Energy Density and Irradiance

From Maxwell s equations one can show that the energy density of electromagnetic radiation depends on the square of the electric and magnetic field strengths [4-6]. For radiation in a vacuum, the relationship is 

Equation (3.22) is written in cgs units, which are particularly cmivenient here because the electric and magnetic fields in a vacuum have the same magnitude  

Since the fields in a plane wave are by definition independent of position perpendicular to the propagation axis (y), the average denoted by the bar in Eq. (3.25) requires only averaging over a distance in the y direction. If this distance is much longer than X (or is an integer multiple of X), the average of cos (2 rvt - 2n y/X + 5) is 1/2, and Eq. (3.25) simplifies to 

If a beam of light in a vacuum strikes the surface of a refractive medium, part of the beam is reflected while another part enters the medium. We can use Eq. (3.28) to relate the irradiances of the incident and reflected light to the amplitudes of the corresponding flelds, because the fields on this side of the interface are in a vacuum. But we need a comparable expression that relates the transmitted irradiance to the amplitude of the field in the medium, and for this we must consider the effect of the field on the medium. 

As light passes through the medium, the electric field causes electrons in the material to move, setting up electric dipoles that generate an oscillating polarization field (P). In an isotropic, nonabsorbing and nonconducting medium P is proportional to E and can be written 

---

In this chapter we consider classical and quantum mechanical descriptions of electromagnetic radiation. We develop expressions for the energy density and irradiance of light passing through a homogeneous medium, and we discuss the Planck black-body radiation law and linear and circular polarization. Readers anxious to get on to the interactions of light with matter can skip ahead to Chap. 4 and return to the present chapter as the need arises. 

With the local-field correction factor, the relationships between the energy density and irradiance in the medium (p(v) and /(v)) and the amplitude of the local field (l <,c(o)l) become ... 

---