Radiometric and Photometric Quantities and Notions

Abstract

The energy conservation law for any electromagnetic field implies, that the time derivative$$ {{{\partial Q}} \left/ {{\partial t}} \right.} $$ of the field energy for optical radiation, which ranges from a wavelength as short as 1 nm to one as long as 1 mm, when propagating in a homogeneous, isotropic, and low-absorbing medium whose properties satisfy the material equations D = εE, B = μH, J = σE and whose elements are in a steady position or in slow motion, is [1.1]: 1.1$$ \frac{{dQ}}{{dt}} = - \frac{{d\Pi }}{{dt}} - \Lambda - \int\limits_{\mathbf{A}} {{\mathbf{S}} \bullet \begin{array}{*{20}{c}} {{\mathbf{r}}\begin{array}{*{20}{c}} {dA} \\ \end{array} } \\ \end{array} } $$ where Π is the work done for the travel time t; Λ is the total loss, caused by resistive dissipation of energy Q, if the medium is a conductor; S is the Poynting vector; r is the outward normal unit vector to any arbitrary boundary surface A situated far away from a source of the field; E and H are the electric and the magnetic vectors; D is the vector of electric displacement, B is the vector of magnetic induction; ε is the dielectric constant (permittivity), μ is the magnetic permeability, and σ is the specific conductivity of the medium. The integral in Eq. 1.1 identifies the flow of energy crossing the boundary surface A reached by the optical wave. Thus, when dealing with a transfer of energy of optical radiation in the absence of moving elements or conductors, the space-time derivative in Eq. 1.1 represents the flow of optical energy crossing such a boundary surface A per unit of time.