260
9 Optical Properties
(a)
(b)
Fig. 9.1 a Complex dielectric function of GaAs at room temperature dashed (solid) line: real (imaginary) part of
dielectric constant. Peak labels relate to transitions shown in part b. b Band structure of GaAs with fundamental band
gap transition (E 0 ) and higher transitions (E 0 + 0 , E 1 , E 1 + 1 , E
0 , and E 2 ) as indicated
(a)
(b)
Fig. 9.2 a Experimental (generalized spectroscopic ellipsometry) tensor elements of the complex dielectric function of
β-Ga 2 O 3 at room temperature. Adapted from [828]. b Stereographic projection of the angular orientation of the optic
and singular optic axes of β-Ga 2 O 3 . Some crystallographic orientations are indicated. The color refers to the photon
energy. The splitting of the two optic axes into four singular optic axes at the onset of absorption is denoted by two red
arrows. Adapted from [831]
9.3 Reflection and Diffraction
From Maxwell’s equations and the boundary conditions at a planar interface between two media with
different index of refraction for the components of the electric and magnetic fields the laws for reflection
and diffraction are derived. We denote the index of refraction as n and also n r in the following. The
interface between two media with refractive indices n 1 and n 2 is depicted in Fig. 9.3. In the following
we assume first that no absorption occurs.
Snell’s law [833] for the angle of diffraction is
n 1 sin φ = n 2 sin ψ .
(9.10)
9 Optical Properties
(a)
(b)
Fig. 9.1 a Complex dielectric function of GaAs at room temperature dashed (solid) line: real (imaginary) part of
dielectric constant. Peak labels relate to transitions shown in part b. b Band structure of GaAs with fundamental band
gap transition (E 0 ) and higher transitions (E 0 + 0 , E 1 , E 1 + 1 , E
0 , and E 2 ) as indicated
(a)
(b)
Fig. 9.2 a Experimental (generalized spectroscopic ellipsometry) tensor elements of the complex dielectric function of
β-Ga 2 O 3 at room temperature. Adapted from [828]. b Stereographic projection of the angular orientation of the optic
and singular optic axes of β-Ga 2 O 3 . Some crystallographic orientations are indicated. The color refers to the photon
energy. The splitting of the two optic axes into four singular optic axes at the onset of absorption is denoted by two red
arrows. Adapted from [831]
9.3 Reflection and Diffraction
From Maxwell’s equations and the boundary conditions at a planar interface between two media with
different index of refraction for the components of the electric and magnetic fields the laws for reflection
and diffraction are derived. We denote the index of refraction as n and also n r in the following. The
interface between two media with refractive indices n 1 and n 2 is depicted in Fig. 9.3. In the following
we assume first that no absorption occurs.
Snell’s law [833] for the angle of diffraction is
n 1 sin φ = n 2 sin ψ .
(9.10)