Simple formula used to predict superluminal reflection on a multidielectric mirror.

Area of Science:

• Optics and Photonics
• Materials Science
• Electromagnetism

Background:

• Multidielectric mirrors are constructed from repeating patterns of multiple layers.
• Understanding the behavior of these mirrors in the limit of infinite layers is crucial for advanced optical applications.
• Weak absorption within mirror layers can influence their overall optical properties.

Purpose of the Study:

• To analyze the reflection coefficient of a multidielectric mirror as the number of layers approaches infinity.
• To investigate the impact of weak absorption on the mirror's spectral characteristics.
• To identify potential applications in experimental optics, particularly concerning superluminal reflection.

Main Methods:

• Mathematical analysis of the reflection coefficient (ρN) as N tends to infinity.
• Consideration of weak absorption within the repeating mirror patterns.
• Convergence analysis of the reflection coefficient function (ρN) with respect to pulsation (ω).

Main Results:

• The reflection coefficient (ρN) uniformly converges almost everywhere on the electromagnetic spectrum to an intuitive limit (ρ∞).
• The derived limit (ρ∞) provides a simplified and understandable expression for infinite layer mirrors.
• A significant difference in phase-shift was identified between two configurations of a quarter-wave stack.

Conclusions:

• The study provides a theoretical foundation for designing and understanding infinite multidielectric mirrors.
• The findings facilitate the conception of novel experiments, particularly in the realm of superluminal reflection.
• New spectral domains for investigating superluminal reflection in previously unexplored configurations are identified.