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Part I
Optics Technology for Defense Systems
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Chapter 1
Optical Rays
Geometric or ray optics [16] is used to describe the path of light in free space in which propagation distance is much greater than the wavelength of the light—normally microns (see Section 1.2.3 for more exact conditions). Note that we cannot apply ray theory if the media properties vary noticeably in distances comparable to wavelength; for such cases, we use more computationally demanding finite approximation techniques such as finite-difference time domain (FDTD) [154] or finite elements [78, 79]. Ray theory postulates rays that are at right angles to wave fronts of constant phase. Such rays describe the path along which light emanates from a source and the rays track the Poynting vector of power in the wave. Geometric or ray optics provides insight into the distribution of energy in space with time. The spread of neighboring rays with time enables computation of attenuation, which provides information analogous to that provided by diffraction equations but with less computation. Ray optics is extensively used for the passage of light through optical elements, such as lenses, and inhomogeneous media for which refractive index (or dielectric constant) varies with position in space.
In Section 1.1, we derive the paraxial equation that reduces dimensionality when light stays close to the axis. In Section 1.2, we study geometric or ray optics: Fermat's principle, limits of ray theory, the ray equation, rays through quadratic media, and matrix representations. In Section 1.3, we consider thin lens optics for launching and/or receiving beams: magnification, beam expanders, beam compressors, telescopes, microscopes, and spatial filters.
1.1 Paraxial Optics
In 1840, Gauss proposed the paraxial approximation for propagation of beams that stay close to the axis of an optical system. In this case, propagation is, say, in the z direction and the light varies in transverse x and y directions over only a small distance relative to the distance associated with the radius of curvature of a spherically curved surface in x and y (Figure 1.1). The region of the spherical surface near the axis can be approximated by a parabola. The spherical surface of curvature R is
Using the binomial theorem to eliminate the square root,
which is the equation for a parabola.
1.2 Geometric or ray optics
1.2.1 Fermat's Principle
In 1658, Fermat introduced one of the first variational principles in physics, the basic principle that governs geometrical optics [16]: A ray of light will travel between points
and
by the shortest optical path
; no other path will have a shorter optical path length. The optical path length is the equivalent path length in a...
