6.2 From Bulk to Zero-Dimensional Structures
195
wavelength cavity between two DBRs, a quantum-well-like Fabry–Pérot resonator
with finite ground-state energy for the cavity photon can be obtained. Note that the
photonic DOS in 3D (vacuum) is ρ ∝ ω
2 due to the linear dispersion of photons in
vacuum. In a Fabry–Pérot microcavity, the photon obtains an effective mass, kind
of a “rest mass” m e f f = E 0 n
2
/c
2
≈ 10
−5 m 0 , due to its approximately parabolic
dispersion for small wave-vectors k || ≈ 0.
Further processing of such cavity into micropillars can form photonic quantum
dots with atomistic energy levels for light, with which quantum coupling experiments on a single-emitter and empty-field level can be performed. Alternatively,
planar systems can be etched to form waveguides in order to act as a photonic wire.
Similarly, nanofibres or nanoneedles act as wires for light, and photonic-crystal fibres
offer particularly high lateral confinement among the 1D photonic structures. Further
slicing the photonic-crystal fibre into a half-wavelength thick photonic-crystal sheet
can result in a very-high-quality optical resonator with properties of a 0D photonic
quantum box (also referred to as optical quantum dot) based on strong lateral and
out-of-plane confinement potentials. Similarly, if a planar Fabry–Pérot microcavity
is etched into a circular (or square-shaped) micropillar shape with diameters of the
order of few microns, the previously in-plane confined photonic modes experience
strong lateral confinement by a cylindrically shaped cavity region with considerable
refractive index contrast to the surrounding air/vacuum (cf. [6, 12]). In contrast,
shallow confinement in photonic boxes can be achieved by buried sub-micron height
modulations in monolithically grown planar microresonators [22–25]. In fact, one
can also create photonic molecules and artificial lattices from all these optical quantum dots [26–31], which can even exhibit nontrivial topological properties (see for
instance [32–35]). Such examples highlight the unique possibilities one obtains when
reducing dimensionalities and modifying the potential landscape.
For the sake of compactness, Coulomb-binding phenomena, excitons, exciton
complexes, phonons, polaritons and the like, their dispersions, the impact of potential
landscapes on these quasi-particles, or other effects, such as tunneling phenomena,
thermal and quantum-mechanical delocalisation effects, lifetimes, and so forth are
not discussed in this brief introduction. On the one hand, this is omitted here due to
the difficulty to compress the vast amount of contemporary knowledge and to find a
beginning and an end; and on the other hand, due to the fact that excellent textbooks on
semiconductors exist which describe all these fundamental aspects in various levels
of details. Instead, a brief glimpse at the advantages that arise from low-dimensional
structures is given, highlighting few selected examples in the following section.
topologically protected states which deliver very robust, scatter-free/dissipation-free propagation
of their respective particles in such modes. Certain structures could in principle be even designed
to provide only momentum states for unidirectional propagation (on their edge). However, since
topological properties are not the subject of this chapter, such design principles and underlying
theoretical concepts will not be detailed here.
195
wavelength cavity between two DBRs, a quantum-well-like Fabry–Pérot resonator
with finite ground-state energy for the cavity photon can be obtained. Note that the
photonic DOS in 3D (vacuum) is ρ ∝ ω
2 due to the linear dispersion of photons in
vacuum. In a Fabry–Pérot microcavity, the photon obtains an effective mass, kind
of a “rest mass” m e f f = E 0 n
2
/c
2
≈ 10
−5 m 0 , due to its approximately parabolic
dispersion for small wave-vectors k || ≈ 0.
Further processing of such cavity into micropillars can form photonic quantum
dots with atomistic energy levels for light, with which quantum coupling experiments on a single-emitter and empty-field level can be performed. Alternatively,
planar systems can be etched to form waveguides in order to act as a photonic wire.
Similarly, nanofibres or nanoneedles act as wires for light, and photonic-crystal fibres
offer particularly high lateral confinement among the 1D photonic structures. Further
slicing the photonic-crystal fibre into a half-wavelength thick photonic-crystal sheet
can result in a very-high-quality optical resonator with properties of a 0D photonic
quantum box (also referred to as optical quantum dot) based on strong lateral and
out-of-plane confinement potentials. Similarly, if a planar Fabry–Pérot microcavity
is etched into a circular (or square-shaped) micropillar shape with diameters of the
order of few microns, the previously in-plane confined photonic modes experience
strong lateral confinement by a cylindrically shaped cavity region with considerable
refractive index contrast to the surrounding air/vacuum (cf. [6, 12]). In contrast,
shallow confinement in photonic boxes can be achieved by buried sub-micron height
modulations in monolithically grown planar microresonators [22–25]. In fact, one
can also create photonic molecules and artificial lattices from all these optical quantum dots [26–31], which can even exhibit nontrivial topological properties (see for
instance [32–35]). Such examples highlight the unique possibilities one obtains when
reducing dimensionalities and modifying the potential landscape.
For the sake of compactness, Coulomb-binding phenomena, excitons, exciton
complexes, phonons, polaritons and the like, their dispersions, the impact of potential
landscapes on these quasi-particles, or other effects, such as tunneling phenomena,
thermal and quantum-mechanical delocalisation effects, lifetimes, and so forth are
not discussed in this brief introduction. On the one hand, this is omitted here due to
the difficulty to compress the vast amount of contemporary knowledge and to find a
beginning and an end; and on the other hand, due to the fact that excellent textbooks on
semiconductors exist which describe all these fundamental aspects in various levels
of details. Instead, a brief glimpse at the advantages that arise from low-dimensional
structures is given, highlighting few selected examples in the following section.
topologically protected states which deliver very robust, scatter-free/dissipation-free propagation
of their respective particles in such modes. Certain structures could in principle be even designed
to provide only momentum states for unidirectional propagation (on their edge). However, since
topological properties are not the subject of this chapter, such design principles and underlying
theoretical concepts will not be detailed here.