Optical phase noise and carrier-envelope offset noise of mode-locked lasers

Abstract

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,

Self-referencable frequency comb from a 170-fs, 1.5-μm solid-state laser oscillator

“…At higher repetition rates, SESAM mode-locked Er:Yb:glass-lasers have demonstrated close to quantum noise limited performance [33]. A detailed analysis shows that resonators with higher Q-factors have a lower quantum noise limit [15]. Thus, the oscillator was designed for minimum intracavity loss.…”

“…However, noise suppression and operation at multi-gigahertz repetition rates are more challenging than for Ti:Sapphire systems. Femtosecond fiber oscillators can show a considerable amount of excess noise [8][9][10][11][12][13][14], which arises from the spontaneous emission, the low cavity quality factor, and large intracavity nonlinearities [15]. Even at quantum-limited noise performance, fiber lasers can easily exhibit significant timingjitter, which is a challenge for stable frequency comb generation [16].…”

Optical Frequency Comb Generation based on Erbium Fiber Lasers

“…Fourth, at high net cavity dispersion, their overall timing jitter (and fceo linewidth) will be dominated by the product of the dispersion and carrierfrequency noise through the Gordon-Haus effect [27, 30,[85][86][87][88][89][90]. At low net cavity dispersion, multiple other effects can dominate the timing jitter, including a direct ASE contribution [27,30,[85][86][87][88][89][90]. A lower net cavity dispersion will also, generally, produce a broader output bandwidth, as can be seen from the general relationship between soliton spectral width and dispersion.…”

“…However, one could argue that this is a misconception. First, the free-running linewidth of the detected offset frequency can be reduced by an order of magnitude through the use of a lower noise pump laser and by minimizing the cavity dispersion [27][28][29][30][31][32][33]. Second, this free-running phase noise is well-behaved in the sense that the basic comb structure is always preserved.…”

Robustness of controlled quantum dynamics

“…In the context of robustness to control field disturbances, the theory and methodologies developed herein are most conveniently applied to disturbances wherein the frequency domain correlation function is a physically natural representation, which is the case for intensity and phase noise in laser control [20,21,39,40].…”