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By Francis C. Moon
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Example text
9) are functions of θ only and the third is a function of φ only, yet the terms equal each other’s negative. Again, both sets are constant. 11) Solutions of the separated differential equations and tabulated functions are in the Appendix. Solutions of the radial equation are spherical Bessel, Neumann, and Hankel functions, respectively, jν (σ), yν (σ), and hν (σ). A particularly important linear combination is Hankel functions of the second kind and integer order: h (σ) where “ ” represents any integer value of “ν”.
6) In the limit as the radius becomes many times larger than either radius a or wavelength λ, Eq. 7) =1 Energy and momentum are carried in by the plane wave; both are transferred to the scatterer. The input power is equal to the term proportional to Re(α + β ). The total power first extracted from the beam is defined as extinction power, and is always positive. 9) =1 Absorbed power, the negative of Eq. 7), does not reappear in the field but may be calculated by subtracting the scattered power from the extinction power.
Panofsky, M. Phillips, Classical Electricity and Magnetism, 2nd edition, Addison-Wesley (1961). A. Sommerfeld, Electrodynamics, Academic Press (1952). A. Stratton, Electromagnetic Theory, McGraw-Hill (1941). B. Westgard, Electrodynamics: A Concise Introduction, Springer-Verlag (1997). CHAPTER 2 Selected Boundary Value Problems The analyses in this chapter characterize the radiation properties of passive, linear systems and provide a benchmark for later comparison with the regenerative absorption and emission processes of Chapters 5 and 6.