Effective photon continuum

Figure 3.9. The Fourier transform of spectra of Fig. 3.8 Projection PK(a>) of the pure excitonic state on the eigenstates of the coupled system of an exciton K and the effective photon continuum in a 2D lattice, for various values of the wave vector K (KXd). The vertical peak represents a discrete state, whose weight is represented by a rectangle (a-d). For an exciton with K < K0, the continuum band (matter-contaminated photons) dominates the spectrum, with a quasi-lorentzian resonance (a,/). For K > K0, the discrete state dominates (d,e). In the intermediate region (b, c) the spectrum reflects the complicated behavior of its Fourier transform cf. Fig. 3.8. 

Figure 3.10. Scheme of the 2D polaritons and radiatively very unstable 2D excitons in the coupled system of an exciton K and an effective photon continuum (a) The two subsystems are not coupled, (b) The coupled system with a discrete state split off below the continuum, called the 2D polariton excitonic solutions exist only in a small segment of the Brillouin zone,... 

A similar analysis may be made for the 1D case.126 The interaction energies / (co) then show an enhancement of the order of k/a 103 relative to the parameters of the isolated point dipole, which is easily overwhelmed by nonradiative processes. Using the simple golden rule image, we may say that the transition dipole shows a huge increase from 0D to 3D systems, while the effective photon continuum density varies in an opposite (in fact complementary) way as follows, with radiative-power optimization for 2D systems ... 

The photon continuum allows the irreversible radiative decay, the states ip act as an effective continuum that enables irreversible decay into this manifold. The probabiUty of finding the molecule in the ip, manifold at time, complementary to (6.29), is given by... 

For other situations, especially when the material continuum is slowly varying and tiny changes in the laser frequencies in the one photon transition have absolutely no effect on the product ratios, our method allows for control, via the optical induction of resonances, in complete generality. 

The analysis of the classical dynamics shows a transition to chaotic motion leading to diffusion and ionization [6]. In the quantum case, interference effects lead to localization and the quantum distribution reaches a steady state that is exponentially localized (in the number of photons) around the initially excited state. As a consequence, ionization will take place only when the localization length is large enough to exceed the number of photons necessary to reach the continuum. 

The combined effect of the individual energy distribution functions which are of relevance for the photoionization process and for the detection of photoelectrons, can now be discussed. As a first step, the photoionization process alone, i.e., without any detection device, is discussed with the help of Fig. 2.9. The y-axis represents an energy scale with respect to the ground state, and different states of neon are plotted along the x-direction. For photons with sufficient energy hv and with a distribution function GB( ph, Eph), one reaches the continuum above the Is... 

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