Frequency combs

Schliesser, A. Brehm, M. Keilmann, F. van der Weide, D., Frequency comb infrared spectrometer for rapid, remote chemical sensing, Opt. Express 2005, 13, 9029 9038... 

The absolute frequency of the fundamental IS — 2S transition in atomic hydrogen has now been measured to 1.8 parts in 1014, an improvement by a factor of 104 in the past twelve years. This improvement was made possible by a revolutionary new approach to optical frequency metrology with the regularly spaced frequency comb of a mode locked femto-second multiple pulsed laser broadened in a non-linear optical fiber. Optical frequency measurement and coherent mixing experiments have now superseded microwave determination of the 2S Lamb shift and have led to improved values of the fundamental constants, tests of the time variation of the fine structure constant, tests of cosmological variability of the electron-to-proton mass ratio and tests of QED by measurement of g — 2 for the electron and muon. 

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. 

Fig. 7. Possible setup for a frequency measurement of the 2S-10S transition relative to the 1S-2S transition utilizing the new developments with frequency comb generation by mode locked lasers. The measurements are done at the same time in the same trap. The 1S-2S transition is used as the frequency reference (A). The 2S-10S transition is driven by a diode laser (B). The frequency difference between vis-2s/8 and iC2S-ios/2 is measured with the help of an optical comb. The scheme can be applied to other 2S-nS transitions as well...

A possible setup for the frequency measurement is depicted in Fig. 7. A frequency doubled diode laser at 972 nm is locked to the dye laser at 486 nm, which is the primary laser for driving the 1S-2S transition. A frequency comb generated by a mode locked laser is used to measure the frequency difference between the 972 nm diode laser and the 759 nm laser needed for the 2S-10S transition. Note that this experiment provides its own frequency standard, for the 1S-2S transition serves as the optical frequency reference. 

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 achievable pulse length is determined by the total number of modes that can contribute to the pulse. The broader the frequency comb the shorter the possible pulse length, ideally reaching the so-called Fourier limit. In fact, the spectral width is usually limited by the width over which the GVD and higher order terms can be compensated for by mode pulling [5,6]. Cavity modes that are outside this bandwidth are suppressed without the help of the Kerr-lens effect and do not oscillate. 

This equation maps two radio frequencies ay and ay onto the optical frequencies ay. While ay is readily measurable, ay is not easy to access unless the frequency comb contains more than an optical octave, as shown in section 7. The individual modes can be separated, for example with an optical grating, if the spectral width of the carrier function is narrower than the mode separation Au)c ay. This condition is easy to satisfy, even with a free running Ti Saphire laser. 

So we see that spectral broadening of the comb [29,30] is achieved by imposing a large frequency chirp on each of the pulses. Provided that the coupling efficiency into the fiber is stable, the periodicity of the pulse train is maintained. The discussion of section 3 is thus equally valid if the electric field E(t) as measured for example at the fiber output facet instead of the laser output coupler. As described below we have used a frequency comb widened to more than 45 THz by a conventional single mode fiber to perform the first phase coherent vacuum UV to radio frequency comparison in our Garching laboratory [16,31], In recent experiments we have confirmed that the fiber does not affect the mode spacing constancy within our experimental uncertainty of a few parts in 1018 [13]. 

Fig. 3. The offset frequency uv that displaces the modes of an octave spanning frequency comb from being exact harmonics of the repetition rate u>r is measured by frequency doubling some modes at the red side of the comb and beat them with modes at the blue side...

Fig. 4. The first self-referenced frequency chain that has been used in Refs. [16,19,31] uses an optical frequency interval divider (oval symbol) [34] that fixes the relation between the frequencies /, 4/ and 7/ by locking f + 7f to 2 x 4/. The 3.39 /Am laser at / is locked through the divider after the frequency comb locked the difference between 3.5/ and 4/...

Previously we have shown that the repetition rate of a mode locked laser equals the mode spacing to within the experimental uncertainty of a few parts in 1016 [26] by comparing it with a second frequency comb generated by an efficient electro-optic modulator [41]. Furthermore the uniform spacing of the modes was verified [26] even after further spectral broadening in a standard single mode fiber on the level of a few parts in 1018 [13]. To check the integrity of the femtosecond approach we compared the / 2/ interval frequency chain as sketched in Fig. 3 with the more complex version of Fig.4 [19]. We used the 848 nm laser diode of Fig. 4 and a second 848 nm laser diode locked to the frequency comb of the / 2/ chain. The frequencies of these two laser diodes measured relative to a quartz oscillator, that was used as a radio frequency reference for the frequency combs, are 353 504 624 750 000 Hz and 353 504 494 400 000 Hz for the / 2/ and the 3.5/ 4/ chain respectively. We expect a beat note between the two 848 nm laser diodes of 130.35 MHz which was measured with a radio frequency... 

As shown in Fig. 7 we compared the frequency of the cesium Di line at 895 nm with the 4th harmonic of the methane stabilized He-Ne laser operating at 3.4 pm (/ = 88 THz). The laser that creates the frequency comb, the fourth harmonic generation and the HeNe laser are identical with the systems shown in Fig. 4. However, the HeNe laser was stabilized to a methane transition in this experiment and was used as a frequency reference instead of the Cs fountain clock. The frequency of this laser has been calibrated at the Physikalisch Technische Bundesanstalt Braunschweig/Germany (PTB) and in our own laboratory [51] to within a few parts in 1013. 

R. Holzwarth, J. Reichert, Th. Udem, T.W. Hansch, J.C. Knight, W.J. Wadsworth, P.St.J. Russell Broadening of Femtsecond Frequency Combs and Compact Optical to Radio Frequency Conversion . In Conference on Lasers and Electro-Optics CLEO, OSA Technical Digest, p. 197. 

Abstract. We present a frequency comparison and an absolute frequency measurement of two independent -stabilized frequency-doubled Nd YAG lasers at 532 nm, one set up at the Institute of Laser Physics, Novosibirsk, Russia, the other at the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany. The absolute frequency of the l2-stabilized lasers was determined using a CH4-stabilized He-Ne laser as a reference. This laser had been calibrated prior to the measurement by an atomic cesium fountain clock. The frequency chain linking phase-coherently the two frequencies made use of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser where the comb mode separation was controlled by a local cesium atomic clock. A new value for the R.(56)32-0 aio component, recommended by the Comite International des Poids et Mesures (CIPM) for the realization of the metre [1], was obtained with reduced uncertainty. Absolute frequencies of the R(56)32-0 and P(54)32-0 iodine absorp tion lines together with the hyperfine line separations were measured. 

The frequency chain works as follows to the second harmonic of the He-Ne laser at 3.39 jum a NaCl OH color center laser at 1.70 pm is phase locked. To the second harmonic of the color center laser a laser diode at 848 nm is then phase locked. This is accomplished by first locking the laser diode to a selected mode of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser (Coherent model Mira 900), frequency-broadened in a standard single-mode silica fiber (Newport FS-F), and then controlling the position of the comb in frequency space [21,11]. At the same time the combs mode separation of 76 MHz is controlled by a local cesium atomic clock [22]. With one mode locked to the 4th harmonic of the CH4 standard and at the same time the pulse repetition rate (i.e. the mode separation) fixed [22], the femtosecond frequency comb provides a dense grid of reference frequencies known with the same fractional precision as the He-Ne S tandard [23,21,11]. With this tool a frequency interval of about 37 THz is bridged to lock a laser diode at 946 nm to the frequency comb, positioned n = 482 285 modes to lower frequencies from the initial mode at 848 nm. 

Fig. 3. Set-up of the frequency chain used to measure the absolute frequency of the two iodine spectrometers. The chain links the 532 nm radiation of the frequency doubled Nd YAG lasers (563 THz) to a methane-stabilized He-Ne laser at 3.39 /rm (88 THz). The two input frequencies of the frequency interval divider stage at 852 nm and 946 nm determine the frequency of the NdtYAG lasers at 1064 nm. The input frequencies are phase-coherently linked to the methane-stabilized He-Ne laser at 3.39 /xm by use of a frequency comb generated with a Kerr-lens mode-locked femtosecond laser...

In extension to this frequency chain we installed an optical frequency interval divider [23] to extrapolate to 1064 nm (see Fig. 3). The center frequency of the optical divider stage is given by the Nd YAG laser at 946 nm laser with its frequency determined via the beat note with the comb locked laser diode at 946 nm. The higher input frequency of the divider stage is set by a diode laser at 852 nm which is heterodyned with another diode laser at 852 nm, also phase locked to the frequency comb. The lower input frequency of the divider stage is determined by the iodine stabilized Nd YAG laser at 1064 nm. While scanning the frequency doubled 1064 nm Nd YAG laser over the iodine line the two beat notes at 852 nm and 946 nm are measured with a rf-counter. They are then used to determine the absolute frequency of the 1064 nm Nd YAG laser. 

In this paper, we address two aspects of this general problem. First, we discuss the problem of frequency standards in the optical spectrum. (An analogue in the microwave region of the spectrum is the cesium beam frequency standard.) If one or a few of these reference frequencies can be accurately calibrated (perhaps by a frequency synthesis chain- -) then it may be possible to compare optical spectra to these standards. As an example of the precision that might be achieved, we discuss only optical standards based on stored ions. Second, we discuss the problem of frequency comparison of unknown frequencies to the standards. Here we primarily restrict discussion to generation of wideband frequency "combs". 

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