Propagation of an Electromagnetic Plane Wave

Infrared reflectance spectroscopy, like UV-visible reflectance spectroscopy, is based on the specular reflection of the incident light on the substrate surface. It is therefore relevant to give briefly, in this section, the basic equations describing the propagation of an electromagnetic plane wave in an absorbing medium and its reflection at the boundary which separates two contiguous phases of different optical properties. 

The instantaneous value of the oscillating electric field vector E, obtained as a solution of Maxwell s equations, may be represented at a position vector r of space and at time t by the following expression  

Electromagnetic waves travel through homogeneous, isotropic, nonabsorbing media with the phase velocity v, which is related to the index of refraction n hy n = c/v = where e is the optical dielectric constant 

If the medium is absorbing, the radiation propagates as an exponentially damped wave represented by the expression  

Since the refractive index and the dielectric constant are related by n = Ve, or = n, the dielectric constant e of an absorbing medium is also complex, i.e.  

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