medicine, for instance, ultrafast lasers have emerged as a novel treatment method for combating cancer and treating stones. The integration of ultrafast lasers and time-frequency technology in the field of optical frequency comb measurement has yielded remarkable advances, such as the development of optical atomic clocks, microwave photonics, and other emerging technologies. Furthermore, the optical frequency comb has the potential to be implemented in space missions. Ultrafast mode-locked fiber lasers are being used more and more widely and have high application value. Mode-locked technology is the main way to generate ultra-short pulses. Currently, among the main mode-locked methods, mode-locked laser based on the nonlinear amplifying loop mirror has the characteristics of fast response time, high damage threshold, high environmental stability, low phase noise and short output pulse, which is considered to be the most promising ultrafast laser for large-scale application. Unfortunately, this kind of laser often requires external disturbance or high pump energy when it is started, which greatly reduces the reliability of the laser and increases the application cost. In order to improve the reliability of mode-locked laser in practical applications, femtosecond fiber lasers based on Jones matrix are reported.

  Methods  In this paper, a mode-locked laser based on a non-reciprocal phase shift for a nonlinear amplifying loop mirror is set up (Fig.1). The non-reciprocal phase shifter consists of a Faraday rotator, a half waveplate, a λ/8 waveplate, and a mirror. By rotating the angle of the waveplates, the laser takes into account the characteristics of self-starting and wide spectrum, and the gratings are inserted into the cavity to balance the positive dispersion and outside of the cavity to compress pulses. The transfer function of nonlinear amplification loop mirror is established by using Jones matrix to analyze self-starting performance of the mode-locked fiber laser (Fig.9). The influence of different wave plate angles in loop mirror on the roundtrip transmission of the cavity is analyzed (Fig.2).

  Results and Discussions  The fiber lasers are demonstrated by using Yb-doped fiber and Er-doped fiber as gain media respectively. Gratings (1 000 lines/mm) are used in the Yb-doped fiber laser to balance the positive dispersion. The fundamental frequency with repetition rate of 600 MHz (Fig.3) and 280 MHz (Fig.5) is observed by an oscilloscope. The designed lasers have the characteristics of narrow pulse width (Fig.4, Fig.6), good stability (Fig.7) and high self-starting success rate. The laser has been integrated and packaged, which can meet the application requirements of femtosecond laser in micro-nano processing, laser medical treatment, optical frequency comb and other fields.

  Conclusions  A nonlinear amplifying loop mirror femtosecond laser is designed, which achieved repetition rates of 600 MHz and 280 MHz at wavelengths of 1 µm and 1.5 µm, respectively. At a pump power of 960 mW, the ytterbium-doped fiber laser output an average power of 180 mW and a pulse width of 249 fs. The erbium-doped fiber laser output a power of 104.7 mW, with a direct output pulse width of 109 fs and a compressed pulse width of 60 fs. The spectrum had a flat top and supported output pulses in the hundreds of femtosecond range, which could effectively reduce thermal accumulation during laser processing and improve processing efficiency. This laser structure achieved high integration with an easy-to-dismantle package, a broad spectrum, and supported self-starting mode-locking, multiple output channels, and stable operation, making it a suitable seed source for future femtosecond laser products.