The timing jitter, optical phase noise, and carrierenvelope offset (CEO) noise of passively mode-locked lasers are closely related. New key results concern analytical calculations of the quantum noise limits for optical phase noise and CEO noise. Earlier results for the optical phase noise of actively mode-locked lasers are generalized, particularly for application to passively mode-locked lasers. It is found, for example, that mode locking with slow absorbers can lead to optical linewidths far above the Schawlow-Townes limit. Furthermore, modelocked lasers can at the same time have nearly quantum-limited timing jitter and a strong optical excess phase noise. A feedback timing stabilization via cavity length control can, depending on the situation, reduce or greatly increase the optical phase noise, while not affecting the CEO noise. Besides presenting such findings, the paper also tries to clarify some basic aspects of phase noise in mode-locked lasers.PACS 42.50.Lc; 42.60.Fc IntroductionThe noise properties of mode-locked lasers, in particular the timing jitter [1, 2], the optical phase noise, and the carrier-envelope offset (CEO) noise [3,4], are important for many applications, e.g. in frequency metrology and data transmission. These types of noise can have different origins, the most important of which are usually mechanical vibrations of the laser cavity, thermal effects in gain medium and/or laser cavity, and quantum fluctuations. As is well known, the latter are related mainly to spontaneous emission in the gain medium and to vacuum noise entering the laser cavity through the output coupler mirror and other elements with optical losses. Depending on the circumstances, the noise performance can be close to quantum limited or many orders of magnitude above the quantum limit. One may expect that quantum-limited performance in terms of timing jitter and optical phase noise should usually come in combination, but in the following it will be demonstrated that e.g. mirror vibrations can lead to strongly enhanced optical phase noise,

We design single-wall carbon nanotube (SWNT) thin-film saturable absorbers (SAs) integrated onto semiconductor distributed Bragg reflectors for mode-locking solid-state Er:Yb:glass lasers. We characterize the low nonsaturable loss, high-damage-threshold SWNT SAs and verify their operation up to a pulse fluence of 2 mJ/cm(2). We demonstrate passive fundamental continuous-wave mode locking with and without group-delay dispersion compensation. Without compensation the laser produces chirped 1.8 ps pulses with a spectral width of 3.8 nm. With compensation, we obtain 261 fs Fourier-transform-limited pulses with a spectral width of 9.6 nm.

We report on nearly quantum-limited timing-jitter performance of two passively mode-locked Er:Yb:glass lasers with a repetition rate of 10 GHz. The relative timing jitter of both lasers was measured to be 190 fs (100 Hz-1.56 MHz) root mean square. The remaining cavity-length fluctuations are below 7.5 pm in the 6 Hz-8 kHz frequency range, indicating the stability of a rugged miniature cavity setup. By actively controlling the cavity length we reduced the timing jitter to 26 fs (6 Hz-1.56 MHz). We also discuss the influence of cavity length on the practically achievable timing jitter.

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