Optical Electromagnetics I

Abstract

In this chapter, the optical spectrum is defined and subdivided into many sub-bands, which are traditionally determined by transparency in various media. Propagation of the electromagnetic field in vacuum, as based on Maxwell’s equations, and basic notions of geometrical and physical optics, are covered. The theoretical and conceptual foundation of the remaining chapters is established in this chapter and the next. Optical electromagnetic propagation is generally and often accurately described by classical geometrical optics or ray optics. When diffraction or wave interference is of concern, then the more complete field of physical optics is used. Geometrical optics requires precise knowledge of the spatial and spectral dependence of the index of refraction. This requires electrodynamics, which is most appropriately described by quantum optics. These topics are covered in the first five chapters. The definitions of the optical spectrum and the various models for describing propagation are introduced in the following. The optical electromagnetic field covers the range of frequencies from microwaves to the ultraviolet (UV) or wavelengths from 10 cm to 100 nm. This is a very liberal definition covering six orders of magnitude, yet the description of propagation is very similar over this entire band, and distinct from radio-wave propagation and x-ray propagation. A listing of the nomenclature for the different spectral bands within the range of optical wavelengths is given in Table 1.1. Other commonly used units of spectral measure such as wave number, frequency, and energy are also listed in the table. These various quantities are related to wavelength by the following formulas: where c is the speed of light (c = 2.99792458 × 108 m/sec), λ is wavelength, f is frequency in hertz, E is energy, h is Planck’s constant (h = 6.6260755(40) × 10−34 J sec), and ν is frequency in wave numbers (the number of wavelengths per centimeter). Although wavelength is commonly used by applied scientists and engineers, frequency is the most appropriate unit for the theoretical description of light–matter interactions. Because of the importance of spectroscopy in the discussion of optical propagation, the spectroscopic unit of wave number will be consistently used.