J. Stenger

Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements

Abstract.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.

Ultraprecise Measurement of Optical Frequency Ratios

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 nu(SH) at 532 nm to the fundamental nu(0) at 1064 nm, nu(SH)/nu(0) = 2.000 000 000 000 000 001x (1 +/- 7x10(-19)).

Carrier-envelope offset dynamics of mode-locked lasers

We investigate coupling mechanisms between the amplitude and the carrier-envelope offset phase in mode-locked lasers. We find that nonlinear beam steering in combination with the intracavity prism compressor is the predominant mechanism that causes amplitude-to-phase conversion in our laser. A second mechanism, induced by self-steepening, is also identified. These mechanisms are important for stabilizing the carrier-envelope offset phase and also explain the extremely low pulse-to-pulse energy fluctuations observed in some lasers with carrier-envelope lock. The coupling mechanisms described have important implications for applications of few-cycle optical pulses.

Intensity-induced mode shift in a femtosecond laser by a change in the nonlinear index of refraction

The modes of the comb spectrum of a Kerr-lens mode-locked laser are frequency shifted versus the corresponding cw modes of the cavity by an intensity-induced change in the index of refraction in the Kerr medium. We demonstrate this effect and discuss novel schemes for fast frequency control of the comb spectrum.

Kerr-lens mode-locked lasers for optical frequency measurements

The frequency of the intercombination line 3P1 - 1S0 of Calcium at 657 nm is phase-coherently measured in terms of the output of a primary cesium frequency standard using an optical frequency comb generator comprising a < 10 fs Kerr-lens mode-locked Ti:Sapphire laser and an external microstructure fiber for self-phase-modulation. The measured frequency value of vCa equals 455 986 240 494 276 Hz agrees within its relative uncertainty of 4 X 10-13 with the values previously measured with a traditional harmonic frequency chain and the value recommended for the realization of the SI unit of length. Furthermore, we investigate the coherence properties of the broadened frequency comb and find no indications for incoherent scattering processes in the microstructure fiber.

Optical Frequency Measurement Using Frequency Multiplication and Frequency Combs

We review the development of phase-coherent optical frequency measurement from its start with the harmonic frequency chain to the present use of optical comb generators. We demonstrate that the frequency fluctuations of a femtosecond comb laser—used in optical frequency measurement—can be eliminated completely from the measurement process, allowing ultimate frequency measurement performance. This principle was applied to the frequency measurements of the Ca cloud standard and the Yb + single-ion standard. The latter measurements confirm the suitability of these optical standards as future atomic clocks.

Single ion spectroscopy for optical clocks

The 435 mum 171Yb+ transition is a good candidate for an atomic clock based on an optical transition. We have stored single 171Yb ions for several months in RF traps. The ions are cooled, repumped and the clock transition is interrogated by (frequency-doubled) diode lasers. The interrogation laser linewidth was 30 Hz determining the resolvable linewidth of the Yb+ transition interrogated. The absolute frequency of this transition was measured using an optical comb generator, self referenced by broadening the spectrum to above one octave, with respect to a Cs fountain clock. Of all systematic frequency shifts to which this transition is subject an estimate indicates that the electric quadruple shift appears is the largest. To obtain a magnitude of the quadruple shift (and the quadruple moment) the clock frequencies of two independently stored and cooled 171Yb ions were compared while varying the static electric field in one trap. The measured frequency shift amounting to ~1 Hz/V. This result would seem to permit clocks with much higher accuracy than the clocks based on microwave transition, particularly if the technique of aligning the ions with respect to the electric field were applicable. Anticipating even more precise clocks, we are presently investigating a blue nuclear transition in 229Th. Such a nuclear transition should be even better shielded from environmental influences than transitions in the electron shell. This nuclear transition has not yet been directly optically observed. We are presently investigating the luminescence after incoherent broad band optical excitation. The triply ionized 223Th is then a suitable system for trapped single ion spectroscopy. The cooling transition lies conveniently in the near infrared and the nuclear clock transition can be read out by nuclear/electron shell double resonance

High-sensitivity noise measurement of a passively mode-locked Erbium fiber laser

We investigated the phase noise and the repetition rate of a passively mode-locked stretched-pulse Erbium fiber laser and measured at the 16800th harmonic a side-band phase noise smaller than 60dBc/Hz and a pulse-to-pulse-jitter of 0.3fs.

Phase-coherent frequency measurements of the calcium- and ytterbium-optical frequency standards with a Kerr-lens modelocked femtosecond laser

Summary form only given. Recent progress in femtosecond pulse generation and the advent of microstructure optical fibers have substantially facilitated optical frequency measurements. These schemes start with the highly periodic pulse train of a Kerr-lens modelocked laser which corresponds in the frequency domain to a comb-like frequency spectrum of equidistant lines. The spectral span of this comb is determined by the inverse duration of an individual pulse while the spacing between the lines is determined by the pulse repetition frequency. The fast, spectrally far-reaching Kerr-lens modelocking mechanism enforces a tight coupling of the optical phases of the individual lines. As a result, the frequency of any of these lines is given by an integer multiple of the pulse repetition frequency f/sub rep/ and a frequency /spl nu//sub ceo/ which accounts for the offset of the entire comb with respect to the frequency origin. The spectrum from the femtosecond laser reaching from around 700 nm to 900 nm is further broadened in a microstructure fiber by self-phase modulation to about 500 nm to 1200 nm. Whereas counting of the repetition rate or one of its harmonics is straightforward, the frequency /spl nu//sub ceo/ requires to count the beat between a number of modes around 550 nm and a number of frequency-doubled modes at 1100 nm. An unknown frequency /spl nu//sub opt/ of an external optical signal is measured by counting the frequency of the beat-note /spl nu//sub opt/-/spl nu//sub comb/ between this signal and a suitable. comb line /spl nu//sub comb/. Thus, by refering the three radiofrequencies f/sub rep/, /spl nu//sub ceo/ /spl nu//sub opt/-/spl nu//sub comb/ to the primary cesium standard, the frequency of the optical signal can precisely be measured. We report the first application of this method to phase-coherent measurements of two different optical frequency standards operating in the PTB: cold-atom-based Ca standard and the single-ion ytterbium standard.

Kerr-lens mode-locked lasers as ultra-low noise microwave sources

Summary form only given. Kerr-lens mode-locked (KLM) femtosecond lasers provide a dense comb of phase coherent reference frequencies and thus are versatile tools for optical frequency measurements. We demonstrate that the quantum-limited pulse timing noise level of such a laser is substantially smaller than the noise generated by state-of-the-art microwave oscillators.