We investigate the dynamics of the carrier-envelope-offset (CEO) frequency, f CEO , controlled by a pump current on the self-referencing of an optical frequency comb generated from a diode-pumped solid-state laser at 1.56 μm. We observe a reversal point in the tuning of f CEO with the pump current. Between the low-and high-frequency region in the dynamic response of f CEO to pump current modulation, we observe a significant phase shift of ≈180 deg in the transfer function. As a result, it is impossible to stabilize f CEO at a pump current above the reversal point, although the free-running CEO beat at this point has a higher signal-to-noise ratio than underneath the reversal point at which the locking is straightforward. Our results indicate that a high signal-to-noise ratio and a low-noise CEO beat are not sufficient indicators for the feasibility of comb self-referencing in cases for which CEO dynamics play a dominant role.In the past decade, fully stabilized optical frequency combs became a key component for many applications, such as optical atomic clocks, ultra-low-noise microwave generation or broadband high-resolution spectroscopy. Among the different existing comb technologies, Ti:Sapphire-based combs were the first to be selfreferenced [1]. This traditional technology is still commonly employed because of its low intrinsic noise and, to date, it constitutes the only laser capable of directly generating the octave-spanning spectrum required for comb self-referencing [2]. Ti:Sapphire lasers, however, suffer from some practical constraints, such as their complexity, high cost, and inefficient pumping. On the other hand, fiber oscillator systems are convenient and robust, but they are intrinsically noisier and thus require the use of more elaborate noise reduction techniques and higher feedback bandwidth to achieve a tight lock of the carrierenvelope-offset (CEO) beat. A promising alternative comb technology is the semiconductor saturable absorber mirror (SESAM)-mode-locked diode-pumped solidstate laser (DPSSL), which combines positive aspects of the other two comb technologies, such as low intrinsic noise, high repetition rate capability, and efficient diode pumping.A key step in the achievement of a fully stabilized optical frequency comb is the detection of the CEO beat in an f to 2f interferometer [3] and its subsequent phaselock to a stable rf reference using a feedback loop. The pump power of the femtosecond laser generally is used to control and stabilize the CEO frequency f CEO . This is traditionally accomplished using an acousto-optic modulator in a Ti:Sapphire laser, whereas direct control of the injection current is the standard method applied to diode-pumped lasers, such as fiber lasers and DPSSLs.Many physical effects contribute to the change of f CEO with the pump power in a frequency comb, as it is exhaustively discussed in Newbury and Washburn [4]. The response of f CEO to a change in the pump power thus is not simple and generally leads to a nonlinear behavior, which may affect the CEO sta...