Rami Arieli: " The Laser Adventure" Chapter 2.3 page 1

We saw that the process of photon absorption by the atom is a process of raising the atom (electron) from a lower energy level into a higher energy level (excited state), by an amount of energy which is equivalent to the energy of the absorbed photon.

Our discussion involved a microscopic system in which one photon interacts with one atom.

In a macroscopic system, when electromagnetic radiation passes through matter, part of it is transmitted, and part is absorbed by the atoms.

The intensity (I) of the transmitted radiation through a thickness (x) of homogeneous material, is described by the experimental equation of exponential absorption (Lambert Law):

I=I0exp(-ax)
I0 = Intensity of incoming radiation.
a = Absorption coefficient of the material.
The thicker the material (bigger x), the lower the intensity after the material (the transmitted beam).

The transmission (T) of this material is described by the relation between the transmitted intensity (I) to the incident intensity (I0):

T=I/I0

From the last two equations we get the Transmission:

T = exp(-ax)

It is common to use units of centimeter (10-2 [m]), to measure the width of the material (x), so the units of the absorption coefficient (a) are:

[cm-1] = [1/cm].

Every material is transparent differently to different wavelengths, so the absorption coefficient (a) is a function of the wavelength: a(l). This fact is very important (as we shall see) to understand the interaction of electromagnetic radiation with matter, in the variety of applications of the laser.