The Physics of Semiconductors by Marius Grundmann

Author:Marius Grundmann
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(19.5)

which is the inverse of the group velocity .

Fig. 19.21D scattering problem: (a) General scattering of an index of refraction distribution, (b) N-period stack, (c) two-layer (quarter-wave) stack

We follow one-dimensional scattering theory as presented in [1327]. At this point we do not rely on any specific form of n(x) (Fig. 19.2a). The (complex) transmission coefficient t for any index structure is

(19.6)

where . is the total phase accumulated during propagation through the structure. It can be written as the product of the physical thickness of the structure d and the effective wave number k. Hence we have the dispersion relation

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