Effective photons in weakly absorptive dielectric media and the Beer–Lambert–Bouguer law

Abstract

We derive effective photon modes that facilitate an intuitive and convenient picture of photon dynamics in a structured Kramers-Kronig dielectric in the limit of weak absorption. Each mode is associated with a mode field distribution that includes the effects of both material and structural dispersion, and an effective line-width that determines the temporal decay rate of the photon. These results are then applied to obtain an expression for the Beer-Lambert-Bouguer law absorption coefficient for unidirectional propagation in structured media consisting of dispersive, weakly absorptive dielectric materials.

Quantum theory of light in a dispersive structured linear dielectric: a macroscopic Hamiltonian tutorial treatment

“…The method of Bhat and Sipe (10), mentioned above, also models correctly absorptive dielectric media in the nontransparent frequency range. See also (13) for a recent approach.…”

Hybrid Methodology for Retrieving Thermal Radiative Properties of Semi-Transparent Ceramics

“…The attenuation of the ray intensity along the trajectory is computed by using the Beer–Lambert–Bouguer law. A recent example of mathematical formulation of the Beer–Lambert–Bouguer law is proposed by Judge …”

“…A recent example of mathematical formulation of the Beer−Lambert−Bouguer law is proposed by Judge. 35 Emittance behaviors versus thickness and wavenumber are shown through a set of numerical simulations done for a refractive index n = 1.75 and extinction coefficients k going from 10 −6 to 10 −4 (Figure 7). For all the investigated pairs of optical indexes and wavenumbers, the EA model gives good fits of the thickness dependence of the normal spectral emittance of the virtual samples (R 2 > 0.99).…”