text: Consider a system of localized, non-interacting absorbing centers. Based on the semi-classical radiation absorption theory within the electric dipole approximation, the electric vector of the circularly polarized waves propagates along the +z direction. In this system,  is the angular frequency, and  = n – ik is the complex refractive index. As the light travels, the attenuation of the beam is expressed as
  where  is the intensity of light at position ,  is the absorption coefficient of the medium in the  direction, and  is the speed of light. Circular dichroism (CD) is then defined by the difference between left () and right () circularly polarized light, , following the sign convention of natural optical activity. In the presence of a static, uniform external magnetic field applied parallel to the direction of propagation of light, the Hamiltonian for the absorbing center takes the form  for  describing the system in the external magnetic field and  describing the applied electromagnetic radiation. The absorption coefficient for a transition between two eigenstates of ,  and , can be described using the electric dipole transition operator  as 
  The  term is a frequency-independent correction factor allowing for the effect of the medium on the light wave electric field, composed of the permittivity  and the real refractive index .