Light-matter interactions


One of the most fundamental light-matter interactions is the absorption of a photon that causes an electron to move up from its ground state to an excited state. The excited state could be virtual or a quantum level in a molecule depending on the energy of the photon and the difference between the energy levels in the molecule. At a microscopic scale, absorption can be described as the polarizability, P, of the media in response to the optical field, E, via the electrical susceptibility, χ . 

refers to the first-order susceptibility, which is in response to the optical field where just one photon is absorbed. Multiphoton absorption, where more than one photon can be absorbed by the molecule at once, can also be included in this equation. 

The different optical fields could be of the same or different wavelengths depending on the source. The electric susceptibility tensor encodes the material properties such as the molecular and vibrational energy levels, complex-valued refractive index, birefringence, and microscale structures.  

At a macroscale, absorption manifests as attenuation to the intensity of light, dictated by the absorption coefficient, . For a beam of light travelling through a material of thickness z, Beer-Lambert's law dictates the intensity, I(z), at the other side. 

The absorption coefficient depends on the wavelength of light and the complex-valued refractive index at the incident wavelength. 


Anything that causes a change to the trajectory of light can be called scattering. Scattering is responsible for the twinkling of stars, the turbidity of milk, and the color of rainbows. Conventionally, reflection and refractions fall under this category. Scattering can either be elastic or inelastic. In elastic scattering, the excitation and emission wavelengths are the same. Typically, scattering is combined with the phenomenon for absorption. For instance, Beer-Lambert's law can be modified to include a scattering coefficient, µs.

For smaller objects on the scale of 0.1-100 µm, depending on the size and shape of the particle, scattering can be described as Rayleigh, Mie, or as geometric scattering. Rayleigh scattering occurs when the particle size is smaller or the same size as the wavelength of light and is homogenous in all directions. Mie scattering describes the scattering when the particle size is 1-10 times the wavelength. For Mie particles, typically over 90% of the light is forward scattered and 1-5% is back-scattered. Geometric scattering is described using Snell's law where the particle sizes are considerably larger compared to the wavelength. 


When absorbing a photon, an electron in a molecule becomes "excited" into a higher energy level. This higher level is unstable, so eventually the electron will relax down to its ground state and can release that energy as a photon in a process called fluorescence. While the electron is in the excited state, a very small (generally nanosecond-scale) amount of time passes and a small amount of energy can dissipate in vibrational relaxation. This causes the energy of the emitted photon to be somewhat less than the originally absorbed energy. This results in the emitted photon having a longer wavelength than the absorbed photon. Additionally, the lag between the excitation and emission events is the fluorescence lifetime, which has the temporal profile of exponential decay. Fluorophores have unique absorption and emission spectra and fluorescence lifetimes that are generally dependent on their chemistry, but  can also be altered by their environment.