Free photon

The total number of recoU-free photons arriving at the detector per time unit is then obtained by integration over energy... 

There are situations in which a definite wave function cannot be ascribed to a photon and hence cannot quantum-mechanically be described completely. One example is a photon that has previously been scattered by an electron. A wave function exists only for the combined electron-photon system whose expansion in terms of the free photon wave functions contains the electron wave functions. The simplest case is where the photon has a definite momentum, i.e. there exists a wave function, but the polarization state cannot be specified definitely, since the coefficients depend on parameters characterizing the other system. Such a photon state is referred to as a state of partial polarization. It can be described in terms of a density matrix... 

Energy-transfer processes in which free photons exist as intermediates are sometimes referred to as trivial transfer mechanism. This term is misleading in the sense that such processes (e.g., in combination with internal reflection) can cause very complex and interesting phenomena [61, 65-67]. Radiationless energy-transfer processes have been studied extensively since the pioneering work of Forster [68, 69] and Dexter [70] (see, e.g., [40, 67, 71-73]). Here, we concentrate on the description of one-photon events, specifically with respect to radiationless energy-transfer processes. 

The individual components, the electronic Hamiltonian the free photon Hamiltonian Hy and the electron-photon coupling Hamiltonianare given by [37]... 

The second two terms of the sum (711) can be eliminated using a combination of the free-photon minimal prescription and the quantum hypothesis... 

First, we envisage the weak exciton-photon coupling (which allows an intuitive description of the phonon effects on the nature of the secondary emissions). Therefore we write the hamiltonian of the total system as sums of free photons (Hy), free excitons (He), and free phonons (Hp), with the appropriate interactions Hey (Section I) and Hep (see Sections II, A, B, C.), including intramolecular vibrations too. 

However, in real crystals we observe transitions between free photons (the incident and the emerging photons, and not the photons trapped in polariton states), so that we cannot consider the crystal as an infinite 3D system, and there arises a dimensionality problem (with one-to-one correspondence between photons and excitons). Thus, the resolvent G(z) has to refer to an excitonic finite system coupled to a continuum of photons.78 As Tep does not operate on photons, we find for y the following exact relation ... 

This split-off discrete state rejoins, for cK co0, the exciton energy ha>0 it behaves qualitatively in the same way as the lower branch of the 3D polariton.33 35 For this reason we call it the 2D polariton. It is the projection of the exciton K> on this 2D polariton (radiatively stable) that constitutes (1) the finite limit value of the curves AK t) for t- oo (Fig. 3.8), and (2) the weight of the discrete peak in the spectrum PK((o) (Fig. 3.9). The transition, in the 2D polariton branch, between the photon and the pure exciton characters occurs around the value K0 = co0/c in an area of width AK = r0/c (with ro = 15cm 1). Thus, the 2D polariton may be considered as a photon mode trapped in the 2D lattice, where it acquires its own dispersion.115,116,126 Therefore, the 2D polaritons cannot be excited by free photons, but they may be coupled to evanescent waves, by ATR for example.115,116... 

This leads to the consequence that the momentum of a free photon, kph, propagating in a dielectric medium... 

Fig. 1. Dispersion relation of (a) free photon in a dielectric, (b) free photon propagating in a coupling prism, and dispersion relations of surface plasmons at the interface between the metal and the dielectric before (PI) and after (P2) the deposition of a thin dielectric layer.

First, there is need for one free photon" so that we have to produce a transitions between 3 + 7) and 3 — 7). 

Note that the ground state energy pertains to the many-electron sector. Free photons and positrons are not present in the ground state considered. 

An additional approximation can be obtained if one uses the decomposition of the electron-electron interaction mediated by the free photon propagator D , into a longitudinal and a transverse part (according to Eq. (A.IO)) to introduce the corresponding decomposition for and... 

The form of the free photon propagator depends on the choice of gauge, that is the parameter 1 in the Lagrangian (2.1). In Landau gauge, corresponding to the choice A = oo, one has... 

While the other two basic elements of perturbation theory, the free photon propagator (A.9) and the simple vertex, remain unchanged, it seems worth pointing out that the full photon propagator... 

Maxwell s equations (1.9) can be formally integrated with the aid of the free-photon propagator According to the total current introduced above, the resulting total radiation held may be decomposed as... 

As discussed in Section 2 the form of the free photon propagator D vi ) depends on the choice of gauge. In Sections 2-4 Feynman gauge (A = 1) is used, for which D y is explicitly given by... 

Using the polarization tensors (261),(262), the free photon propagator (203) and the longitudinal and transverse polarization functions the Dyson... 

Estimate the fluorescence detection rate (number of detected fluorescence photons/s) on the Na transition 5s -> 3p, obtained in the Doppler-free free-photon experiment of Fig. 2.32, when a single-mode dye laser is tuned to v/2 of the transi-... 

The individual components, the electronic Hamiltonian the free photon Hamiltonian... 

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