Optical properties of cylindrical nanowires

Chapter 1.General solution1.4.3 Cross sections and efficienciesIn stead of using the energy rates it is more convenient to take the normalizedforms of them: cross sections, or, better, efficiency factors. The former aresurfaces, defined asC abs = W absI 0, C sca = W scaI 0, C ext = W extI 0, (1.58)where I 0 =c8π |Ẽ0| 2 is the incident intensity. Dividing these optical crosssections by the geometrical cross section G, dimensionless efficiency factorsare found:Q abs = C absG , Q sca = C scaG , Q ext = C extG . (1.59)Note that equation (1.56) has a synonym in terms of efficiency factors:Q ext = Q sca + Q abs . (1.60)For a circular cylinder with radius R and length L the geometrical cross sectionequals 2RL. Note that the efficiency factors indeed are dimensionless.With the far field scattered electric field (1.51) and a similar expressionfor the scattered magnetic field now it is a matter of patience to derive:∫ 2πQ sca I = 1 (|T 11 (π − φ)| 2 + |T 12 (π − φ)| 2 ) dφπx 0{}= 2 ∞∑|b 0I | 2 + 2 (|b nI | 2 + |a nI | 2 ) , (1.61)xn=1Q ext I = 2 x Re{T 11(π = φ)}}= 2 ∞∑{bx Re 0I + 2 (b nI ) , (1.62)n=120∫ 2πQ sca II = 1 (|T 22 (π − φ)| 2 + |T 21 (π − φ)| 2 ) dφπx 0{}= 2 ∞∑|a 0II | 2 + 2 (|b nII | 2 + |a nII | 2 ) , (1.63)xn=1Q ext II = 2 x Re{T 22(π = φ)}}= 2 ∞∑{ax Re 0II + 2 (a nII ) , (1.64)n=1