Spectral line profile density

Rayleigh scattered light from dense transparent media with nonuniform density. If these nonuniformities are time-independent, there will be no frequency shift of the scattered light. If, however, time-dependent density fluctuations occur, as e. g. in fluids, due to thermal or mechanical processes, the frequency of the scattered light exhibits a spectrum characteristic of this time dependence. The type of information which can be obtained by determining the spectral line profile and frequency shift is described in an article by Mountain 235). 

In Sect.2.8, we saw that a sufficiently strong radiation field can significantly change the population densities and N2 of an atomic system by induced absorption and emission. This saturation of the population densities also causes additional line broadening. The spectral line profiles of such partially saturated transitions are different for homogeneously and for in-homogeneously broadened lines [3.19]. We treat first the homogeneous case. 

At the same time very often the real optical field interacting with atoms ha.s rather broad spectral profile, width of which is broader or comparable with the inhomogeneous width of the atomic transition. In this case, a broad spectral line approximation for quantum density matrix approach has proved to be verj- rewai d-ing. This approximation was introduced in the 1960s by C. Cohcn-Taimoudji for excitation of atoms with ordinai-y light sources [10]. This was an era before lasers. Later on it was adjusted for application for exedtation of atoms wdth multimode lasers [11] and for excitation of molecules in the case of large angular momentum states [3, 12]. 

A primary source is used which emits the element-specific radiation. Originally continuous sources were used and the primary radiation required was isolated with a high-resolution spectrometer. However, owing to the low radiant densities of these sources, detector noise limitations were encounterd or the spectral bandwidth was too large to obtain a sufficiently high sensitivity. Indeed, as the width of atomic spectral lines at atmospheric pressure is of the order of 2 pm, one would need for a spectral line with 7. = 400 nm a practical resolving power of 200 000 in order to obtain primary radiation that was as narrow as the absorption profile. This is absolutely necessary to realize the full sensitivity and power of detection of AAS. Therefore, it is generally more attractive to use a source which emits possibly only a few and usually narrow atomic spectral lines. Then low-cost monochromators can be used to isolate the radiation. 

One consequence of the high Q attained in these structures is that they become sharply tuned the system described above would show a FWHM of 1.5 MHz, comparable with the Doppler width of spectral lines in this region. Thus spectral lines viewed in a cavity may appear as an increased loss that lowers the Q at high pressures whereas at lower pressures their profile becomes distorted because the incident power density varies markedly with offset from the cavity resonant frequency. 

FIGURE 6-6. Eberhard effect on a spectral line density profile. 

Since the emitted or absorbed radiant power P co)dco is proportional to the density ni co)dco of molecules emitting or absorbing in the interval dco, the intensity profile of a Doppler-broadened spectral line becomes... 

For most treatments, the spectral density, J(a>), Eq. 2.86, also referred to as the spectral profile or line shape, is considered, since it is more directly related to physical quantities than the absorption coefficient a. The latter contains frequency-dependent factors that account for stimulated emission. For absorption, the transition frequencies ojp are positive. The spectral density may also be defined for negative frequencies which correspond to emission. 

We note that in a classical formula Planck s constant does not appear. Indeed, the zeroth moment Mo of the spectral density, J (o), does not depend on h, as the combination of Eqs. 5.35 and 5.38 shows. On the other hand, the classical moment y of the absorption profile, a(cu), is proportional to /h because the absorption coefficient a depends on Planck s constant see the discussions of the classical line shape below, p. 246. In a discussion of classical moments it is best to focus on the moments Mn of the spectral density, J co), instead of the moments, yn, of the spectral profile. 

Detailed balance. Classical line shapes are symmetric so that all classical, odd spectral moments M of the spectral function vanish. The odd moments of actual measurements are, however, non-vanishing because measured spectral density profiles satisfy the principle of detailed balance, Eq. 5.73. This problem of classical relationships may be largely alleviated by symmetrizing the measured profile prior to determining the moments, using the inverse Egelstaff procedure (P-4) discussed on p. 254 this generates a close approximation to the classical profile from the measurement and use of classical formulae is then justified. 

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