Radiative Damping

In this section we will show how the sphere polarizability can be modified to satisfy the optical theorem [17]. 

The term i Pcisphico) is named radiative damping [18] of the sphere polarizability. This imaginary term takes directly into account that the dipole induced in the (metallic or dielectric) sphere by the external incident field, re-irradiates the energy in the free-space. As this scattering process occurs in different directions, then, the net effect is that the incident field is attenuated in the propagation direction as it will be for a pure absorption process. 

Correcting Eq. (1.299) with Eq. (1.307), the absorption cross section becomes  

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In chemisorbed systems, the molecular orbitals of the adsorbate are mixed with the electronic states of the substrate, producing strong adsorption bonds, i.e. the frequency of the adsorbate mode is well above the highest phonon frequency of the substrate. The relaxation of these vibrational excited states via emission of substrate phonons has only a low probability, because many phonons have to be enoitted during the decay. Non-radiative damping by electron-hole pair excitation appears to be the dominant relaxation path in these systems. 

A. Ben-Reuven. Radiatively damped collisions of ultracold atoms. In L. Frommhold and J. W. Keto, eds., Spectral Line Shapes 6, p. 206, Am. 

Fig. 3. The schematic representation of a virtual two photon process which is allowed when there is a nonzero matrix element of the radiative damping matrix rnm connecting two states n and m. This process is negligible unless n and m are nearly degenerate...

Waldeck D. H., Alivisatos A. P. and Harris C. B. (1985), Non-radiative damping of molecular electronic excited states by metal surfaces . Surface Sci. 158, 103-125. 

The molecule in the excited electronic state (levels p and s) can undergo nonthermal relaxation processes, for example, dissociation, ionization, and radiative damping. These processes are irreversible because their products are removed from the system, and they are accounted for by the damping rates Tj and Tp in Eqs (18.58b) and (18.58c), respectively. 

In order to discuss more correctly the question of radiative width we keep in mind the fact that the operator (4.88) provokes not only a radiative damping of exciton states, but also changes their dispersion rule. To obtain this dispersion, we add to (4.88) operators of the free exciton and transverse photon fields, as was done in Sections 4.1 and 4.2, and diagonalize the total Hamiltonian so obtained. Recall for comparison that in the case of an ideal 3D crystal after such diagonalization of the total Hamiltonian the radiative width of new excitations (polaritons) disappeared. We show below that in ID and 2D the results are completely different. 

Ghazi, A.V., V. Ramanathan, and R.E. Dickinson, Acceleration of upper stratospheric radiative damping Observational evidence. Geophys Res Lett 6, 437, 1979. 

It should be noted that vibrational relaxation is taken here into account in a highly simplified way—a damping process that takes place in addition to radiative damping. This is sufficient for our purpose because, as stated above, vibrational relaxation is essentially irreversible and because we are interested in the population change only within the originally excited... 

In Section 15.3.3, we discussed the excitation of higher electronic states using laser light to drive optical dipole transitions. The interaction was strongly damped by spontaneous emission from the upper level indeed, the molecules were detected by means of the scattered photons. In this section, we consider some ways to manipulate the hyperfine sublevels within the ground state of the molecule. In contrast to optical transitions, the coherences between these ground-state levels are not radiatively damped. 

Returning to eq. (79) we may try to estimate the new decay time resulting from the cooperative emission in strong superradiance. Such a decay time is also called superradiant lifetime and its inverse is called radiative damping constanf . Calculating this lifetime as (Yariv 1967)... 

Grigorchuk NI. Radiative damping of surface plasmon resonance in spheroidal metalhc nanoparticle embedded in a dielectric medium. / Opt Soc Am B 2012 29 (12) 3404-3411. 

These equations have been also obtained by Carminati et al. [17] and directly show a d dependence at large nanoparticle-molecule distances. In the Carminati model the metal nanosphere is considered as a point-like (located in rp) polarizable entity with polarizability (i.e. due to radiative damping, see Sec. 1.6.4). Thus... 

The radiative damping matrix F is of greater importance for discussing radiative transitions and is closely related to the Fermi Golden Rule. It is defined in a manner that accounts for some type of interference effects (i.e., anticrossing-type interference effects) ... 

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