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- 5.Optics Geometrical optics
Electromagnetic waves Communications, antenna, radar, and microwave engineers must deal with the generation, transmission, and reception of electromagnetic waves. Device engineers working on ever-smaller integrated circuits and at ever higher frequencies must take into account wave propagation effects at the chip and circuit-board levels. Communication and computer network engineers routinely use waveguiding systems, such as transmission lines and optical fibers. Novel recent developments in materials, such as photonic bandgap structures, omnidirectional dielectric mirrors, birefringent multilayer films, surface plasmons, negative-index metamaterials, slow and fast light, promise a revolution in the control and manipulation of light and other applications. These are just some examples of topics discussed in this book. The book is organized around three main topic areas: The propagation, reflection, and transmission of plane waves, and the analysis and design of multilayer films. Waveguiding systems, including metallic, dielectric, and surface 386
waveguides, transmission lines, impedance matching, and S-parameters. Linear and aperture antennas, scalar and vector diffraction theory, plane-wave spectrum, Fourier optics, superdirectivity and superresolution concepts, antenna array design, numerical methods in antennas, and coupled antennas. The text emphasizes connections to other subjects. For example, the mathematical techniques for analyzing wave propagation in multilayer structures, multisegment transmission lines, and the design of multilayer optical filters are the same as those used in DSP, such as the lattice structures of linear prediction, the analysis and synthesis of speech, and geophysical signal processing. Similarly, antenna array design is related to the problem of spectral analysis of sinusoids and to digital filter design, and Butler beams are equivalent to the FFT. Electromagnetic radiation (EM radiation or EMR) is the radiant energy released by certain electromagneticprocesses. Visible light is an electromagnetic radiation. Other familiar electromagnetic radiations are invisible to the human eye, such as radio waves, infrared light and X-rays. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronizedoscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy andwave propagation, forming a transverse wave. Electromagnetic waves can be characterized by either thefrequency or wavelength of their oscillations to form the electromagnetic spectrum, which includes, in order of increasing frequency and decreasing wavelength: radio waves, microwaves, infrared radiation, visible light,ultraviolet radiation, X-rays and gamma rays. Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Quanta of EM waves are called photons, which aremassless, but they are still affected by gravity. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near fieldrefers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the quantum theory of electromagnetism, EMR consists of photons, the elementary particles responsible for all electromagnetic interactions. Quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of an individual photon is quantized and is greater for photons of higher frequency. This relationship is given by Planck's equation E = hν, where E is the energy per photon, ν is the frequency of the photon, and h isPlanck's constant. A single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light. The effects of EMR upon biological systems (and also to many other chemical systems, under standard conditions) depend both upon the radiation's power and its 387
frequency. For EMR of visible frequencies or lower (i.e., radio, microwave, infrared), the damage done to cells and other materials is determined mainly by power and caused primarily by heating effects from the combined energy transfer of many photons. By contrast, for ultraviolet and higher frequencies (i.e., X-rays and gamma rays), chemical materials and living cells can be further damaged beyond that done by simple heating, since individual photons of such high frequency have enough energy to cause direct molecular damage. 5.Optics Geometrical optics Geometrical optics, or ray optics, describes light propagation in terms of rays. The ray in geometric optics is an abstraction, or instrument, useful in approximating the paths along which light propagates in certain classes of circumstances. The simplifying assumptions of geometrical optics include that light rays: propagate in rectilinear paths as they travel in a homogeneous medium bend, and in particular circumstances may split in two, at the interface between two dissimilar media follow curved paths in a medium in which the refractive index changes may be absorbed or reflected. Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical aberrations. A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.[1] Geometrical optics is often simplified by making the paraxial approximation, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques ofGaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications. Wave optics A slit that is wider than a single wave will produce interference-like effects downstream from the slit. It is easier to understand by thinking of the slit not as a long slit, but as a number of point sources spaced evenly across the width of the slit. This can be seen in Figure 2 . 388
Single Slit Diffraction - Four Wavelengths This figure shows single slit diffraction, but the slit is the length of 4 wavelengths. To examine this effect better, lets consider a single monochromatic wavelength. This will produce a wavefront that is all in the same phase. Downstream from the slit, the light at any given point is made up of contributions from each of these point sources. The resulting phase differences are caused by the different in path lengths that the contributing portions of the rays traveled from the slit. 
The variation in wave intensity can be mathematically modeled. From the center of the slit, the diffracting waves propagate radially. The angle of the minimum intensity (θmin) can be related to wavelength (λ) and the slit's width (d) such that: dsinθmin=λ.
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