Файл: Weber H., Herziger G., Poprawe R. (eds.) Laser Fundamentals. Part 1 (Springer 2005)(263s) PEo .pdf

Application: Θe, Θo, no, and nΘ e phase di erences (interferences) and reflection coe cient, Θo and Θew ray separation in a crystal.

Example 3.1.13. Calcite: no = 1.658, ne = 1.486, η = 45◦: #1: Θ = 0◦: C = 1.244822, nΘ e = 1.565,

Θo = Θe = 0◦, Θew = −6.224◦; #2: Θ = 45◦: nΘ e = 1.636, C = 0.438329, Θo = 25.23◦, Θe = 25.6◦, Θew = 21.33◦.

General formulation of (3.1.85)–(3.1.89): see [76Fed, Table 9.1] for more detailed discussions.

3.1.5.8 Photonic crystals

Starting with the forbidden (stop) bands in case of multi-layer Bragg reflection [88Yeh, p. 123] a material class is under development which stops light propagation along as many directions and for as many wavelengths as possible. This suppresses the spontaneous emission for laser applications and opens new possibilities in the microand nano-optics [95Joa, 01Sak, 04Bus]. Photonic crystal fibers [04Bus] can be designed for special light propagation properties and high-power fiber lasers [03Wad].

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3.1.5.9 Negative-refractive-index materials

The common excitation of electrical dipoles and magnetical dipoles by light in a medium can result in a negative dielectric permittivity Re (ε) < 0 in combination with a negative magnetic permeability Re (µ) < 0 . Then, in Snell’s law (3.1.72) an e ective index nˆ < 0 is possible [68Ves] which results in imaging by a slab of this material without curved surfaces [00Pen] and other interesting e ects [05Ram]. Such metamaterials can be generated by microtechnology, now for mmand terahertz-waves, but with the trend towards visible radiation [05Ele].

3.1.5.10 References to data of linear optics

[62Lan] contains optical constants, only. In later editions, the optical constants are listed together with other properties of substances. An overview is given in the content volume [96Lan].

3.1.6 Geometrical optics

Geometrical optics represents the limit of the wave optics for λ 0 .

The development sin σ = σ − 3!1 σ3 + 5!1 σ5 − . . . with σ the angle in Snell’s law characterizes the di erent approaches of geometrical optics. Table 3.1.10 gives an overview of di erent approximations of geometrical optics.

3.1.6.1 Gaussian imaging (paraxial range)

The signs of the parameters determined in [03DIN, 96Ped] are applied in Sect. 3.1.6.1.1, later on f = f is used.

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Table 3.1.10. Di erent approximations of geometrical optics.

3.1.6.1.1 Single spherical interface

Figure 3.1.30 shows the imaging by a spherical interface in the paraxial range (small x, x , h).

Gaussian imaging equation:

Remark : The symbol f means outside this section, Sect. 3.1.6.1, the positive focal length for a positive (converging) lens.

Newton’s imaging equation:

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