J.R. Sambles et al. Let us examine in detail an important limit of Snell's law. Suppose that the radiation is incident from a high index medium, n,=VE, on to a low index medium n2=VE2,(where E1, E2 are the relative permittivities) with n2 <n,. Then Snell's law, the conservation of in-surface-plane momentum condition, gives medium 2 sinO2=√e1sin0 Since the greatest in-surface-plane component available in medium 2 is when 02=90, there is a limiting angle Incidence Be, given by Figure 1. Representation of p-polarized electromagnetic 02=√a2/√a (2) radiation incident upon a planar interface between two media at beyond which, for radiation incident from medium an angle of incidenceθ 1, there can be no propagating wave in medium 2. This limiting angle is called the critical angle. Radiation linearly polarized radiation may be readily represented incident beyond the critical angle has more momentum by a sum of the above two cases along the surface plane than can be supported by Now consider that the second medium is a medium 2. For such radiation incident from medium I non-magnetic material, that is at the frequency of the the oscillating E field will cause the charges in medium incident radiation the relative permeability is unity. Then 1, including those at the 1-2 interface, to oscillate. Thus as far as the B part of the electromagnetic oscillation is even though the radiation is now totally reflected at the concerned there is no discontinuity at the interface. In interface there are oscillating charges here which have this case, which represents the majority of materials, it associated radiation fields penetrating into medium 2 govern the behaviour of the radiation on encountering they are spatially decaying fields (evanescent) which the interface. For simplicity we shall throughout this article ignore optical activity, that is the property (the radiation, decaying in amplitude in medium 2 in a chirality)of a material which allows it to rotate the plane direction normal to the interface. At the critical angle the propagating along an axis of symmetry in the syste s decay length is infinte but this falls rapidly to the order of polarization of an incident photon even if it of the wavelength of light as the angle of incidence is Photons, with momentum hk. when in a medium of further increased. This evanescent field for radiation refractive index n,, are regarded as having momentum incident beyond the critical angle is useful for coupling (strictly pseudomomentum)hkn,=hk ,(where k= 2x/a). radiation to surface plasmons as we shall see later. If these arrive at a planar interface they may impart For the moment let us return to the boundary momentum in a direction normal to the interface and so conditions on the E and B field components of our there is no need to conserve the normal component of incident radiation. Since there is no boundary ortho- hoton momentum, hk, For the reflected signal, since gonal to Ex this component is conserved across the hIk,I is conserved, unless the photon frequency is boundary. However this is not the case for E,, the normal changed, and hkx is conserved for a smooth planar component of E. It is the normal component of D, D interface, then it follows that k,, of the reflected signal which is continuous (there is no free charge) and Ez is simply -kzl, the usual law of reflection at a planar is forced to change if a is changed since Dz interface E,EoEn =E2EoEx2. This discontinuity in E, results in On the other hand inside the second medium the polarization changes at the interface refractive index is n, so the radiation has a new From these simple considerations it is obvious that wavelength, A2= A/nz and a new wavevector k2=n2k. while s-polarized incident radiation will not normally In this medium the radiation propagates in a new cause the creation of charge at a planar interface, direction, conserving k, but allowing k, to change. Now p-polarized radiation will automatically create time k,1=k, sin 6, and k,2= k2 sin 6, where 0, is the angle dependent polarization charge at the interface of refraction. Since the tangential momentum component Suppose now we consider one of the two materials to is conserved, kxI=kx2 and n, sin 0,=n2 sin 0, which is be a metal. A metal may be regarded as a good conductor Snell,s law(resulting from the translational invariance of of electricity and heat and a reflector of radiation. This the system parallel to the interface) is a rather loose definition of a metal which relates to