Morphology and plasmonic properties of self-organized arrays of ...

18 CHAPTER 1. THEORYThe corresponding relations for the intensities, called reflectance and transmittance,are given byR p,s = |r p,s | 2T p,s = N bcosθ tN a cosθ i|t p,s | 2(1.24a)(1.24b)interfaceplane ofincidenceE PE SΔ45°11Ψr Sr PFigure 1.6: An interpretation of Ψ and ∆ upon reflection of a linearly polarized monochromaticbeam at an interface between two media. The incident beam has two equally larges and p components. The p component experiences a reflection coefficient r p , the s componenta reflection coefficient r s (from ref. [125]).As we will see later, other useful coefficients to describe the reflection of light froma surface are the so-called ellipsometric angles Ψ and ∆, defined through the polar form[126]ρ = tanΨ e i∆ = r pr s= |r p|e iδp|r s |e iδs = |r p||r s | ei(δp−δs) (1.25)FromthepreviousdefinitionitfollowsthattanΨistheratiobetweentheamplitudesofthep- and s-components of the reflected electric field; ∆ instead is a more subtle parameter.In (1.25), δ p and δ s are the differences of the phases of the s and p components between thereflected and incident electric fields; ∆ is the ulterior difference between these values. Asimple graphical interpretation of these parameters is reported in fig. 1.6, from ref. [125].1.1.3 Reflection from thin filmsA configuration of considerable importance for the optical measurements related to thiswork is the ambient/film/substrate system, composed of a thin film on top of a semiinfinitesubstrate.Thethicknessofthefilmiscomparablewiththewavelengths ofinterest,so that multiple reflections between the interfaces must be taken into account.