## 3 Noise Measurement and Reduction in Mode-Locked Lasers
### Tining Jitter
#### 3.1.2 Timing Jitter Reduction Methods  
_Intrinsic noise optimization:_ After the realization of high-resolution timing jitter measurement, the next interesting ongoing topic is the reduction of timing jitter of mode-locked lasers. The first type of effective method aims at the optimization of the laser oscillator's intrinsic noise. It can be seen from the theoretical models that the output pulse trains' timing jitter could be optimized through cavity loss reduction, cavity dispersion optimization, and intensity noise stabilization. In 2011, [PERSON] et al. reported the characterization of timing jitter PSDs of mode-locked lasers in soliton regime, self-similar regime, and stretched-pulse regime [64]. Furthermore, they experimentally confirmed that timing jitter PSD varies with different intracavity net dispersion. When the cavity dispersion is close to zero, the Gorden-Haus jitter is the lowest. This is consistent with the presented theoretical model in Section 2. On the other hand, by inserting a narrowband optical filter in the laser cavity, one can also reduce Gorden-Haus jitter. The main principle of this technology is that the Gorden-Haus jitter originates from the frequency fluctuation of the pulse spectrum through the cavity's non-zero net dispersion. The function of an intracavity narrow bandwidth filter is capable of partly eliminating the frequency fluctuation of the pulse spectrum, which in turn can reduce the Gorden-Haus timing jitter. Literature [79] reported for the first time that an optical filter with a bandwidth of 0.7 nm was inserted into a carbon nanotube mode-locked femtosecond laser to reduce timing jitter. In 2015, the timing jitter of femtosecond lasers with intracavity filters were studied systematically [80]. After insertion of a 7-nm narrow bandwidth optical filter in the cavity, since the Gorden-Haus jitter is largely removed, the net dispersion in the cavity has a minor impact on the timing jitter. However, if the bandwidth of the filter in the cavity is too narrow, e.g., less than 1 nm, the performance of timing the jitter will be deteriorated due to the broadening of the average pulse width in the cavity [81; 82]. On the other side, reducing the pulse's intensity noise is also a feasible way. In nonlinear polarization rotation (NPR) mode-locked lasers with high repetition rates, the timing jitter at Fourier frequencies below 100 kHz is mainly introduced by intensity noise [44]. In this case, the intensity noise of the laser can be stabilized to reduce the timing jitter. In literature [83], after the intensity noise of the output pulse is reduced by pump current modulation, the timing jitter power spectrum is lowered by 10 dB in the frequency range of 3 kHz to 30 kHz. _Phase lock technology:_ The second type of timing jitter reduction is using phase locking technology to force the repetition rate to inherit the reference's stability. The low-noise reference sources can be atomic clocks referenced signal generators, a sapphire load resonator oscillator, or a narrow linewidth CW laser. To achieve the stabilization of the repetition rate, high bandwidth actuators are demanded to modulate the cavity length. One method is to place the end mirror of the laser cavity on a piezoelectric transducer. Through rapidly changing the voltage applied to the piezoelectric transducer, the cavity length could be modulated. The special design of the mount of the piezoelectric transducer enables the 180-kHz modulation bandwidth [84]. Recently, [PERSON] et al. demonstrated a piezoelectric transducer-actuated mirror with a modulation bandwidth of 500 kHz using a simple mechanical design and electronic circuits [85]. For fiber lasers, the fiber can be wound on piezoelectric transducers. Literature [86] reported several specially designed fiber windings which enable the modulation of the repetition rate with >100 kHz bandwidth. On the other hand, inserting an electro-optic modulator in the laser cavity is also applicable.