Lamb-Dip Frequency Stabilization of Lasers

The steep zero crossing of the third derivative of narrow Lamb dips gives a good reference for accurate stabilization of the laser frequency onto an atomic or molecular transition. Either the Lamb dip in the gain profile of the laser transition or Lamb dips of absorption lines of an intracavity sample can be used. 

In the infrared spectral range. Lamb dips of a vibration-rotation transition of CH4 at 1 = 3.39 pm or of CO2 around 10 pm are commonly used for frequency stabilization of the HeNe laser at 3.39 pm or the CO2 laser. In the visible range various hyperfine components of rotational lines within the - system of the I2 molecule are mainly chosen. The experimental setup is the same as that shown in Fig. 2.18. The laser is tuned to the wanted hfs component and then the 

Using a double servo loop for fast stabilization of the laser frequency onto the transmission peak of a Fabry-Perot Interferometer (FPI) and a slow loop to stabilize the FPI onto the first derivative of a forbidden narrow calcium transition, Barger et al. constructed an ultrastable cw dye laser with a short-term linewidth of approximately 800 Hz and a long-term drift of less than 2 kHz/h [218]. Stabilities of better than 1 Hz have also been realized [219, 220]. 

This extremely high stability can be transferred to tunable lasers by a special frequency-offset locking technique [221]. Its basic principle is illustrated in Fig. 2.20. A reference laser is frequency stabilized onto the Lamb dip of a molecular transition at coq. The output from a second, more powerful laser at the frequency (D is mixed in detector D1 with the output from the reference laser at the frequency coq- An electronic device compares the difference frequency coq — co with the frequency co of a stable but tunable RF oscillator, and controls the piezo P2 such that a o — CO = co dt all times. The frequency co of the powerful laser is therefore always locked to the offset frequency co = coo — co which can be controlled by tuning the RF frequency co.  

For Lamb-dip spectroscopy with ultrahigh resolution, the output beam of the powerful laser is expanded before it is sent through the sample cell in order to minimize transit-time broadening (Vol. 1, Sect. 3.4). A retroreflector provides the coun-terpropagating probe wave for Lamb-dip spectroscopy. The real experimental setup is somewhat more complicated. A third laser is used to eliminate the troublesome region near the zero-offset frequency. Furthermore, optical decoupling elements have to be inserted to avoid optical feedback between the three lasers. A detailed description of the whole system can be found in [222]. 

An outstanding example for the amount of information on interactions in a large molecule that can be extracted from a high-resolution spectrum is represented by the work of Borde et al. on saturation spectroscopy of SFg [7.20]. Many details of the various interactions, such as spin-rotation coupling, Coriolis coupling, hyperfine structure, etc., which are completely masked at lower resolution can be unravelled when sufficiently high resolution can be achieved. For illustration Fig.7.19 depicts a section of the saturation spectrum of SFg taken by this group. 

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Saturated dispersion and polarization spectroscopy. The general relation between absorption and dispersion is well known. The saturation of absorption also corresponds to a change in the index of refraction of the vapour, which is called saturated dispersion and was already predicted by Lamb in his theory of gas Lasers 1161. This saturated dispersion plays a role in the frequency stabilization of Lasers on the Lamb dip 1201. Clear evidence of saturated dispersion was given by using a ring interferometer 21. But, in practice, the observation of saturated dispersion is much easier by interferences of polarized light. That introduces us to polarization spectroscopy. 

The idea of using the same medium as absorber and active material has been proposed and realized by several authors 340-343) Leg and Skolnick 40) used a neon gas discharge at low current and low pressure as saturable absorber inside the cavity of a He-Ne laser oscillating at X = 6328 A. The Lamb-dip halfwidth obtained was 30 Mc/sec compared to 1500 Mc/sec for the doppler line. The disadvantage of this arrangement is that the frequency of the neon transitions depends upon pressure and current 341) in the absorption cell, and this limits the stability and reproducibility of the Lamb dip center frequency. 

The last two chapters discussed spectroscopic studies which used coincidences between laser lines and transitions in other atoms or molecules. These investigations have been performed either with lasers as external light sources, or inside the laser cavity. In the latter case coupling phenomena occur between the absorbing species and the laser emission, one example of which is the saturation effect employed in Lamb dip spectroscopy and laser frequency stabilization. This chapter will deal with spectroscopic investigations of the laser medium itself and some perceptions one may obtain from it. 

The accuracy of stabilizing the two lasers onto molecular transitions increases with decreasing linewidth. Therefore, the narrow Lamb dips of Doppler-broadened molecular transitions measured with saturation spectroscopy (Sect. 2.2) are well suited [921]. This was proved by Bridges and Chang [922] who stabilized two CO2 lasers onto the Lamb dips of different rotational lines within the vibrational transitions (00°1) (10°0) at 10.4 pm and (00°1) (02°0) at 9.4 pm. The superimposed beams of the two lasers were focused into a GaAs crystal, where the difference frequency was generated. 

Two lasers are stabilized onto the Lamb dips of two molecular transitions. The width Av of the Lamb dip is 10 MHz and the rms fluctuations of the two laser frequencies is = 0.5 MHz. How accurately measured is the separation vi - V2 of the two transitions, if the signal-to-noise ratio of the heterodyne signal of the two superimposed laser beams is 50 ... 

With techniques of sub-Doppler spectroscopy, even small collisional broadening effects can be investigated with high accuracy. One example is the measurement of pressure broadening and shifts of narrow Lamb dips (Sect. 2.2) of atomic and molecular transitions, which is possible with an accuracy of a few kilohertz if stable lasers are used. The most accurate measurements have been performed with stabilized HeNe lasers on the transitions at 633 nm [975] and 3.39 um [976]. When the laser frequency co is tuned across the absorption profiles of the absorbing sample inside the laser resonator, the output power of the laser Pl(co) exhibits sharp... 

In principle at least, CO isotope lasers can most conveniently serve as reference lasers in the 4.9 to 8.0 pm wavelength domain. In terms of spectral purity, sealed-off operation ) a d abundance of readily available lasing transitions CO isotope lasers are at least as good as their COi counterparts. Lamb-dip stabilization of CO lasers was also accomplished 3) nearly 15 years ago. However, the resettability of the Lamb-dip stabilization method is at least 100 times less accurate than the 4.3 pm fluorescence stabilization of CO2 lasers. The absolute accuracy of presently available CO laser transition frequencies is also only good to within about one or two MHz. If one MHz or so accuracy is not sufficient, a direct comparison of a CO reference laser line with an appropriately selected frequency doubled line-center stabilized CO2 laser transition is always possible and was so demonstrated several years ago. ... 

Often the narrow Lamb dip at the center of the gain profile of a gas laser transition is utilized (Sect. 7.2) to stabilize the laser frequency [5.78,5,79]. However, due to collisional line shifts the frequency vq of the line center slightly depends on the pressure in the laser tube and may therefore change in time when the pressure is changing (for instance, by He diffusion out of a HeNe laser tube). 

The Lamb dip in the distribution An(v ) of the population difference An = n - (92/92)1 2 appears not only in the inhomo9eneously broadened absorption profile a(v) but in case of inversion (An < 0) also in the 9ain profile -a(o)) of an amplifyin9 medium with an inhomo9eneous linewidth. If the frequency of a sin9le-mode 9as laser is tuned over the Doppler-broadened 9ain profile, the output intensity shows a dip around the center frequency wq [10.30]. This Lamb dip in the laser output can be used to stabilize the laser frequency to the center of the qain profile (see below). 

Lamb dip stabilization onto very narrow saturation peaks allows one to achieve a very good frequency stability, especially when pressure or power broadening or transit broadening can be minimized, as in the case of the 3.39 ym He-Ne laser stabilized onto a CH transition. 

Since the two transitions are coupled only by those molecules within the velocity range Av which have been pumped by one of the lasers, the doubleresonance signals show similarly small homogeneous linewidths as in saturation spectroscopy with a single laser. However, for precise spectroscopy the common Bennet hole should be exactly at the oentev of the population distribution and not anywhere around v = 0. This can be achieved for instance by using the Lamb dip, produced in the standing wave of the pump field, to stabilize the pump laser frequency w to the center frequency... 

In lasers with inhomogeneously-broadened transitions it is found that oscillation usually occurs simultaneously on a ntunber of longitudinal cavity modes. The reasons for this behaviour are explained and we examine one method for stabilizing the intensities and inter-mode frequency differences in multi-mode operation. Next we consider several different techniques which have been used to obtain oscillation on a single longitudinal mode and this leads on naturally to a discussion of the output power versus oscillation frequency of single-frequency gas lasers. The experimental observation and theoretical interpretation of the Lamb dip is the main topic of section 13.8. 

Frequency stabilization using the Lamb dip. The power output versus frequency characteristic of a single-mode laser provides one way of detecting changes in the oscillation frequency and Fig.13.15 shows how this may be used to... 

Block diagram of laser frequency stabilization scheme using the Lamb dip. (After Bloom (1968).)... 

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