Abstract
In the previous chapter, electromagnetic waves were introduced as a fundamental phenomenon. All electromagnetic radiation fields can be described using the equations and elementary solutions presented there. The general and exact solution is, however, either too complex or cannot be determined at all. Therefore, the special characteristics of each problem will be used to simplify the description.
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- 1.
Examples: a window with an edge one-meter long, seen from a distance of five meters, λ = 550 nm: N F = 3.6 × 105. The sun, radius approx. 700,000 km, distance approx. 150 million km, λ = 550 nm: N F ≅ 6 × 1012.
- 2.
According to P. Fermat (1650).
- 3.
The step-index fiber is described here. There are also the so-called graded-index fibers, in which the refractive index declines continuously as it approaches the border. Then the light beam is not reflected sharply at the border, but rather is diverted by to the fiber center in a soft curve.
- 4.
There are also wave length regions in which anomalous dispersion occurs: here the refractive index increases with growing wavelength.
- 5.
As will be treated later in the section on image defects, the spherical surface only represents an approximation toward the real, ideal parabolic form of a lens. The reason for the spherical form lies in the significantly simpler manufacture.
- 6.
This rule is true as long as the refractive index of the lens material is larger than that of its surroundings.
- 7.
In the case of a diverging lens, its elongation has to pass through the focal point, since it lies on the object side because f < 0.
- 8.
The object distance is always positive.
- 9.
Chromatic (Greek) colored; monochromatic: unicolored.
- 10.
Aberration (Latin): deviation, error.
- 11.
Ludwig von Seidel, 1821–1896.
- 12.
Astigmatism (Greek.): without a spot.
- 13.
polychromatic (Greek): multicolored.
- 14.
Indicated here is an approximation of Kirchhoff’s diffraction integral for directed propagation. In a general case, the inclination factor \( K(\theta ) = \tfrac{1}{2}\left( {1 + \cos \theta } \right) \) has to be inserted into the integral, the factor allowing for the inclination against the propagation direction of the primary wavefront. The inclination towards ensures that a wavefront does not propagate backwards but forwards, a point that has not yet been incorporated in the Huygen–Fresnel principle.
References
Boyd, Robert W.: Nonlinear Optics. Academic Press, 2003
Shen, Yuen-Ron: The Principles of Nonlinear Optics. John Wiley, 1984
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Poprawe, R., Boucke, K., Hoffman, D. (2018). The Propagation of Electromagnetic Waves. In: Tailored Light 1. RWTHedition. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01234-1_4
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DOI: https://doi.org/10.1007/978-3-642-01234-1_4
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