Homogeneously broadened

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

Unlike high-resolution NMR spectra of bulk solutions where NMR linewidths well below 1 Hz can be obtained routinely, NMR spectra of liquids permeating porous solids in most cases will not exhibit such a high spectral resolution. First of all, the interaction of liquid phase molecules with pore walls of the catalyst and rapid diffusion-driven intrapore transport will lead to a pronounced homogeneous broadening of the observed NMR lines. Smaller pore sizes and the presence of paramagnetic impurities in the solid material usually aggravate the situation and thus should be avoided. Another reason why NMR spectra of liquids in porous... 

FIGURE 4.2 Linewidth increase with temperature for an S = 1/2 system. The linewidth of a feature in the low-spin heme spectrum from cytochrome a in bovine heart cytochrome oxidase has been fit as a convolution of a constant component from inhomogeneous broadening and a temperature-dependent component from homogeneous broadening (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

The width of a band in the absorption spectrum of a chromophore located in a particular microenvironment is a result of two effects homogeneous and inhomogeneous broadening. Homogeneous broadening is due to the existence of a continuous set of vibrational sublevels in each electronic state. Inhomogeneous broadening results from the fluctuations of the structure of the solvation shell... 

Energy transfer in solution occurs through a dipole-dipole interaction of the emission dipole of an excited molecule (donor) and the absorptive moment of a unexcited molecule (acceptor). Forster<40) treated the interaction quantum mechanically and derived and expression for the rate of transfer between isolated stationary, homogeneously broadened donors and acceptors. Dexter(41) formulated the transfer rate using the Fermi golden rule and extended it to include quadrupole and higher transition moments in either the donor or the acceptor. Following the scheme of Dexter, the transfer rate for a specific transition is... 

This Lorentzian line-shape function has been sketched in Figure 1.4(b). The natural broadening is a type of homogeneous broadening, in which all the absorbing atoms are assumed to be identical and then to contribute with identical line-shape functions to the spectrum. There are other homogeneous broadening mechanisms, such as that due to the dynamic distortions of the crystalline environment associated with lattice vibrations, which are partially discussed in Chapter 5. 

Figure 9. Selective irradiation of dioxane. Homonuclear irradiation of a homogeneously broadened resonance at 67.9 MHz. Spectral details PW = 40 ysec (90° C), D2 = 10 sec, 4 scans accumulated, quadrature detection 15% acetone-dc,...

FIGURE 5.5 (a) Components of the CARS signal. The last three terms in Equation 5.1 are plotted versus detuning A = C0p-co -O. O is the center frequency of a homogeneously broadened Raman line with linewidth F. The curves are calculated with an assumption that2 R = 1.2 = 0)- (b) Schematic of the FM CARS process. Solid curve, sum of the contribu-... 

B. A. Cowans and J. B. Grutzner, Examination of homogeneous broadening in solids via rotationally sjmchronized spin-echo NMR spectroscopy. /. Magn. Reson., 1993,105,10-18. 

To achieve the instability of homogeneous broadened line lasers, a satisfaction of much more difficult conditions is required large gain and the so-called bad-cavity properties. This special regime for damping constants and mode intensity is fulfilled in the far-infrared lasers [36]. In 1985 Weiss et al. [37,38] experimentally found a period doubling route to chaos in the NH3 laser. Further experimental investigation of chaotic dynamics in such lasers was reported later [39]. 

Why is the two-photon ionization spectrum so broad Is the spectrum mainly homogeneously broadened or inhomogeneously broad-... 

In the absence of noise, the system [179] describes the generation of a singlemode laser field interacting with a homogeneously broadened two-level medium [180]. The variables and parameters of the Lorenz system can be interpreted in terms of a laser system as q is the normalized electric field amplitude, the normalized polarization, q3 the normalized inversion, a = fe/y1 r = A+l, b = 72/71, with k the decay rate of the field in the cavity, yj and y2 the relaxation constants of the inversion and polarization, and A the pump parameter. Far-infrared lasers have been proposed as an example of a realization of the Lorenz system [162]. A detailed comparison of the dynamics of the system (42) and a far-infrared laser, plus a discussing the validity of the Lorenz system as laser model, can be found in Ref. 163. 

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