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The propagation of an electromagnetic wave through an assembly of particles embedded within a homogeneous matrix is known to depend, to a large extent, both on the distribution and on the specific features of the particles themselves. The simplest case is that of a plane wave that impinges on a particle. As a result of the field-particle interaction, the incident wave undergoes , i.e., a detector along the path of the wave records a smaller intensity than would be recorded in the absence of the particle. Extinction itself, however, is the result of two concurrent processes: the particle, on one hand, and, on the other hand, the impinging radiation. The absorption process implies the transformation of the electromagnetic energy into some other form, in general heat. This can be accounted for by attributing to the particle a complex index of refraction whose choice falls into the realm of the solid state physics and will not be further discussed here. In turn, the scattering process can be roughly described by stating that the incident field excites the particle to emit a wave that at a large distance looks like a more or less spherical outgoing wave superposed to the original incident field. The whole process is uniquely determined by the boundary conditions that the components of the field must satisfy across the surface of the particle and at infinity. The form of the equations that stem from the boundary conditions, however, may turn out to be unmanageably complicated depending on the shape of the particle, so it is not surprising that, until recently, the scattering has been exactly calculated only for particles of simple shape.

In this chapter, we study the propagation of electromagnetic waves through a nonhomogeneous medium composed of a dispersion of nonspherical particles within an otherwise homogeneous isotropic matrix. Our purpose is to relate the scattering features of the individual particles to the macroscopic optical properties of the medium as a whole. In particular we will consider how the propagation depends on the polarization of the field and derive a number of relations and develop a notation that will prove useful later. All the relations we will deal with can be established in general terms under conditions that are met by several media of interest, such as atmospheric aerosols and the interstellar medium.

Besides scattering and absorption, that occur as a result of the interaction of the radiation field with particles, the interaction also yields mechanical and thermal effects that may be important in determining the behavior of the particles. This Chapter is just devoted to a discussion of these effects.

The theory in Chaps. 2 and 3 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 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.

In Chap. 4 we dealt with the relations between the transition matrix of individual particles and the macroscopic optical properties of a dispersion of them. Since the knowledge of the transition matrix of the particles concerned has turned out to be of paramount importance for the interpretation of the observational data, this chapter is devoted to the description of the procedure for calculating the transition matrix of single and aggregated spheres. Limiting our effort to such kinds of scatterers is less restrictive than one may think because, as we outlined in Sect. 1.1, the parameters that individuate the morphology of an aggregate can be chosen so as to fit the properties of a large class of actual particles.

In this chapter, we study the scattering of electromagnetic waves from particles near to or deposited on the plane surface that separates two homogeneous media of different optical properties. The plane surface will be termed , whereas we will call the one in which the particles and the detecting instrumentation are located. The medium that fills the accessible half-space is assumed to be nonabsorptive and to have, therefore, a refractive index.

The theory developed so far is suitable to investigate the optical properties both of single particles and of dispersions of particles that are of interest in several fields of physics. With the proviso that careful tests are necessary to verify the adequacy of the model in the sense explained in Sect. 1.1, aggregates of spheres may be suitable to model the nonspherical particles of atmospheric aerosols and the ice crystals that occur in the high atmosphere, as well as the cosmic dust grains that are of interest in astrophysics. In turn, spheres containing one or more spherical inclusions may be used to approximate the scattering properties of biological cells or of water droplets containing pollutants, but also to approximate the properties of the porous and fluffy particles that occur in the cosmic dust. Therefore we felt it convenient to devote the present and the next chapter to discussing applications of the theory developed so far with the purpose of highlighting the scattering features of the model particles, either in free space or in the presence of a plane surface. While the applications we present in this chapter can be easily specialized to atmospheric physics or to astrophysics, Chaps. 9 and 10 are specifically addressed to the study of the atmospheric ice crystals and of the cosmic dust, respectively.

The detection and characterization by nondestructive methods of particles deposited on a plane substrate is a problem that is frequently met in several fields of physics. For instance, particles are often studied after deposition on a suitable substrate. Of course, the effect of the substrate needs to be discriminated. This chapter is devoted to the study of the results that can be obtained from calculations of the scattering pattern of model particles deposited on or in the vicinity of a plane surface. Our purpose is not so much interpreting the spectra from actual particles but to point out for the interested reader the kind of information that can be gained by such calculations.

The aggregates (both external and internal) that were considered in Chap. 6 were not meant to simulate specific kinds of particles, but rather to illustrate the capabilities of the cluster model in association with the transition matrix approach in describing the optical properties of some system of interest. In the present chapter, on the contrary, we describe a specific application to the atmospheric ice crystals. The study of their scattering properties is an important topic in view of the role that they play in the meteorological phenomena and in the thermal budget of Earth. In particular, two problems are currently among the most studied ones: the contribution of the atmospheric ice crystals to the greenhouse effect, and the possibility of discriminating their shape by means of polarimetric radar devices.

The importance of the cosmic dust forming the interstellar medium (ISM) has long been recognized in astronomy. The interaction of the cosmic dust grains with the radiation field of the stars, beyond yielding extinction and polarization of the starlight by linear dichroism, also yields mechanical interactions such as the radiation pressure and the radiation torque that, together with the gravitational interactions, determine the dynamics of the grains themselves. According to Chaps. 4 and 7, all these phenomena, both optical and mechanical, can be traced back to the transition matrix of the dust grains. Moreover, the technique of Sect. 5.5 is appropriate to investigate also the state of polarization of the electromagnetic radiation that penetrates into the cavities contained in the interstellar dust grains. Therefore, a great deal of information could be gained by applying to the ISM the methods and procedures that have been expounded in the preceding chapters. Accordingly, this chapter is devoted to the discussion of some astrophysical problems which we deal with through the theory of electromagnetic scattering.