492
19 Dielectric Structures
(a)
50nm
Si
Mo
Si
(b)
Fig. 19.7 a Cross-sectional TEM of Mo/Si superlattice with 2.7 nm Mo (dark) and 4.0 nm Si (bright) layers on Si(001)
substrate. From [1592]. b Reflection spectrum for a SL with nominal period of 6.5 nm and 88.5 ◦ angle of incidence.
Data points are shown as circles, the solid line is a fit with a period of 6.45 nm. Adapted from [1593]
systems. Dielectric thin films can also be designed for anti-reflection coatings, edge filters or pass and
stop band filters as detailed in [1588].
19.1.5 Formation of a 3D Band Structure
For other applications, e.g. waveguides with minimized footprint, 3D (or at least 2D) photonic band
gap structures are needed. Details can be found in dedicated textbooks [1594–1596]. In [1597] planar,
cylindrical and spherical Bragg mirrors are discussed.
Since we want a photonic band gap that is present for all directions of propagation, a Brillouin zone
with a shape close to a sphere is preferable. Then, the main directions are at similar k-values (Fig. 19.8).
One of the best suited is the fcc lattice. Since the L-point is centered at ≈14% lower frequency than
the X-point, the forbidden gaps for different directions must be, however, sufficiently wide to create a
forbidden frequency band overlapping at all points along the surface of the Brillouin zone. For example,
the bcc lattice has a Brillouin zone that is less symmetric than that of the fcc lattice (see Fig. 3.38) and
thus is less suited for the creation of an omnidirectional photonic band gap. However, the photonic
(a)
k y
k z
k x
W
K
L
U
X
X
(b)
k
X
L
X
L
Fig. 19.8 a The Brillouin zone of the fcc lattice. b Schematic forbidden gaps at the L- and X-points
19 Dielectric Structures
(a)
50nm
Si
Mo
Si
(b)
Fig. 19.7 a Cross-sectional TEM of Mo/Si superlattice with 2.7 nm Mo (dark) and 4.0 nm Si (bright) layers on Si(001)
substrate. From [1592]. b Reflection spectrum for a SL with nominal period of 6.5 nm and 88.5 ◦ angle of incidence.
Data points are shown as circles, the solid line is a fit with a period of 6.45 nm. Adapted from [1593]
systems. Dielectric thin films can also be designed for anti-reflection coatings, edge filters or pass and
stop band filters as detailed in [1588].
19.1.5 Formation of a 3D Band Structure
For other applications, e.g. waveguides with minimized footprint, 3D (or at least 2D) photonic band
gap structures are needed. Details can be found in dedicated textbooks [1594–1596]. In [1597] planar,
cylindrical and spherical Bragg mirrors are discussed.
Since we want a photonic band gap that is present for all directions of propagation, a Brillouin zone
with a shape close to a sphere is preferable. Then, the main directions are at similar k-values (Fig. 19.8).
One of the best suited is the fcc lattice. Since the L-point is centered at ≈14% lower frequency than
the X-point, the forbidden gaps for different directions must be, however, sufficiently wide to create a
forbidden frequency band overlapping at all points along the surface of the Brillouin zone. For example,
the bcc lattice has a Brillouin zone that is less symmetric than that of the fcc lattice (see Fig. 3.38) and
thus is less suited for the creation of an omnidirectional photonic band gap. However, the photonic
(a)
k y
k z
k x
W
K
L
U
X
X
(b)
k
X
L
X
L
Fig. 19.8 a The Brillouin zone of the fcc lattice. b Schematic forbidden gaps at the L- and X-points