Spectral Line Profiles in Liquids and Solids

Many different types of lasers use liquids or solids as amplifying media. Since the spectral characteristics of such lasers play a significant role in applications of laser spectroscopy, we briefly outline the spectral 

In general the atoms or molecules used for laser action are diluted to 

10 - 10 moles/1iter, or the ruby laser, where the concentration of the 

In liquids, the distances R-(AtB.) show random fluctuations analogous 

Inelastic collisions of A with molecules B of the liquid host may cause 

Many different types of lasers use liquids or solids as amplifying media. Since the spectral characteristics of such lasers play a significant role in applications of laser spectroscopy, we briefly outline the spectral linewidths of optical transitions in liquids and solids. Because of the large densities compared with the gaseous state, the mean relative distances R(A, B ) between an atom or molecule A and its surrounding partners By are very small (typically a few tenths of a millimeter), and the interaction between A and the adjacent partners Bj is accordingly large. 

In general, the atoms or molecules used for laser action are diluted to small concentrations in liquids or solids. Examples are the dye laser, where dye molecules are dissolved in organic solutions at concentrations of 10 to 10 moles/liter, or the ruby laser, where the concentration of the active Cr ions in AI3O3 is on the order of 10 . The optically pumped laser molecules A interact with their surrounding host molecules B. The resulting broadening of the excited levels of A depends on the total electric field produced at the location of A by all adjacent molecules By, and on the dipole moment or the polarizability of A. The linewidth Aco/jt of a tran- 

In liquids, the distances / /(A, By) show random fluctuations analogous to the situation in a high-pressure gas. The linewidth Acoik is therefore determined by the probability distribution P(Rj) of the mutal distances i y (A, Bj) and the correlation between the phase perturbations at A caused by elastic collisions during the lifetime of the levels /, Ej (see the analogous discussion in Sect. 3.3). 

Examples of such continuous absorption and emission line profiles are the optical dye spectra in organic solvents, such as the spectrum of Rho-damine 6G shown in Fig. 3.26, together with a schematic level diagram [3.40]. The optically pumped level Ei is collisionally deactivated by radiationless transitions to the lowest vibrational level Em of the excited electronic state. The fluorescence starts therefore from Em instead of Ei and ends on various vibrational levels of the electronic ground state (Fig. 3.26a). The emission spectrum is therefore shifted to larger wavelengths compared with the absorption spectrum (Fig. 3.26b). 

In crystalline solids the electric field E(R) at the location R of the excited molecule A has a symmetry depending on that of the host lattice. Because the lattice atoms perform vibrations with amplitudes depending on the tem-peratur T, the electric field will vary in time and the time average E(T, t, R)) will depend on temperature and crystal structure [3.41-3.43]. Since the oscillation period is short compared with the mean lifetime of A ( /), these vibrations cause homogeneous line broadening for the emission or absorption of the atom A. If all atoms are placed at completely equivalent lattice points of an ideal lattice, the total emission or absorption of all atoms on a transition Ei Ek would be homogeneously broadened. 

Inelastic collisions of A with molecules B of the liquid host may cause radiationless transitions from the level Ej populated by optical pumping to lower levels En- These radiationless transitions shorten the lifetime of , and cause collisional line broadening. In liquids the mean time between successive inelastic collisions is of the order of 10 to 10 s. Therefore the spectral line Ei Ek is greatly broadened with a homogeneously broadened profile. When the line broadening becomes larger than the separation of the different spectral lines, a broad continuum arises. In the case of molecular spectra 

Problem 3.1. Determine the natural linewidth, the Doppler width, pressure broadening and shifts for the neon transition 3s2 2p4 at A = 632.8 nm in a He-Ne discharge 

Problem 3.2. What is the dominant broadening mechanism for absorption lines in the following examples  

If the upper level fe) can decay by spontaneous processes with a relaxation constant y, its mean population probability is 

Since the induced absorption rate within the spectral interval y is, according to (2.57) and (2.105) 

If both levels a) and b) decay with the relaxation constants y and yt, respectively, the line profile of the homogeneously broadened transition a) b) is again described by (3.73), where now (Vol. 2, Sect. 2.1 and [107]) 

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