Dielectric interfaces and mirrors in the amplitude and phase representation

Abstract

Reflection and refraction at an abrupt dielectric interface at normal incidence are evaluated using an amplitude and phase (amph) formalism. The optical properties of a stack with two quarter-wavelength layers are then calculated. The characteristics of a mirror constructed with quarter-wavelength layers are discussed using the amplitude and phase representation. Floquet nonlinear theorem is invoked to describe the multi-layered system. Results are consistent with Fresnel formulae and conventional matrix methods for stratified periodic media. However, the amph formalism offers several advantages: (i) it is capable of showing the field properties as it propagates though the stack, (ii) it gives a lucid physical insight because the variables involved have a clear physical meaning, and (iii) the mathematical description is simple.

Keywords:

• wave propagation
• stratified media
• wave invariants

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