Demonstration of an Optical Frequency Synthesizer with Zero Carrier-Envelope-Offset Frequency Stabilized by the Direct Locking Method

摘要

The optical frequency synthesizer (OFS) based on an octave-spanning femtosecond mode-locked lasers (FML) has ever shown the exceptional optical frequency traceability to microwave frequency standards based on Cs atoms in simple and reliable way. Owing to this feature it has become an essential tool for a variety of applications, such as absolute optical frequency measurement [1, 2, 3, 4], high resolution spectroscopy [5], and determination of fundamental physical constants [6] for the past decade. And the stabilizing technology is being developed incessantly to expand its use to wider application fields. The mode frequencies of the optical comb are then given as the sum of f_(ceo) and N f_(rep), where N is an integer of an order of 10~(6). Although this OFS stabilization scheme has shown unprecedented absolute frequency accuracy, satisfying numerous applications in precision science, this method is inconvenient for the formulation of a zero f_(ceo) when the OFS frequencies must have the exact harmonics of f_(rep). An OFS with zero f_(ceo) has several advantages; the optical frequency measurement can be made simpler without measuring f_(ceo), the optical clockwork can be made easier and thus potentially more stable [7], and the frequency grid for optical communication channels, which should be exact multiples of a prescribed frequency spacing [8], can be realized easily. There have often been attempts to formulate a zero f_(ceo). One approach is to insert an acousto-optic modulator (AOM) in one arm of a self-referencing f-2f interferometer to give the comb frequency a pre-shift by the same amount of the frequency used for f_(ceo) stabilization but with an opposite sign [9, 10]. Another approach involves adopting the generation of the difference frequency in a nonlinear crystal (DFG) [7, 11, 12], utilizing the fact that the difference frequency between two modes from the same frequency comb cancels f_(ceo) as contained simultaneously in the two modes. On the other hand, in the field of ultrafast phenomena, a new approach known as the "direct locking method (DLM)" [13, 14, 15, 16] has been developed, satisfying the need for carrier-envelope-phase (CEP) stabilization. The DLM is a time-domain approach with no pulse-to-pulse phase slip, in contrast to other CEP stabilization approaches operating in the frequency domain.