Plane waves vacuum interface, reflection

Relations between the Plane-Wave Modes B. Total Reflection at a Vacuum Interface VII. Axisymmetric Wave Modes... 

Case 2 of a dissipative medium is now considered where x = 0 defines the vacuum interface in a frame (x,y, z). The orientation of the xy plane is chosen such as to coincide with the plane of wave propagation, and all field quantities are then independent on z as shown in Fig. 3. In the denser medium (region I) with the refractive index = n > 1 and defined by x < 0, an incident (7) EM wave is assumed to give rise to a reflected (r) EM wave. Here is the angle between the normal direction of the vacuum boundary and the wave normals of the incident and reflected waves. Vacuum region (II) is defined by x > 0 and has a refractive index of = 1. The wavenumber [35] and the phase (47) of the weakly damped EM waves then yield... 

The boundary conditions can also have a decisive influence on the type of representation. A first example is given by the transmitted wave at a vacuum boundary, as discussed in Section VI.B. Here the incident and reflected plane waves can be matched at the interface by a plane transmitted wave, but hardly by a transmitted beam of axisymmetric photon wavepackets. 

If an electromagnetic wave in a vacuum, is incident on a medium having a refractive index n and a plane interface, at an angle a to the normal, then the wave will be partly or wholly reflected at an angle a to ad on the opposite side of the normal, where a = a (Fig. 1). However, it is also possible that part of the light penetrates into the medium and while doing so is refracted towards the normal and at an angle to the normal. Thus the index of refraction... 

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