Frequency-comb technique

Another reason for predicting levels in atomic hydrogen and deuterium is that transitions to their lower levels fall in the visible spectrum or are in close range frequencies belonging to this domain can be measured very accurately. In particular, as much as about 15 digits can be obtained on such frequencies, with the recent frequency-comb technique this technique provides about 100,000 equally-spaced laser lines located in the visible spectrum, whose frequency can be known to about 1 Hz (see, e.g. [7]). 

All the projects benefit hugely from the successful development in the frequency measurements techniques thanks to the optical frequency comb technique [48],... 

The best frequency stability in the optical range can be achieved with the optical frequency-comb technique, which will be discussed in Vol. 2, Sect. 9.7 [377]. The relative frequency fluctuations go down to Av/uq < 10 , which implies an absolute stability of about 0.5 Hz. 

To relate optical frequencies to the cesium time standard remains a very important issue in precision metrology. In this context the development of the opticai-frequency-comb technique using mode-locked lasers has been very important [9.400]. 

The enormous difficulty of making optical frequency measurements has been a major obstacle to progress. The optical frequency comb generator devised by Hansch overcomes these difficulties, and promises to revolutionize spectroscopy. The technique, based upon a mode-locked laser, makes it possible to connect microwave and optical frequencies, or to determine relative optical frequencies [20,21], In particular, it allows to transport the stability of optical transitions into the microwave frequency range. A report by J. Hall about these developments can be found in these proceedings. 

Abstract. A suitable femtosecond (fs) laser system can provide a broad band comb of stable optical frequencies and thus can serve as an rf/optical coherent link. In this way we have performed a direct comparison of the IS — 2S transition in atomic hydrogen at 121 nm with a cesium fountain clock, built at the LPTF/Paris, to reach an accuracy of 1.9 x 10-14. The same comb-line counting technique was exploited to determine and recalibrate several important optical frequency standards. In particular, the improved measurement of the Cesium Di line is necessary for a more precise determination of the fine structure constant. In addition, several of the best-known optical frequency standards have been recalibrated via the fs method. By creating an octave-spanning frequency comb a single-laser frequency chain has been realized and tested. 

The optical frequency comb (for which Th.W. Hansch and J. Hall received the Nobel Prize) has meanwhile found numerous applieations, as for instance the very aecu-rate measurement of optical frequencies, whieh has been discussed in the previous section. It is much simpler than former techniques but reaches an accuraey that is two to three orders of magnitude higher. 

The application of frequency combs to molecular spectroscopy opens the way to new and very promising techniques, which are based on a combination of laser spectroscopy and Fourier-transform spectroscopy [1342],... 

The second volume of Laser Spectroscopy covers the different experimental techniques, necessary for the sensitive detection of small concentrations of atoms or molecules, for Doppler-free spectroscopy, laser-Raman-spectroscopy, doubleresonance techniques, multi-photon spectroscopy, coherent spectroscopy and time-resolved spectroscopy. In these fields the progress of the development of new techniques and improved experimental equipment is remarkable. Many new ideas have enabled spectroscopists to tackle problems which could not be solved before. Examples are the direct measurements of absolute frequencies and phases of optical waves with frequency combs, or time resolution within the attosecond range based on higher harmonics of visible femtosecond lasers. The development of femtosecond non-collinear optical parametric amplifiers (NOPA) has considerably improved time-resolved measurements of fast dynamical processes in excited molecules and has been essential for detailed investigations of important processes, such as the visual process in the retina of the eye or the photosynthesis in chlorophyl molecules. 

This positive development is partly based on new experimental techniques, such as improvements of existing lasers and the invention of new laser types, the realization of optical parametric oscillators and amplifiers in the femtosecond range, the generation of attosecond pulses, the revolution in the measurements of absolute optical frequencies and phases of optical waves using the optical frequency comb, or the different methods developed for the generation of Bose-Einstein condensates of atoms and molecules and the demonstration of atom lasers as a particle equivalent to photon lasers. 

Several techniques have been proposed for modifying the shape of the short-time spectrum so as to emphasize those portions deemed to be important for speech perception or to reduce the amplitude of those portions assumed to be noise. One approach is adaptive comb filtering[Lim et al., 1978], In this method, the fundamental frequency of voiced speech sounds is estimated, and a comb fdter is then constructed to pass signal power in the regions of the pitch harmonics and to suppress power in the valleys in between. Experimental results with normal-hearing subjects, however, have shown no significant improvement in intelligibility with this type of system [Perlmutter et al., 1977][Lim et al., 1978],... 

The JILA implementation of this technique is illustrated in Fig. 5 [18]. For the first measurement u>r was phase locked to a precise radio frequency reference (a GPS controlled Rb standard) but knowledge and control of u>0 was not required. The entire comb was allowed to freely float and <5i and <52 were measured... 

Recently, a new technique has been developed [1323] that allows the direct comparison of widely different reference frequencies and thus considerably simplifies the frequency chain from the cesium clock to optical frequencies by reducing it to a single step. Its basic principle can be understood as follows (Fig. 9.91) The frequency spectrum of a mode-locked continuous laser emitting a regular train of short pulses with repetition rate 1/AT consists of a comb of equally spaced frequency components (the modes of the laser resonator). The spectral width Aw = 2jt/T of this comb spectrum depends on the temporal width T/Ar of the laser pulses (Fourier theorem). Using femtosecond pulses from a Tusapphire Kerr lens mode-locked laser, the comb spectrum extends over more than 30 THz. 

This technique is quite similar to Fourier-transform spectroscopy, where the phase difference between the two beams in a Michelson interferometer are generated by changing the path difference as a function of time. In the dual comb spectroscopy the phase difference it generated by the different repetition frequencies of the two... 

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