19.1 Photonic Band Gap Materials
497
(a)
(b)
Fig. 19.13 a Schematic photonic band gap structure with perfect (upper left) and disordered (upper right) periodicity.
In the lower left panel the disordered structure is overlayed with the ideal structure (red circles). In the lower right panel,
the difference between ideal and disordered structure is shown. b Optical mean free path in an opal photonic band gap
structure for various lattice constants. Solid line is theory for 5% fabrication accuracy. Adapted from [1611], reprinted
with permission, ©2005 APS
(a)
(b)
Fig. 19.14 Defect mode in 1D photonic band gap: a Transmission of N = 11 quarter-wave stack exhibiting a photonic
band gap (n 1 = 1, n 2 = 2) (dashed line) and of microcavity (solid line) with center n 2 -region of width λ 0 /2 (instead of
λ 0 /4). b Relative width of mode is about 3 × 10 −4
19.1.8 Topological Photonic Band Structures
A review of two-dimensional topological photonics can be found in [1613]. The idea of topologically
non-trivial 2D photonic band structures has been put forward in [1614] theoretically, employing a
Faraday-effect medium breaking time-reversal symmetry. The system is a two-dimensional photonic
crystals with an external magnetic field perpendicular to the plane of light propagation. A hexagonal
array of dielectric cylindrical rods is modeled. The degeneracy of the Dirac points (at the K-points) is
lifted by introducing the Faraday medium outside the rods. The bands close to the gap obtain non-zero
Chern numbers C n = ±1 (breaking inversion symmetry only creates a gap but does not lead to non-zero
Chern number). Reversal of the magnetic field inverts the bands to C n = ∓1. The Berry curvature of
the photonic bands plays a role analogous to that of the magnetic field in the QHE. The calculations
show the existence of unidirectionally propagating photonic edge states between media with up and
497
(a)
(b)
Fig. 19.13 a Schematic photonic band gap structure with perfect (upper left) and disordered (upper right) periodicity.
In the lower left panel the disordered structure is overlayed with the ideal structure (red circles). In the lower right panel,
the difference between ideal and disordered structure is shown. b Optical mean free path in an opal photonic band gap
structure for various lattice constants. Solid line is theory for 5% fabrication accuracy. Adapted from [1611], reprinted
with permission, ©2005 APS
(a)
(b)
Fig. 19.14 Defect mode in 1D photonic band gap: a Transmission of N = 11 quarter-wave stack exhibiting a photonic
band gap (n 1 = 1, n 2 = 2) (dashed line) and of microcavity (solid line) with center n 2 -region of width λ 0 /2 (instead of
λ 0 /4). b Relative width of mode is about 3 × 10 −4
19.1.8 Topological Photonic Band Structures
A review of two-dimensional topological photonics can be found in [1613]. The idea of topologically
non-trivial 2D photonic band structures has been put forward in [1614] theoretically, employing a
Faraday-effect medium breaking time-reversal symmetry. The system is a two-dimensional photonic
crystals with an external magnetic field perpendicular to the plane of light propagation. A hexagonal
array of dielectric cylindrical rods is modeled. The degeneracy of the Dirac points (at the K-points) is
lifted by introducing the Faraday medium outside the rods. The bands close to the gap obtain non-zero
Chern numbers C n = ±1 (breaking inversion symmetry only creates a gap but does not lead to non-zero
Chern number). Reversal of the magnetic field inverts the bands to C n = ∓1. The Berry curvature of
the photonic bands plays a role analogous to that of the magnetic field in the QHE. The calculations
show the existence of unidirectionally propagating photonic edge states between media with up and