S. A. van den Berg

Femtosecond frequency comb based distance measurement in air

Interferometric measurement of distance using a femtosecond frequency comb is demonstrated and compared with a counting interferometer displacement measurement. A numerical model of pulse propagation in air is developed and the results are compared with experimental data for short distances. The relative agreement for distance measurement in known laboratory conditions is better than 10(-7). According to the model, similar precision seems feasible even for long-distance measurement in air if conditions are sufficiently known. It is demonstrated that the relative width of the interferogram envelope even decreases with the measured length, and a fringe contrast higher than 90% could be obtained for kilometer distances in air, if optimal spectral width for that length and wavelength is used. The possibility of comb radiation delivery to the interferometer by an optical fiber is shown by model and experiment, which is important from a practical point of view.

High-accuracy long-distance measurements in air with a frequency comb laser

We experimentally demonstrate that a femtosecond frequency comb laser can be applied as a tool for long-distance measurement in air. Our method is based on the measurement of cross correlation between individual pulses in a Michelson interferometer. From the position of the correlation functions, distances of up to 50 m have been measured. We have compared this measurement to a counting laser interferometer, showing an agreement with the measured distance within 2 microm (4x10(-8) at 50 m).

Long distance measurement with femtosecond pulses using a dispersive interferometer.

We experimentally demonstrate long distance measurements with a femtosecond frequency comb laser using dispersive interferometry. The distance is derived from the unwrapped spectral phase of the dispersed interferometer output and the repetition frequency of the laser. For an interferometer length of 50 m this approach has been compared to an independent phase counting laser interferometer. The obtained mutual agreement is better than 1.5 μm (3×10(-8)), with a statistical averaging of less than 200 nm. Our experiments demonstrate that dispersive interferometry with a frequency comb laser is a powerful method for accurate and non-incremental measurement of long distances.

Direct frequency comb spectroscopy of trapped ions

Frequency comb lasers provide a phase coherent link between radio frequency sources and optical frequencies, now making spectroscopy possible at optical and near-infrared frequencies at an extremely high accuracy of 10−17 [1]. Using the comb laser for direct excitation obviates the need for a continuous wave laser at the transition wavelength, as has been demonstrated in beam experiments, vapour cells and magneto-optical traps [2–4].

Frequency metrology on the 4s(2)S(1/2)-4p(2)P(1/2) transition in Ca-40(+) for a comparison with quasar data

High accuracy frequency metrology on the 4s S-2(1/2)-4p P-2(1/2) transition in calcium ions is performed using laser cooled and crystallized ions in a linear Paul trap. Calibration is performed with a frequency comb laser, resulting in a transition frequency of f = 755 222 766.2 (1.7) MHz. The accuracy presents an improvement of more than one order of magnitude, and will facilitate a comparison with quasar data in a search for a possible change of the fine structure constant on a cosmological time scale.

Direct frequency-comb spectroscopy of a dipole-forbidden clock transition in trapped 40Ca+ ions.

We demonstrate direct frequency-comb (FC) spectroscopy of the dipole-forbidden 4s(2)S(1/2)-3d(2)D(5/2) transition in trapped (40)Ca(+) ions using an unamplified FC laser. The excitation is detected with nearly 100% efficiency using a shelving scheme in combination with single-ion imaging. The method demonstrated here has the potential to reach hertz-level accuracy, if a hertz-level linewidth FC is used in combination with confinement in the Lamb-Dicke regime.

From amplified spontaneous emission to laser oscillation : Dynamics in a short-cavity polymer laser

We present an experimental study of the input-output characteristics of an ultrashort pumped pi -conjugated polymer in solution. By comparing the results for configurations with zero, one, and two mirrors around the polymer, we show that the physics is driven by amplified spontaneous emission and not by cooperative emission. This finding is substantiated by picosecond-time-scale measurements of the evolution of the emission of the polymer. For the two-mirror configuration a sharply defined threshold for laser oscillation is found; the output of the laser exhibits strong pulsations.

Time-frequency distribution of interferograms from a frequency comb in dispersive media

We investigate general properties of the interferograms from a frequency comb laser in a non-linear dispersive medium. The focus is on interferograms at large delay distances and in particular on their broadening, the fringe formation and shape. It is observed that at large delay distances the interferograms spread linearly and that its shape is determined by the source spectral profile. It is also shown that each intensity point of the interferogram is formed by the contribution of one dominant stationary frequency. This stationary frequency is seen to vary as a function of the path length difference even within the interferogram. We also show that the contributing stationary frequency remains constant if the evolution of a particular fringe is followed in the successive interferograms found periodically at different path length differences. This can be used to measure very large distances in dispersive media.

Long distance measurement with sub-micrometer accuracy using a frequency comb laser

The invention of the femtosecond frequency comb (FC) laser has revolutionized the field of high-resolution spectroscopy, by providing very accurate reference frequencies in the optical domain, acting as a ‘frequency ruler’. Similarly, a frequency comb can be viewed as a ruler for distance measurement, which is based on the fact that the vacuum distance between subsequent pulses is known with the accuracy of the used time standard. We have recently demonstrated absolute distance measurements using a FC laser applying a cross-correlation technique [1], which was supported by a theoretical and a numerical study on the formation of cross-correlation in dispersive media [2,3].

Distance measurement in air with a femtosecond frequency comb

A femtosecond frequency comb is a powerful tool in a wide range of metrological applications, one of them being in the field of distance measurement. Due to the locking of the repetition rate of the laser to a time standard, the distance between successive pulses is accurately known, providing direct traceability to the SI definition of the meter. Since the interpulse distance is typically of the order of 1 m, the range of non-ambiguity is large. Such accuracy is easily obtained with other methods like time-of-flight measurements. Several schemes for distance measurement have been proposed and demonstrated [1–4]. In this paper we report on measurement of distances up to 20 m in air, that have been acquired using a scheme based on a Michelson interferometer. The interferometer consists of a long measurement arm and a short reference arm that can be adjusted such that the path length difference between both arms is a multiple of the interpulse distance. Once this is the case, a cross-correlation function can be measured by scanning the reflector of the reference arm with a piezo element. The path-length difference between both arms is then determined from the the center of the cross-correlation function and the interpulse distance, taking into account the refractive index of air.