Collimation ratio

Fig. 4.1 Laser excitation spectroscopy with reduced Doppler width in a collimated molecular beam (a) schematic experimental arrangement (b) collimation ratio (c) density profile n x) in a collimated beam effusing from a point source A...

This represents a Voigt profile, that is, a convolution product of a Lorentzian function with halfwidth y and a Doppler function. A comparison with Vol. 1, (3.33) shows, however, that the Doppler width is reduced by the factor sine = Vx/v = b jld, which equals the collimation ratio of the beam. The collimation of the molecular beam therefore reduces the Doppler width Aa>o of the absorption lines to the width... 

Example 4.1 Typical figures of = 1 mm and / = 5 cm yield a collimation ratio b/ 2d) = 1/100. This brings the Doppler width Avq = Acoolln 1500 MHz down to Av = Atu /2nr 15 MHz, which is of the same order of magnitude as the natural linewidth y of many molecular transitions. 

Fig. 4.6 Section of the spectrum of NO2 excited at Aex = 488 nm in a collimated NO2 beam with a collimation ratio of sine = 1/80 (a) total fluorescence monitored and (b) filtered excitation spectrum, where instead of the total fluorescence only the fluorescence band at X = 535.6 nm for the lower vibrational level (0,10) was monitored by PM2 behind a monochromator [393]...

For molecules the line densities are much higher, and often the rotational structure can only be resolved by sub-Doppler spectroscopy. Limiting the collimation angle of the molecular beam below 2 x 10 rad, the residual Doppler width can be reduced to values below 500 kHz. Such high-resolution spectra with linewidths of less than 150 kHz could be, for instance, achieved in a molecular iodine beam since the residual Doppler width of the heavy I2 molecules, which is proportional to is already below this value for a collimation ratio 6 < 4 x 10 [400]. At... 

The residual Doppler width from the finite collimation ratio e of the molecular beam can be completely eliminated when nonlinear Doppler-free techniques are applied. Since collisions can generally be neglected at the crossing point of the molecular and laser beam, the lower molecular level /> depleted by absorption of laser photons can be only refilled by diffusion of new, unpumped molecules into the interaction zone and by the small fraction of the fluorescence terminating on the initial level i). The saturation intensity h is therefore lower in molecular beams than in gas cells (Example 2.3). 

Example 4.4 AEth = 0.1 eV, eU = 10 keV Av = 3 x 10 Ano. This means that the Doppler width of the ions in the ion source has been decreased by acceleration cooling by a factor of 300 If the laser crosses the ion beam perpendicularly, the transverse velocity components for ions with n = 3 x 10 m/s at a collimation ratio e = 10 are = n, < 3 x 10 m/s. This would result in a residual Doppler width of An 3 GHz, which illustrates that for fast beams the longitudinal arrangement is superior to the transverse one. 

Figure 5.52 illustrates a possible arrangement. The laser beam is crossed perpendicularly with a collimated molecular beam. The Doppler width of the absorption line is reduced by a factor depending on the collimation ratio (Sect. 9.1). The intensity of the laser-excited fluorescence serves as... 

A possible arrangement for saturation spectroscopy in a molecular beam is depicted in Fig. 9.18. The laser beam crosses the molecular beam perpendicularly and is reflected by the mirror Ml. The incident and the reflected beam can only be absorbed by the same molecules within the transverse velocity group = 0ibyA if the laser frequency (o = o)o y matches the molecular absorption frequency coo within the homogeneous linewidth y. When tuning the laser frequency col one observes narrow Lamb dips (Fig. 9.19) with a saturation-broadened width y at the center of broader profiles with a reduced Doppler-width cAcod, from the collimation ratio c 1 of the molecular beam (Sect. 9.1). 

As we have already noted (Sect.6.1.1), a well-collimated atomic beam displays a very small absorption width perpendicular to the atomic beam. As shown in Fig.9.35, the collimation ratio C for an atomic beam is defined as... 

Fiq.l0.4a-c. Section of the excitation spectrum of NO2 obtained with a single-mode argon laser, tunable around x = 488 nm, (a) In an-N02 cell (p = 0.01 torr), (b) in a collimated NO2 beam with a collimation ratio of 1 80, (c) filtered excitation spectrum. Instead of the total fluorescence as in (b) only the (0,1,0) fluorescence band was monitored... 

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