Cross-over signals

If two molecular transitions with a common lower or upper level overlap within their Doppler width, extra resonances, called cross-over signals, occur in the Lamb-dip spectrum. Their generation is explained in Fig. 2.14a. 

Assume that for the center frequencies coi and co2 of the two transitions coi — C02I Acod holds. At the laser frequency co = (coi + ct 2)/2, the incident wave is shifted against coi by Aco = co — coi = (co2 — i)/2. If it saturates the velocity class (Vz dvz) = (co2 — (0 )l2k zb yk on the transition 1 with center frequency co, it is in resonance with molecules in this subgroup. Since the reflected wave experiences the opposite Doppler shift, when it saturates the same velocity class it is in resonance with molecules in the same subgroup in transition 2 with the center 

In Fig. 2.15 the three Lamb dips (two direct resonances and 1 cross-over signal) are illustrated for the case of two transitions with a common lower level. Although these cross-over signals increase the number of observed Lamb dips and may therefore increase the complexity of the spectrum, they have the great advantage that they allow one to assign pairs of transitions with a common level. This may also facilitate the assignment of the whole spectrum see, for example. Fig. 2.14b and [205, 214-216]. 

Assume that for the center frequencies Wj and W2 of the two transitions wj-W2 Awjj holds. At the laser frequency w = (wj+o 2)/2 the incident wave saturates the velocity class (v ldv ) = u 2-w /2k 7k on the transition 1 with center frequency Wj while the reflected wave saturates the same velocity class on the transition 2 with the center frequency a 2- therefore observes, besides the saturation signals at Wj and W2 (where the velocity class Vg = 0 is saturated), an additional saturation signal (cross over) at w = i(wj+W2) because one of the two waves causes a decrease -ANj of the population density in the common lower level or an increase +AN2 in the common upper level, which is probed by the second wave on another tran- 

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Fig. 2.14 (a) Generation of cross-over saturation signals (b) illustration of cross-overs in the helium transition l P. The cross-over signals are marked by 0 above or below the lines [215]... 

Fig. 2.21 Hyperfine and super-hyperfine structures of a rotational-vibrational transition in SP6, showing the molecular transitions and cross-over signals (a) experimental spectrum (b) calculated spectrum [223]...

For the cross-over signal only 1/2 is acting on each transition. Therefore the... 

Figure 3 Spectral separation of two Doppler-broadened profiles by saturation spectroscopy (A) profiles of Doppler-broadened absorption lines with Lamb dips (B) observed Doppler-free profiles (cross-over signals omitted).

The saturation spectrum of the Na D transition 3 Si/2 3 Pi/2 shows the resolved hyperfine components. Estimate the relative magnitude of the cross-over signal between the two transitions 3 Si/2(F = 1) 3 P1/2 (F = 1 and F = 2) sharing the same laser level, if the laser intensity is 2 times the saturation intensity F. 

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