496
19 Dielectric Structures
(a)
(i)
(ii)
(iii)
(iv)
(v)
(b)
(c)
Fig. 19.12 a Cartoon showing, in five steps, the fabrication of an inverse diamond structure with a full photonic band
gap. First, (i) a mixed body-centered cubic lattice is assembled (ii) after which the latex sublattice is removed; (iii) then
the structure is sintered to a filling fraction of ∼50% after that (iv) silicon or germanium infiltration takes place and
finally (v) silica elimination. b Photonic band diagrams of (upper panel) a silicon/silica composite diamond opal and
(lower panel) made of air spheres in silicon resulting from the removal of the silica spheres from the former. The filling
fraction for silicon is 50%. The inset shows the corresponding real space structures. Adapted from [1609], reprinted with
permission, ©2001 AIP. c SEM images of internal facets of silicon inverse opal: (i) (110) facet, (ii) (111) facet. Adapted
from [1610], reprinted with permission, ©2000, Springer Nature
In Fig. 19.14, the transmission curves are shown for the undisturbed quarter-wave stack and the
microcavity with n 2 d
center
2
= 2λ 0 /4 = λ 0 /2. A highly transmissive mode at ω = ω 0 arises that is quite
sharp with = 3 × 10
−4 . Thus, the quality factor Q, also called the Q-factor or finesse,
Q =
ω 0
ω
,
(19.36)
with ω 0 being the resonance frequency and ω being the linewidth, is 3.3 × 10
3 in this case.
If the thickness is varied (Fig. 19.15), the mode shifts away from the center. A similar scenario arises
for higher-order n l /2-cavities, e.g. n 2 d
center
2
= 4λ 0 /4 = λ 0 (Fig. 19.16).
2D or 3D Defect Modes
An example of 2D waveguiding is shown in Fig. 19.17. Point defects can be used for high-finesse
wavelength filtering. Emitters surrounded by a photonic band gap material with a defect mode can
emit into the defect mode only, leading to spectrally filtered, highly directional emission.
19 Dielectric Structures
(a)
(i)
(ii)
(iii)
(iv)
(v)
(b)
(c)
Fig. 19.12 a Cartoon showing, in five steps, the fabrication of an inverse diamond structure with a full photonic band
gap. First, (i) a mixed body-centered cubic lattice is assembled (ii) after which the latex sublattice is removed; (iii) then
the structure is sintered to a filling fraction of ∼50% after that (iv) silicon or germanium infiltration takes place and
finally (v) silica elimination. b Photonic band diagrams of (upper panel) a silicon/silica composite diamond opal and
(lower panel) made of air spheres in silicon resulting from the removal of the silica spheres from the former. The filling
fraction for silicon is 50%. The inset shows the corresponding real space structures. Adapted from [1609], reprinted with
permission, ©2001 AIP. c SEM images of internal facets of silicon inverse opal: (i) (110) facet, (ii) (111) facet. Adapted
from [1610], reprinted with permission, ©2000, Springer Nature
In Fig. 19.14, the transmission curves are shown for the undisturbed quarter-wave stack and the
microcavity with n 2 d
center
2
= 2λ 0 /4 = λ 0 /2. A highly transmissive mode at ω = ω 0 arises that is quite
sharp with = 3 × 10
−4 . Thus, the quality factor Q, also called the Q-factor or finesse,
Q =
ω 0
ω
,
(19.36)
with ω 0 being the resonance frequency and ω being the linewidth, is 3.3 × 10
3 in this case.
If the thickness is varied (Fig. 19.15), the mode shifts away from the center. A similar scenario arises
for higher-order n l /2-cavities, e.g. n 2 d
center
2
= 4λ 0 /4 = λ 0 (Fig. 19.16).
2D or 3D Defect Modes
An example of 2D waveguiding is shown in Fig. 19.17. Point defects can be used for high-finesse
wavelength filtering. Emitters surrounded by a photonic band gap material with a defect mode can
emit into the defect mode only, leading to spectrally filtered, highly directional emission.