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The absorption of light is an important phenomenon which has many applications in all the natural sciences. One can say that all the chemical elements, molecules, complex substances, and even galaxies, have their own “fingerprint” in the light absorption spectrum, as a consequence of the allowed transitions between all electronic and vibronic levels. The UV-Visible (UV-Vis) light (200-800 nm) has an energy comparable to that typical of the transitions between the electrons in the outer shells or in molecular orbitals. Each atom has a fixed number of atomic levels, and therefore those spectra are composed of narrow lines, corresponding to the transitions between these levels. When molecules and macromolecules are considered, the absorption spectrum is no longer characterised by thin lines but by wide absorption bands. This is due to the fact that the electronic levels are split in many vibrational and rotational sub-levels, which increase in number with the increasing complexity of the molecules. IR spectroscopy is often used to investigate these lower energy modes, but for very complex biological molecules not even this technique can resolve each line precisely because the energy split between the various levels is too small. One possible way to obtain higher resolution spectra is to lower the sample temperature, in order to suppress many of the vibrational and rotational modes. For biological molecules, though, lowering the temperature can be a problem if one wants to study, for example, the activity of enzimes, which only work at physiological temperatures. One of the advantages of absorption spectroscopy (IR and UV-Vis) is to be a non-disruptive technique, also for “delicate” molecules like polymers and biomolecules. In the process of light absorption by molecules, once a photon with the right energy is absorbed, the molecule goes into an excited state at higher energy [Born and Wolf 1999, Dunning & Hulet 1996]. Eventually, it spontaneously returns to the ground state, but it can relax following several mechanisms. When excited, the molecule reaches, in general, one of the sub-levels of a higher electronic state. The first process is then, generally, a relaxation to the lower energy state of that electronic level (schematised in figure 1). This process is usually very fast (in the femtosecond scale) and not radiative. From this level, there are several pathways to dissipate the energy: a radiative transition from the lower level of the excited state to the ground state (fluorescence), accompanied by the emission of a photon at lower energy than the absorbed one; a flip of the electronic spin, which leads to a transition between singlet and triplet state (intersystem crossing), often associated with another

Nonlinear Absorption of Light in Materials with Long-lived Excited States