In his Lectures on Physics, Richard Feynman asserts that “ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics”. Whether this prediction is borne out or not, it is impossible to deny the significance of Maxwell's achievement to the history, practice, and future of physics. That is why electrodynamics has a permanent place in the physics curriculum, along with classical mechanics, quantum mechanics, and statistical mechanics. Of these four, students often find electrodynamics the most challenging. One reason is surely the mathematical demands of vector calculus and partial differential equations. Another stumbling block is the non-algorithmic nature of electromagnetic problem-solving. There are many entry points to a typical electromagnetism problem, but it is rarely obvious which lead to a quick solution and which lead to frustrating complications. Finally, Freeman Dyson points to the “two-level” structure of the theory.1 A first layer of linear equations relates the electric and magnetic fields to their sources and to each other. A second layer of equations for force, energy, and stress are quadratic in the fields. Our senses and measurements probe the second-layer quantities, which are determined only indirectly by the fundamental first-layer quantities.

Introduction

Many contemporary technologies exploit the fact that electromagnetic waves can be guided along specified paths through space and transiently stored in low-loss enclosures. The special configurations of conductors and dielectrics used to do this are called waveguides and resonant cavities. In this chapter, we show that electromagnetic fields can be guided and stored because they adjust themselves to satisfy the required boundary (or matching) conditions at the surfaces (or internal interfaces) of a guide or cavity. The nature and characteristics of the waves are fixed by the geometry and topology of the guiding and storage structures. Besides the familiar transverse electromagnetic (TEM) waves, where E and B are both transverse to the direction of propagation, we will find transverse electric (TE) waves where only E is transverse and transverse magnetic (TM) waves where only B is transverse. By and large, our discussion focuses on the applications of waveguides and cavities to specific problems of physics. Textbooks of engineering electro magnetics discuss applications to communication and power transmission.

Guided waves were discovered in 1842 by the Swiss physicist Colladon, who reported that total internal reflection could be exploited to trap light inside the parabolic streams of water produced by drilling holes in a water-filled vessel. Fifty-five years later, Hertz sought and observed meter-scale waves guided by a conducting wire.

Introduction

An incident electromagnetic wave is said to scatter or diffract from a sample of matter when the field produced by the sample cannot be described using Fresnel's theory of reflection and refraction from a flat interface (Section 17.3). In this chapter, we focus on the class of problems where this occurs because the wavelength of the incident monochromatic field is not small compared to the curvature of a material boundary. From a Fresnel point of view, the total field in these cases results from the interference of many different “reflected” and “refracted” waves propagating in different directions. We will encounter other points of view as we proceed. Figure 21.1 shows some typical geometries of interest. There is no universal naming practice, but many authors say that “scattering” occurs from objects with smooth boundaries and “diffraction” occurs from objects with sharp edges.

The physics that produces scattering and diffraction is identical to the physics that produces the Fresnel equations. An incident electromagnetic wave sets the charged particles of a medium into motion. Each accelerated charge produces a retarded field which is felt by, and thus affects the motion of, every other charge in the medium. The motion of every charge and the field it produces must be consistent with the total field each charge experiences.

This chapter describes the spectroscopic techniques that are used in most near-UV, visual, and IR spectrometers. Spectroscopy in this range is particularly important for astrophysics, and instruments for these wavelengths can be constructed using conventional optical elements, such as lenses, prisms, gratings, and normal-incidence mirrors. These instruments share many common features.

Commercially Available Spectrometers

Because optical spectroscopy plays an important role in many different branches of science, medicine, and industry, many manufacturers of optical instrumentation offer commercially produced spectrometers of different types. Most of these devices are not suited for the low light levels from astronomical sources. However, in addition to some instruments that have been designed specifically for astronomical applications (mainly for amateurs), there are commercial “low light level” general-purpose spectrometers on the market, which can be (and are) operated successfully for low-resolution spectroscopy at small telescopes. These commercially available instruments have the advantage of being complete systems, which include high-quality CCD or IR detectors. In many cases they can be conveniently connected to the USB port of a computer for instrument control and data readout. Usually the light from a telescope must be fed to the spectrometer using an optical fiber (see Section 4.5), but some of these spectrometers can be attached directly to a telescope focus. Observers interested in commercially available spectrometers will have no difficulties finding the addresses of potential suppliers by searching for optical spectrometers in the Internet.

So far, we have discussed two basic types of spectroscopic techniques. At high photon energies, the observations were based on the detection of individual photons. Their frequency was determined either by measuring their energy or by measuring their wavelength by means of optical effects. At low (radio) frequencies, the electromagnetic waves were directly recorded, and their frequency distribution was derived using electronic methods. As noted in Chapter 3 (Equation 3.42), under thermal equilibrium conditions, the detection of individual photons requires photon energies hv > kT. Thus, depending on the detector temperature, the transition between photon detection and radio-astronomical methods is expected to take place at FIR or submillimeter wavelengths. In practice, there exists a significant overlap of frequencies at which both types of detection methods can be used, and for which the preferred technique depends on the specific scientific objective. Moreover, in the submillimeter range it is sometimes of advantage to use bolometers, which record light indirectly by measuring the heat that is produced when photons are absorbed. Because of the choice of methods, special techniques have been developed for astronomical observations at these wavelengths, and sometimes combinations of radio and optical techniques are employed. A good example of the diversity of methods used in the FIR/submillimeter range are the three spectroscopic instruments of the Herschel Space Observatory (see Figure 9.4), which (as will be described later) use three different techniques.

The purpose of this chapter is to give a brief introduction to the special methods of the FIR/submillimeter range and to discuss their relative advantages and drawbacks for practical observations.

Although the grating instruments discussed in the preceding chapter dominate present-day astronomical spectroscopy at optical wavelengths, currently there are several other techniques in use at ground-based and space-based observatories. This chapter outlines the principles, the present applications, and the potential of three of these alternative methods.

Fabry-Perot Techniques

Fabry-Perot (FP) devices are based on the interference of light rays that are multiply reflected between partially transmissive mirrors. In astronomy, the main applications of the FP technique are special spectrometers and narrowband interference filters. FP spectroscopy was developed in the final years of the nineteenth century by the French physicists Charles Fabry and Alfred Perot. The technique was soon applied to astronomy. Alfred Perot himself used this method for measuring motions in the solar atmosphere.

The basic principle of the FP technique is outlined in Figure 5.1. The heart of any FP device is a pair of partially transmissive mirrors, separated by the distance l. In the context of FP devices, such a mirror pair is called an etalon (from the French designation of a standard length). In Figure 5.1, the light rays from the telescope are assumed to enter the space between the mirrors at angles γ to the mirror normals from the left (A). As indicated in the figure, the partially transmissive mirrors result in multiple reflections at the two mirror planes. At each reflection a fraction of the light passes through the mirror, while another fraction is returned into the space between the mirrors.

Radio astronomers typically use coherent receivers, which record and analyze the electromagnetic radiation directly. As was pointed out in Section 1.4, this facilitates spectroscopy at radio wavelengths. Making use of electronic frequency filters or of natural resonance effects, receivers can be built that are sensitive to a narrow frequency range only. If such receivers contain electronic components for which the parameters can be varied, the receivers can be “tuned” to specific frequencies. In this case, spectra can be be obtained by tuning narrowband receivers within a certain wavelength range, or by combining receivers that are tuned to different frequencies. As described in Section 1.4, the first radio spectra were obtained in this way, and commercially available radio spectrometers still use this technique. However, if spectra are obtained by tuning a receiver, the different frequencies are measured sequentially and the duty cycle for a given frequency is inversely proportional to the spectral resolution. Therefore, such spectrometers are inefficient and not well suited for the low radiation levels of faint astronomical radio sources. To study the very low signal levels from cosmic sources, more efficient methods must be used, which allow us to record many frequencies simultaneously. Some of these methods are described in the following sections.

The aim of this chapter is to provide an introduction to the technical background of the different types of radio spectrometers at a level that an observer needs to select the optimal instrument for a given task and to assess the potentials and the limitations of the different methods.

The purpose of this book is to provide an introduction to present-day astronomical spectroscopy. Thus, this chapter on the historical development will be restricted to a brief outline of selected milestones that provided the basis for the contemporary techniques and that are helpful for an understanding of the present terminologies and conventions. The reader interested in more details of the historic evolution of astronomical spectroscopy may find an extensive treatment of this topic in two excellent books by John Hearnshaw (1986, 2009). Additional information can be found in older standard works on astronomical spectroscopy, which were published by Hiltner (1964), Carleton (1976), and Meeks (1976). Apart from (still up-to-date) historical sections, these books provide extensive descriptions of methods that have been used in the past, before they were replaced by the more efficient contemporary techniques.

Early Pioneers

Astronomy is known for its long history. Accurate quantitative measurements of stellar positions and motions were already carried out millennia ago. On the other hand, spectroscopy is a relatively new scientific tool. It became important for astronomical research only during the past 200 years. The late discovery of spectroscopy may have been due to the scarcity of natural phenomena in which light is decomposed into its different colors. Moreover, for a long time the known natural spectral effects were not (or not correctly) understood. A prominent example is the rainbow. Reports of rainbows and thoughts about their origin are found in the oldest known written texts, and in most parts of the world almost everybody alive has seen this phenomenon.

This chapter covers astronomical spectroscopy at wavelengths between the UV and the gamma rays, which corresponds to a range of photon energies between about 4 eV and about 1014 eV. Naturally, different techniques are used at the extreme ends of this vast frequency range. However, the methods change continuously with the photon energy, and there exist extended regions in which the different methods overlap. Moreover, some of the basic problems and solutions are common throughout this range. In the literature, the high photon-energy range is often divided into the near ultraviolet (NUV, wavelengths about 200–380 nm), far ultraviolet (FUV, 100–200 nm), extreme ultraviolet (EUV, 10–100 nm), soft X-rays (0.5–10 nm), hard X-rays (2.5 pm–0.5 nm), and gamma rays (<2.5 pm). For convenience, these subdivisions will also be used in this text.

Energetic photons can interact with matter in many different ways. Among the relevant physical processes are the ionization of matter, the photoeffect, Compton scattering, and (at energies > 1 MeV) electron–positron pair production. All these processes can absorb over broad continuum bands. Because of this high absorption probability of energetic photons, optical techniques, which are based on the refraction and reflection of light, either cannot be used at all or require special layouts. The effective absorption cross section decreases again for the very high photon energies of hard X-rays and gamma rays. However, at these high energies, the radiation penetrates the normally reflecting materials, and the refractive index of all materials is uniformly very close to 1.