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Physics of the Electromagnetic Spectrum

Michael Vollmer

Department of Engineering, University of Applied Sciences Brandenburg, Brandenburg an der Havel, Germany

1 Introduction

From a physicist's point of view, electromagnetic (EM) radiation is used in three different ways in the food processing chain (besides the partially nontrivial use of light to advertise food products in super markets). First, food can be preserved by irradiation, second it may be heated, and third, its constituents may be characterized. In order to understand these quite differing uses, one must deal with the properties of electromagnetic radiation and respective possible descriptions as well as with its interaction with matter.

The most simple approach is to start with light which constitutes the visible part of electromagnetic radiation. With regard to food processing, light may, e.g. be focused onto food using appropriate mirrors, thus heating the food as in solar cookers. But what is light and how can light be described in physics terms? The first question is still a very difficult and rather a philosophic one, whereas the second can be readily answered.

Beginning at the onset of modern science in the seventeenth and eighteenth centuries, light has been described as either particle (e.g. Newton) or wave (e.g. Young). Both descriptions were based on interpretations of experiments. In modern language, light constitutes an example of the so-called wave-particle duality. Light may behave as wave in experiments which focus on wave phenomena (involving, e.g. interference), but light can also behave as particle in experiments which focus on respective particle properties (such as the photoelectric effect). As a consequence, the general description must be able to explain wave as well as particle properties of the entity which is called light. This may be condensed in the statement that light can be described in a complimentary way either as electromagnetic wave or as particles which are called photons.

While studying spectral properties of light, it became evident that there are similar entities with similar properties, but invisible to the human eye. In 1800, Herschel discovered infrared (IR) radiation beyond the red edge of a visible light spectrum which was able to heat thermometers, and soon after, ultraviolet (UV) radiation was discovered which blackened photographic papers beyond the blue edge of visible light spectrum. It was already known around 1900 that UV radiation could kill germs and bacteria. An obvious question is whether there are more kinds of radiation which behave similar to light and may hence be described also in a very similar way? The answer is yes, and the general feature of all similar types of electromagnetic radiation is that they may behave as waves as well as as particles. In the following, we will summarize the basic features of electromagnetic waves and the complimentary particle description.

2 Description of Electromagnetic Waves

Electromagnetic phenomena are those which involve electric and magnetic forces between charges and electric currents. In a more generalized physics description, the effect of forces is substituted by the effects of electric and magnetic fields. In a very abstract way, all possible electromagnetic effects may be described by a set of just four differential (or integral) equations, the so-called Maxwell equations (see any standard physics, theoretical physics, or optics textbook, e.g. Berkeley 1965; Etkina et al. 2019; Feynman et al. 1964; Guenther 1990; Halliday et al. 2014; Hecht 2016; Jackson 1975; Saleh and Teich 2019; Tipler and Mosca 2007), and two material equations which relate the fields in vacuum to those in matter. Already in 1865, it was shown that one possible solution of these equations for the electric and magnetic fields are wave equations, i.e. differential equations of the type (shown for the electric field E which depends on space coordinates x, y, z, and time t)

v is the speed of propagation, e0 = 8.8542?×?10-12 As?Vm-1, and µ0 = 1.2566?×?10-6 Vs?Am-1 are well-defined constants; e is the relative dielectric constant (permittivity) and µ is the relative permeability, both describing the electric or magnetic properties of matter. For isotropic materials, e and µ are just dimensionless numbers. The speed of propagation is largest for the case of vacuum with e = 1 and µ = 1, which defines the speed of light in vacuum c

The existence of respective wave phenomena was first proven in 1887 by Hertz.

2.1 Properties of Waves

The simplest periodic processes are oscillations. Consider, e.g. a mass attached to a spring which is set into motion. It oscillates back and forth in the vertical direction as a function of time with a given time interval for one complete oscillation (e.g. from the highest position via the lowest position to again the highest position). This time interval T is called period and is related to the frequency ? of the oscillation according to ? = 1/T.

Whereas oscillations are periodic processes as function of time alone, and the path in space is always the same, waves resemble disturbances which propagate in space. Most waves in physics are periodic processes in space and time. Think, e.g. of a stone which is thrown into a puddle or a lake with a flat surface of water. The stone initiates a deformation of the water surface with partially lower and partially higher water level. Denoting all regions with largest water level as peaks, the phenomenon can be described such that all water peaks propagate with circular geometry and a well-defined velocity in all directions outward. At given location, the water level rises and falls periodically which can be described by a transient period and the respective frequency ?. Besides, the distance between adjacent peaks is also a well-defined quantity. It resembles a spatial period called wavelength ?.

In surprisingly many cases, the geometric form of a snapshot of the elongation of a wave (here the difference of the water surface height with respect to the undisturbed water surface height) can be described by a so-called harmonic function (i.e. a sine or cosine function). Figure 1 depicts three snapshots of such a sine-like wave (think of elongation of water surface along an arbitrary horizontal direction x) recorded at three different times. Within one period T, the disturbance has propagated a distance ?, i.e. the speed of propagation is given by c = ?/T which can also be written as

Obviously, the general description of a wave should depend on the spatial and transient periods. For mathematical convenience, they are included in the so-called spatial frequency and transient angular frequency . Usually, one deals with waves in three dimensions; in this case, the spatial frequency becomes the wave vector which points into the direction of propagation of the wave.

Figure 1 Example of elongation f(x,t) of a harmonic wave along a spatial coordinate x at three different times.

In the water puddle example, the elongation of the water surface was perpendicular to the direction of propagation. Waves with this property are called transverse waves. Electromagnetic waves are transverse waves; in contrast, sound waves in gases are, e.g. longitudinal waves. The geometry of propagation also defines the type of waves. In the case of the water puddle wave (with two-dimensional water surface), the geometry was circular, so the water wave was a circular wave. A point light source in three-dimensional space, imagine, e.g. a distant star, constitutes an example of a spherical wave, as light can propagate in every direction with equal probability. Being very far away from such a point source (in a distance of many light years) means, however, that the radius of curvature is extremely large such that in practice, the wave front can be described as a plane (Figure 2). Whenever this is the case (optics has also other means to transfer a close-by point source into a plane wave), a wave is called a plane wave.

Most waves and therefore also electromagnetic waves are usually modeled as planar harmonic monochromatic waves (i.e. those having one well-defined frequency only). The reason behind is that once a problem is solved for such a plane harmonic monochromatic electromagnetic wave, it can easily be solved for any geometric form and any superposition of waves of different frequencies. The basis for the respective mathematical procedure of Fourier series and transforms is above the scope of this chapter. Whenever dealing with electromagnetic waves, we will therefore model the waves as plane harmonic waves (Figure 3). The electric field of such a wave is, e.g. given by

Each wave transports energy. A water wave close to the beach hitting someone can easily hurt. Similarly, being close to the sound waves of a loudspeaker can damage ears and intense direct exposure to sun light will cause sunburns. For electromagnetic waves, energy...