## Scattering An Overview

Why is light scattered? No single answer will satisfy everyone, yet because scattering by particles is amenable to treatment mostly by classical electromagnetic theory, our answer lies within this theory.

Although palpable matter may appear continuous and often is electrically neutral, it is composed of discrete electric charges. Light is an oscillating electromagnetic field, which can excite these charges to oscillate. Oscillating charges radiate electromagnetic waves, a fundamental property of such charges with its origins in the finite speed of light. These radiated electromagnetic waves are scattered waves, excited by a source external to the scatterer. Incident waves from the source excite secondary waves from the scatterer, and the superposition of all these waves is what is observed. The secondary waves are said to be elastically scattered if their frequency is that of the source (coherently scattered also is used).

Scientific knowledge grows like the accumulation of bric-a-brac in a vast and disordered closet in a house kept by a sloven. Few are the attempts at ridding the closet of rusty or broken or obsolete gear, at throwing out redundant equipment, at putting things in order. For example, spurious distinctions still are made between reflection, refraction, scattering, interference, and diffraction despite centuries of accumulated knowledge about the nature of light and matter.

Why do we think of specular (mirror-like) reflection as occurring at surfaces rather than because of them whereas we usually do not think of scattering by particles in this way? One reason is that we can see and touch the surfaces of mirrors and ponds. Another reason is the dead hand of traditional approaches to the laws of specular reflection and refraction.

The empirical approach arrives at these laws as purely geometrical statements about what is observed, and a discreet silence is maintained about underlying causes (always a safe course). The second approach is by way of continuum electromagnetic theory: reflected and refracted waves satisfy the partial differential equations of the electromagnetic field (the Maxwell equations). Perhaps because this approach, which yields the amplitudes and phases

Fundamentals of Atmospheric Radiation: An Introduction with 400 Problems. Craig F. Bohren and Eugene E. Clothiaux Copyright © 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-40503-8

of waves, entails imposing conditions at boundaries, reflected and refracted waves are mistakenly thought to originate from boundaries rather than from all the matter they enclose. This second approach comes to grips with the nature of light but not of matter, which is treated as continuous. The third approach is to recognize explicitly that reflection and refraction are consequences of scattering of waves by discrete matter. Although this scattering approach was developed by Paul Ewald and Carl Wilhelm Oseen early in the last century, it has diffused with glacial slowness. When the optically smooth interface between optically homogeneous media is illuminated, the reflected and refracted waves are superpositions of vast numbers of secondary waves excited by the incident wave. Moreover, every molecule, not just those at or near the interface, contributes to the total. Thus reflected and refracted light is, at heart, an interference pattern of light scattered by discrete molecules (see Sec. 7.2.1 for more about this). The fourth approach is to recognize the discreteness of both matter and radiation fields. This is the method of quantum electrodynamics, presumably the most rigorous but, alas, nearly impossible to apply except for very simple systems (e.g., the hydrogen atom).

No optics textbook would be complete without sections on interference and diffraction, a distinction without a difference: there is no diffraction without interference. Moreover, diffraction is encumbered with many meanings: a synonym for scattering; small deviations from rectilinear propagation; wave motion in the presence of an obstacle; scattering by a flat obstacle; any departure from geometrical (ray) optics; scattering near the forward direction; and scattering by a periodic array. A term with so many meanings has no meaning. Even the etymology of diffraction is of little help, coming from a Latin root meaning to break, the origin of fraction, fracture, fractal, and fracas.

There is no fundamental difference between diffraction and scattering. Scattering by a sphere (see Sec. 3.5.1) is sometimes called diffraction by a sphere. For many years we have offered a million-dollar prize to anyone who can devise a detector that distinguishes between scattered and diffracted waves, accepting the one but rejecting the other. So far no one has collected, and the money continues to draw interest in a numbered Swiss bank account.

The only meaningful distinction is that between approximate theories. What are called diffraction theories often obtain answers at the expense of obscuring if not completely distorting the physics of the interaction of light with matter. For example, an illuminated slit in an opaque screen may be the mathematical source but it is not the physical source of a so-called diffraction pattern. Only matter in the screen can give rise to secondary waves that superpose to yield the observed pattern. Yet generations of students have been taught that empty space is the source of the radiation from a slit. To befuddle them even more, they also have been taught that two slits give an interference pattern whereas one slit gives a diffraction pattern. But every pattern of scattered light called a diffraction pattern is a consequence of interference. And every theory bearing the label diffraction is a wave theory because only such theories can account for interference.

A variation on the bogus notion that empty space is the source of electromagnetic waves is the oft-repeated mantra that a changing electric field "produces" a magnetic field, and a changing magnetic field "produces" an electric field. Not true. Electric fields are produced by charges, magnetic fields by charges in motion (currents). There are always material sources of electromagnetic fields; they do not arise out of empty space.

If we can construct a mathematical theory (called for no compelling reason diffraction theory) that enables us to avoid having to consider the nature of matter, all to the good. But this theory and its quantitative successes should not blind us to the fact that we are pretending. Sometimes the pretense cannot be maintained, and when this happens a finger is mistakenly pointed at "anomalies", whereas what is truly anomalous is that a theory so devoid of physical content could ever give adequate results.

A distinction must be made between a physical process and the superficially different theories used to describe it. There is no fundamental difference between specular reflection and refraction by films, diffraction by edges or slits, and scattering by particles. All are consequences of light exciting matter to radiate. The only difference is in how this matter is arranged in space and the approximate theories sufficient for a quantitative description of the scattered light. Different terms for the same physical process are incrustations deposited during the evolution of our understanding of light and its interaction with matter.

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