Wave optics

Abstract

The quest to understand the nature of light nature of light is centuries old, and today there can be at least three answers to the single question of what light is depending on the experiment used to investigate light’s nature: (i) light consists of rays that propagate, e.g., rectilinear in homogeneous media, (ii) light is an electromagnetic wave, and (iii) light consists of small portions of energy, so-called photons. The first property will be treated in Chap. 2 about geometrical optics, which can be interpreted as a special case of wave optics for very small wavelengths. On the other hand, the interpretation as photons is unexplainable with wave optics and, above all, contradictory to wave optics. Only the theory of quantum mechanics and quantum field theory can simultaneously explain light as photons and electromagnetic waves. The field of optics treating this subject is generally called quantum optics. In this chapter about wave optics wave optics the electromagnetic property of light light electromagnetic property is treated and the basic equations describing all relevant electromagnetic phenomena are Maxwell’s equations. Starting with the Maxwell equations, the wave equation and the Helmholtz equation will be derived. Here, we will try to make a tradeoff between theoretical exactness and a practical approach. For an exact analysis see, e.g., [3.1]. After this, some basic properties of light waves such as polarization, interference, and diffraction will be described. The propagation of coherent scalar waves is especially important in optics. Therefore, the section about diffraction will treat several propagation methods such as the method of the angular spectrum of plane waves, which can be easily implemented on a computer, or the well-known diffraction integrals of Fresnel-Kirchhoff as well as Fresnel and Fraunhofer. In modern physics and engineering, lasers are very important, and therefore the propagation of a coherent laser beam is of special interest. A good approximation for a laser beam is a Hermite-Gaussian mode, and the propagation of a fundamental Gaussian beam can be performed very easily if some approximations of paraxial optics are valid. The formulae for this are treated in the last section of this chapter.