is the wavenumber, 
Figure 1.2 Bottom: Typical absorption spectrum registered as a function of wavelength. Top: Representative experimental absorption (continuous line) and emission (dashed line) spectra registered as a function of wavelength.
The wavenumber is usually reported in units of cm−1. Combining Eqs. (1.19) and (1.20), it is found that
(1.21)
Concluding this paragraph, it is worth mentioning that the absorption phenomenon is one of the basic processes of the radiation–matter interaction and it is extended in a wide range of energy of the electromagnetic spectrum. The underling physical process is related to the specific atomic or molecular species absorbing the energy from the electromagnetic wave [8, 9]. The frequency range of interest for this chapter includes the visible (Vis) radiation and goes from the near infrared (NIR) to the ultraviolet (UV). In particular, the visible range in vacuum extends in frequency from about 3.8⋅1014 to 7.5⋅1014 Hz, in wavelength from 800 to 400 nm, and in energy from 1.6 to 3.1 eV [1].
1.1.2 Emission: Fluorescence and Phosphorescence
The absorption of light at a given wavelength λ by a sample is physically associated to an energy transfer from the radiation electromagnetic field to the electrons of the matter constituting the sample. In this phenomenon, the electrons are typically promoted from one energy level (ground state) to another level of higher energy (excited state). In the process, the electron system is put out of thermal equilibrium; so, each electron spontaneously tends to return to its initial energy level, releasing the acquired energy. In an ideal experiment, a stationary state can be observed in which by continuously illuminating the sample with a radiation at λ, in a given spatial direction, another radiation is emitted by the sample isotropically in space with wavelength λ′ > λ. This phenomenon is known as photoluminescence and can sometimes be observed also by naked eye, illuminating a sample with high‐energy photons, typically in the UV part of the spectrum, and revealing an emission in the visible range (an example of this effect is observed in the luminescence emergency panels, emitting light when they are in the dark after being illuminated by electric lamps or sunlight). It is worth underlining that typically, as shown in Figure 1.2, the absorbed radiation wavelength (energy) and the emitted wavelength (energy) are related by
(1.22)
due to some internal processes subtracting energy to the electrons when they return to their ground state. The difference between the photon energy at which the absorption maximum amplitude occurs and the energy where the emission maximum amplitude occurs is called Stokes shift [2, 5].
In considering the phenomenology of the emission process, we can distinguish two kinds of phenomena. Both of them are related to the emission of light, but their time dependence is very different. In particular, one emission process lasts for a long time (more than μs) after the removal of exciting light (like in the luminescence emergency panels) and is called phosphorescence . The other rapidly (less than 0.1 μs) decreases in amplitude as the exciting light is turned off and is known as fluorescence . An experimental procedure to distinguish these processes consists in recording the emission amplitude at a given wavelength as a function of time after the excitation light is turned off. In Figure 1.3 is reported the result of a typical time‐resolved photoluminescence experiment. The excitation light impinges on the sample up to the time 1 ms, to let the system reach a stationary state, and the emission is recorded at a selected wavelength λ em. The emission intensity amplitude recorded is constant, in accordance to the stationary state. At the time t 0 = 1 ms, the excitation is rapidly removed by turning it off or by an opportune shutting system. The signal is then continuously recorded at t > 1 ms at λ em and it is found that its amplitude decreases. In the figure is reported a typical decay with single exponential law:
Figure 1.3 Typical decay curve as a function of time of the emission. For t < 1 ms, the exciting light is illuminating the sample, for t ≥ 1 ms it is turned off.
By this procedure, it is possible to record the characteristic time τ that defines the lifetime, or the decay time, of the photoluminescence, and obtain the time needed to reach a value of the emission amplitude 1/e of its stationary value in a given experiment [2, 10]. Values of τ up to ~10 ns are typical of fluorescence phenomena and larger lifetimes, up to 103 s, are characteristic of phosphorescence, enabling empirically to distinguish them [2, 5, 10]. In the following, a microscopic interpretation of the reported phenomena is given. It is worth mentioning that specific instrumentations are needed to carry out time‐resolved photoluminescence [2, 5].
1.2 Microscopic Point of View
The empirical observations of absorption and emission phenomena contain very important information on the electronic and molecular properties of matter. In this view, it is fundamental to understand what kind of knowledge can be obtained from such experiments. In this paragraph, the theoretical bases that enable to determine microscopic features about the electronic states from the macroscopic measurements will be deepened.
1.2.1 Einstein Coefficients
A simplified model of the atom constituted by two nondegenerate energy levels is assumed to evaluate the interaction with radiation. As reported in Figure 1.4, the lower energy level is E 1 and the higher energy level is E 2. This system interacts with the thermal equilibrium radiation field at temperature T.
According to Planck’s theory, the energy distribution of the radiation is given by [8, 11, 12]
