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We introduce a novel concept for optical frequency measurement and division which employs a Kerr-lens mode-locked laser as a transfer oscillator whose noise properties do not enter the measurement process. We experimentally demonstrate, that this method opens up the route to phase-link signals with arbitrary frequencies in the optical or microwave range while their frequency stability is preserved.

Absolute frequency measurement of the 435.5 nm 171 Yb + clock transition with a Kerr-lens mode-locked femtosecond laser

We developed a novel technique for frequency measurement and synthesis, based on the operation of a femtosecond comb generator as transfer oscillator. The technique can be used to measure frequency ratios of any optical signals throughout the visible and near-infrared part of the spectrum. Relative uncertainties of 10 −18 for averaging times of 100 s are possible. Using a Nd:YAG laser in combination with a nonlinear crystal we measured the frequency ratio of the second harmonic νSH at 532 nm to the fundamental ν0 at 1064 nm, νSH/ν0 = 2.000 000 000 000 000 001 × (1 ± 7 × 10 −19 ).The development of optical frequency comb generators based on Kerr-lens mode-locked femtosecond lasers [1,2] has enormously stimulated the field of optical frequency synthesis and metrology. Using this technique, the absolute frequencies of a number of narrow transitions in cold atoms or single stored ions such as H, Ca, Yb + or Hg + have been measured by phase-coherently linking those signals to primary cesium-clock controlled hydrogen masers [3][4][5][6]. The measurement instabilities approached those of the hydrogen masers, indicating that neither the optical frequency standards nor the frequency combs themselves were limiting parts of the setups.Any absolute frequency measurement is finally limited by the frequency instability of the device realizing the unit of frequency, Hertz, such as a radio or microwave reference like the hydrogen maser. A possibility to avoid this limitation is the measurement of optical frequency ratios, which are unitless. Thus, frequency ratios for oscillators with better stability than that of the radio or microwave reference can be determined with smaller uncertainty than the absolute frequencies if a technique is available to realize the frequency ratio without introducing additional noise.Such a technique is the transfer oscillator concept, which has been realized with a harmonic frequency chain [7]. However, the measured frequency ratios were restricted to small integer numbers. In this Letter, we describe a novel technique based on the operation of a femtosecond frequency comb generator as a transfer oscillator. Our technique has the capability of generating arbitrary ratios of any optical frequencies throughout the visible and near-infrared part of the spectrum, while frequency fluctuations of the comb modes do not enter the measurement but cancel out.We demonstrate the superior short-term instability by two measurements: first, we measured the frequency ratio of signals from a single-Yb + -ion frequency standard [8] and from an I 2 -frequency-stabilized Nd:YAG laser [9]. Second, we used the Nd:YAG laser and measured the frequency ratio of the second harmonic at 532 nm to its fundamental at 1064 nm, thereby testing how accurately the 2:1 frequency ratio is realized by second harmonic generation. We demonstrate the capability of our technique of frequency-ratio measurements with relative uncertainty better than 10 −18 . Kerr-lens mode-locked femtosecond lasers emit a periodic train of short pulses. The...

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,