Multipole Expansions and Transition Matrix
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The theory in Chap. 2 yields a number of useful relations but gives no prescription for calculating the quantities of interest. In this chapter we use the theory of the multipole fields to establish equations that are suitable for actual calculations. In fact, by expanding both the incident and the scattered field in a series of spherical vector multipole fields, one is lead to introduce the transition matrix that proved to be one of the most fruitful concepts in the theory of scattering. Beyond encompassing all the information on the morphology and on the orientation of the scattering particle with respect to the incident field, the transition matrix has well-defined transformation properties under rotation of the coordinate frame. These properties will be shown to be the key tool for the description of the propagation of light through an assembly of nonspherical particles.
KeywordsTransition Matrix Electrostatic Field Scattered Field Polarizability Tensor Incident Field
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