Bridging the microscopic and macroscopic theories for light reflected from disordered plane-parallel dielectric slabs

Area of Science:

• Condensed matter physics
• Wave propagation in random media

Background:

• Dielectric layers with random variations present complex wave reflection phenomena.
• Discrepancies exist between macroscopic (Maxwell) and microscopic (Boltzmann) theories for such systems.

Purpose of the Study:

• To compare the reflection coefficient from Maxwell equations with Boltzmann theory for random dielectric layers.
• To investigate averaging methods for reconciling these two theoretical frameworks.
• To enhance the accuracy of Boltzmann scattering coefficient calculations.

Main Methods:

• Derivation of reflection coefficient from Maxwell equations for randomly varying dielectric layers.
• Application of Boltzmann theory to the same system.
• Frequency and ensemble averaging techniques to compare theoretical results.
• Microscopic parameter analysis for Boltzmann scattering coefficient.

Main Results:

• The reflection coefficient is an oscillatory function of laser frequency for monochromatic fields.
• Suitable averaging enables a direct comparison between Maxwell and Boltzmann theories.
• Improved Boltzmann scattering calculations show better agreement with Maxwell data.

Conclusions:

• Maxwell and Boltzmann theories can be reconciled for random dielectric systems through appropriate averaging.
• The study provides a pathway to refine microscopic scattering theories using macroscopic wave equations.
• Enhanced Boltzmann theory offers a more accurate prediction of wave reflection in disordered media.