# Mode-Locking Dynamics in an All-PM Figure-Nine Tm-Doped Fiber Laser
###### Abstract  
We report a study on pulse dynamics in figure-nine Tm-doped all-polarization maintaining fiber laser. We analyzed laser operation from self-starting with multi-pulse dynamic to single-pulse operation by decreasing the pump power from the mode-locking threshold. By choosing a reliable setting of waveplates, our laser was generating pulses at the central wavelength of 1985 nm with a half-width of the spectrum, pulse duration, and pulse energy equal 6.4 nm, 650 fs, 177 pJ for the output port and 19.2 nm, 1279 fs, 57 pJ for the reject port in the single-pulse state. In the multi-pulse state, we recorded optical spectra, temporal waveforms, and average power at both exit ports. By analyzing temporal traces and output to reject port ratio power, we can distinguish between eight states of operation which follow an exact pattern. In the case of the single-pulse regime, we performed a further laser characterization, including relative intensity noise. fiber laser; mode-locked laser; soliton; nonlinear amplifying loop mirror +
Footnote †: journal: Applied  
At least as much interest is contemporarily devoted to Kerr-lens mode-locking [22] as well as additive pulse mode-locking techniques (APM) [23] such as nonlinear polarization rotation (NPR) [24], nonlinear optical loop mirror (NOLM) [25], and nonlinear amplifying loop mirror (NALM) [26]. APM operation results from coherent interferometric addition of pulses with different phases which depend on their intensity. A phase difference may be the result of any of the following factors: (a) birefringence; (b) a nonlinear phase shift; (c) phase bias. Birefringence-depended shift is caused by the propagation of each pulse in a different polarization state of a birefringent medium. Effects of birefringence can be omitted once PM architecture, which allows working with linearly polarized beams, is applied. The nonlinear phase shift is induced by a self-phase modulation experienced by the pulses with different intensities propagating in a nonlinear medium via the optical Kerr effect [27]. A phase bias is a power-independent phase shift that can be introduced by a non-reciprocal phase shifter (NRPS) [28]. The usual implementation of NRPS consists of at least one Faraday rotator and a set of waveplates. Such a component shifts the transmission curve of the cavity enabling self-starting operation and is used mainly in all-PM NALM-based lasers in figure-nine configuration [26; 29; 30; 31]. Shifting the transmission leads to a maximum of the roundtrip transmission for lower intensities and in the case of figure-nine lasers, the most common bias is \(-\frac{\pi}{2}\). [PERSON] et al. demonstrated the effect of bias values on the self-starting threshold and the phase noise, concluding that \(-\frac{\pi}{2}\) provides the lowest self-starting threshold and highest phase noise value [32]. NALM-based lasers have some advantages over other ML techniques in terms of relatively lower intrinsic noise [33], robustness [34; 35], and a lack of coupling between phase and amplitude noise [36]. The latter makes them an ideal candidate in applications such as optical frequency combs. Figure-nine lasers with two exit ports, the output port, and the reject port possess significant differences in the relative amplitude noise (RIN) values between both exit ports [37]. In particular, the output port transmitted by a polarization discriminator possesses lower RIN values than the portion of the radiation that was reflected from it. Moreover, the rejected pulses tend to have a rather complicated optical spectrum and spectral phase [38]. In contrast, our recent studies have shown that for a laser operating in the net-zero dispersion regime (stretched-pulse), both ports can have a flat spectral phase [31]. In the net-normal dispersion regime (dissipative soliton) the reject port can overperform the transmitted port if proper spectral filtering and dispersion map is used [39].