## 3 Self-Referenced DPSSLs with Bulk Gain Material
### One-Micrometer Ytterbium-Doped Lasers
A maximum average output power of 1.7 W was generated at 1062 nm with 64 fs pulse duration at a repetition rate of 1.0 GHz by pumping the gain crystal with a commercial highly multimode fiber-coupled laser diode at 980 nm with an \(M^{2}\) value of about 32. The maximum output power of the pump was 60 W, but only a small fraction of 8 W was used in these experiments. The Z-shape cavity contained a flat output-coupler used as a folding mirror that offered two output beams with an equal output power. One of the output ports was used for SC generation and CEO detection, whereas the other one remained available for comb applications. The high average output power available from a single output port of the laser and the short pulse duration provided a sufficient peak power for coherent octave-spanning SC generation in a 1 m long PCF without any amplification or pulse compression. An average power of 500 mW launched in the PCF followed by a quasi-common-path _f_-to-_2\(f\) interferometer produced a strong CEO beat at 680 nm with more than 25 dB SNR in a RBW of 1 MHz. The free-running CEO beat had a FWHM linewidth of several hundreds of kilohertz that was significantly larger than for other formerly self-referenced DPSSLs [26, 27, 29], which made its stabilization more challenging. This larger linewidth was observed despite several precautions taken to minimize some potential noise sources, such as preventing optical feedback into the pump diode by slightly tilting some optical components in the pump beam, or by minimizing mechanical perturbations of the multimode fiber that can increase the relative intensity noise (RIN) of the pump diode that is ultimately transferred to CEO noise. Passive filters were also used to prevent AC noise components to enter into the standard DC power supply used to drive the pump diode, and to attenuate at the same time electrical noise from the power supply entering in the pump diode. The large free-running linewidth of the CEO beat observed in this DPSSL resulted in some part from the use of a multi-transverse-mode pump diode without wavelength-stabilizing element, and from its gigahertz repetition rate, as the fluctuations of _f_CEO scale linearly with _f_rep as a consequence of Equation (2). For this reason, high repetition rate lasers require a larger loop bandwidth to achieve a tight lock. In the Yb:CALGO laser of [21], a tight CEO lock was achieved by feedback to the pump current with a large bandwidth of \(\sim\)300 kHz. This was realized with a fast current modulation electronics installed in parallel to the DC power supply of the pump diode that could be directly modulated only at low frequency (\(<\)1 kHz). The derivative part of a PID servo controller was essential to extend the overall loop bandwidth up to \(\sim\)300 kHz, much higher than the measured roll-off frequency of _f_CEO for pump current modulation (\(\sim\)20-30 kHz) originating from the gain upper-state lifetime and photons lifetime in the cavity. Therefore, a tight CEO lock was successfully achieved with \(\sim\)300 kHz feedback bandwidth and an in-loop residual integrated phase noise of 744 mrad [1 Hz-5 MHz]. The stabilization of _f_CEO was also accompanied by a strong improvement of the RIN and of the timing jitter of the gigahertz laser in the frequency range from \(\sim\)100 Hz up to the loop bandwidth, indicating that they originate from a common noise source. This also implies that the pump current has a coupled influence on _f_CEO and _f_rep, in a similar way as described in detail in the case of an Er:fiber comb [67]. A large contribution to the frequency fluctuations of _f_CEO in diode-pumped femtosecond lasers usually originates from pump diode intensity noise that is transferred to _f_CEO by different mechanisms [68]. This was evidenced by [PERSON] _et al._, in an Er:fiber laser [69] and is even more pronounced in high repetition rate DPSSLs pumped by multi-transverse-mode laser diodes.