By Frederick Wooten (Auth.)
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Before proceeding with a simplification of Eq. 119), it is worth noting that the real dielectric function ε that appears in Maxwell's equations is a longitudinal dielectric function. 120) This is the reason for the relative simplicity of Eq. 113). It is clear from Eq. 120) that the dielectric function appearing in Maxwell's equations is a longitudinal dielectric function. Thus ε and the corresponding complex dielectric function έ will now be designated as eL and êL. 8 shows how one is led to the definition given by Eq.
Suppose we are concerned with the longitudinal response of the system to a longitudinal perturbation. We want to know eL(q, ω). A longitudinal perturbation causes a longitudinal induced current. We can pick out the longitudinal component of the induced current density by just taking the scalar product of J md (q, ω) with the unit vector q/q in the direction of propagation q. 126) where J];nd(q9co) is a scalar quantity. We can now make a vector out of «/îndiq»ω) by just multiplying it by the unit vector.
A band diagram for the noble metals is shown schematically in Fig. 16. The d bands lie several volts below the Fermi energy. Thus, only interband transitions of conduc tion electrons are possible at low energies, and an onset of interband 58 Chapter 3 Absorption and Dispersion transitions from the d bands to higher-lying conduction band states takes place in the visible or ultraviolet. 35) where ε / and ε2 are described by Eqs. 31) and ε ^ and s2h are described by Eqs. 15). Band structure effects are included by using an effective mass in these equations rather than using the free-electron mass.
Optical Properties of Solids by Frederick Wooten (Auth.)