Chapter 19
Dielectric Structures
Abstract Dielectric structures, in particular periodic dielectric structures are treated. A general onedimensional model is developed describing Bragg mirrors. Examples for photonic band gap materials
in one, two and three dimensions are given. Different types of dielectric cavities and microscopic resonators including Fabry-Pérot and whispering gallery resonators are treated. Quantum electrodynamic
physical effects from light matter coupling such as Purcell effect and strong coupling are treated.
19.1 Photonic Band Gap Materials
Layered structures of dielectric materials with different index of refraction are used as optical elements
such as filters or reflection and anti-reflection coatings [1588]. In this section we discuss the use of
such concepts in one-, two- and three-dimensional photonic band gap materials.
19.1.1 Introduction
A structure with a so-called photonic band gap (PBG) exhibits an energy range (color range) in which
photons cannot propagate in any direction. In the photonic band gap, there are no optical modes, no
spontaneous emission and no vacuum (zero-field) fluctuations. We recollect that spontaneous emission
is not a necessary occurrence: Looking at Fermi’s golden rule (9.30) for the transition probability
integrated over all final states
w(E) =
2π
|M|
2
ρ f (E) ,
(19.1)
we see that the decay rate depends on the density ρ f of final states at energy E. In the case of spontaneous
emission, this is the (vacuum) density D em of electromagnetic modes (per energy per volume) that
varies ∝ ω
2 :
D em (E) =
8π
(hc) 3 E
2
.
(19.2)
In a homogeneous optical medium c must be replaced with c/n (cmp. Sect. 10.2.3).
If the band gap of a PBG is tuned to the electronic gap of a semiconductor, the spontaneous emission,
and also induced emission, can be suppressed. Thus, one mode has to be left by ‘doping’ the structure.
In this mode all emission will disappear and an efficient single-mode (monochromatic) LED or ‘zerothreshold’ laser could be built. A schematic comparison of the band structure of electrons and photons
is given in Fig. 19.1.
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_19
485
Dielectric Structures
Abstract Dielectric structures, in particular periodic dielectric structures are treated. A general onedimensional model is developed describing Bragg mirrors. Examples for photonic band gap materials
in one, two and three dimensions are given. Different types of dielectric cavities and microscopic resonators including Fabry-Pérot and whispering gallery resonators are treated. Quantum electrodynamic
physical effects from light matter coupling such as Purcell effect and strong coupling are treated.
19.1 Photonic Band Gap Materials
Layered structures of dielectric materials with different index of refraction are used as optical elements
such as filters or reflection and anti-reflection coatings [1588]. In this section we discuss the use of
such concepts in one-, two- and three-dimensional photonic band gap materials.
19.1.1 Introduction
A structure with a so-called photonic band gap (PBG) exhibits an energy range (color range) in which
photons cannot propagate in any direction. In the photonic band gap, there are no optical modes, no
spontaneous emission and no vacuum (zero-field) fluctuations. We recollect that spontaneous emission
is not a necessary occurrence: Looking at Fermi’s golden rule (9.30) for the transition probability
integrated over all final states
w(E) =
2π
|M|
2
ρ f (E) ,
(19.1)
we see that the decay rate depends on the density ρ f of final states at energy E. In the case of spontaneous
emission, this is the (vacuum) density D em of electromagnetic modes (per energy per volume) that
varies ∝ ω
2 :
D em (E) =
8π
(hc) 3 E
2
.
(19.2)
In a homogeneous optical medium c must be replaced with c/n (cmp. Sect. 10.2.3).
If the band gap of a PBG is tuned to the electronic gap of a semiconductor, the spontaneous emission,
and also induced emission, can be suppressed. Thus, one mode has to be left by ‘doping’ the structure.
In this mode all emission will disappear and an efficient single-mode (monochromatic) LED or ‘zerothreshold’ laser could be built. A schematic comparison of the band structure of electrons and photons
is given in Fig. 19.1.
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_19
485