Specular reflection and transmission of electromagnetic waves by disordered metasurfaces

Planar, disordered assemblies of small particles incorporated in layered media -- sometimes called ``disordered metasurfaces'' in the recent literature -- are becoming widespread in optics and photonics. Their ability to scatter light with exotic angular and spectral features in reflection and transmission, as well as their suitability to scalable fabrication techniques, makes them promising candidates for certain applications, ranging from thin-film photovoltaics to visual appearance design. This chapter introduces the basic concepts and theoretical models for the specular (a.k.a. coherent) reflectance and transmittance of electromagnetic waves by disordered metasurfaces. After describing the classical scattering formalism for discrete media, we establish known analytical expressions for the reflection and transmission coefficients of disordered particle monolayers on layered substrates. Two classical models, based on the independent scattering approximation (ISA) and the effective field approximation (EFA), are presented. Their accuracy is examined by comparing predictions with those obtained from rigorous full-wave computations using an in-house multiple-scattering code. This chapter may serve as a starting point to students and researchers who wish to dive into the topic and explore the potential of disordered metasurfaces for applications.