Thus F 1 is the coordinate frame of body 1. Appendix A contains a glossary of symbols that may be helpful in finding where each symbol is first defined. However, this drawback is more than compensated by the fact that the notation is less cluttered. This may make it more difficult to jump into the middle of a derivation and understand what everything means. Thus it may be necessary to read the text to determent the frame in which each vector is expressed. One feature of the Hughes system is that the superscript representing the frame is dropped. Local polarizability of the Nth order ( N=1, 2, …) ω Nth-order nonlocal nonlinear polarizability ( n=2, 3, …) χ ¯ ( N ) Linear polarizability defined with respect to Maxwell field χ b Linear polarizability defined with respect to the transverse component of Maxwell field χ B 1 Running indices for Cartesian coordinates ρ M Polarization (dipole density) operator q = ω / cĬoefficient matrix to determine F μ ν ε 0Īngle between M ν 0 and light polarization direction ξ, η, ζ Number density, charge, mass, resonant frequency, and damping parameter, respectively, of Lorentz oscillator P ˆ ( r ) Transition dipole moment for | v 〉 ← | 0 〉 N 0, Q, M, ω 0, γ Interaction Hamiltonian between light and matter M ν 0
Matter Hamiltonian for the scheme (B) H ccĬoulomb interaction among induced charge densities H int Matter Hamiltonian for the scheme (A) H B Reciprocal lattice vector G ( r, r ′, ω )
Oscillator strength of transition | v 〉 ← | 0 〉 F μ νĮxpansion coefficient of induced polarization g Transverse component of Maxwell field E νĮnergy eigenvalue of matter, with ν=0 for ground state E ν0Įxcitation energy of transition | v 〉 ← | 0 〉 f ν 0 Mutually orthogonal unit vectors perpendicular to k+ g E Radiative interaction between induced polarizations Dĭisplacement field
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