Reflection and Transmission at an Interface

A very important case of the plane-wave propagation is the reflection at a surface. We consider a plane-wave traveling from a non-dissipative medium with a real refractive index n to second medium with a general complex refractive index n. The incident wavevector is  

Without loss of generality it is possible to consider only two t3 es of incident plane-waves with linear polarization i) s-polarized i.e. with a real vector Ef perpendicular (parallel] to the plane of incidence (to the interface plane] ii] p-polarized with Ef parallel 

Recalling the boundary conditions [1] for an interlace (characterized by a surface normal n and no surface current or charges)  

Here the fields E and E are now complex as they can have a phase shift with respect the incident field. The wavevector describes a reflected plane-wave propagating in the same non-dissipative medium as the incident field and thus  

The boundary condition for the electric field at the plane z = 0 (see Eq. (1.52)) implies  

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Fig. 3. Reflection and transmission at an interface at which there is a thin layer of (partially) transparent material, referred to as medium 2.

Basic Theory for Reflection and Transmission at an Interface and the Basic Ellipsometry Equation... 

Fig. 35-4 (a) A tunneling ray in a graded medium is partially reflected at the turning-point caustic and partially transmitted at the radiation caustic. The shading denotes power flow within the ray tubes and the hatching indicates the region in which the fields are evanescent, (b) Partial reflection and transmission at an interface between graded and uniform media. 

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