494
19 Dielectric Structures
(a)
(b)
Fig. 19.9 a Calculated photonic band gap structure of a fcc dielectric structure composed of air spheres in a dielectric
background of refractive index n = 3.5. The filling ratio is 86% air and 14% dielectric material. Dotted and solid lines
represent coupling to s- and p-polarized light, respectively. b Density of states for the band structure of part (a). Reprinted
from [1598] with permission, ©1990 APS
(a)
(b)
Fig. 19.10 a Calculated photonic band structure for a diamond dielectric structure consisting of overlapping air spheres
in a dielectric material with n = 3.6. Filling ratio of air is 81%. The frequency is given in units of c/a, a being the
cubic lattice constant of the diamond lattice and c being the velocity of light. The gap is indicated as grayed rectangle.
b Gap-to-midgap frequency ratio for the diamond structure as a function of filling ratio for dielectric spheres n = 3.6 in
air (solid circles) and air spheres in dielectric n (open circles). Optimal case: air spheres with 82% filling ratio. Adapted
from [1598], reprinted with permission, ©1990 APS
19.1.6 Disorder
A real photonic band gap structure deviates from the ideal, perfectly periodic system by slight variations of the position and possibly also the size of the dielectric ‘atoms’. This is schematically shown
in Fig. 19.13a. The difference between the real and ideal structure is a (bipolar) spatial distribution
of which acts as a source of scattering and hence exponential attenuation of coherent beams
propagating through photonic crystals over lengths l, named the ‘(extinction) mean free path’. After
propagating over such distance l, a light beam is converted to a diffuse glow that corrupts the functionality of any photonic integrated circuit. Experimentally for opals a mean free path consistent with
5% fabrication accuracy has been found (Fig. 19.13b). For such disorder and a lattice constant a ≈ λ,
the mean free path is about only 10 wavelengths, l ≈ 10λ.
19.1.7 Defect Modes
Similar to a perfect periodic atomic arrangement leading to the formation of the electronic band
structure, a perfectly periodic dielectric structure leads to the photonic band structure. As we know
19 Dielectric Structures
(a)
(b)
Fig. 19.9 a Calculated photonic band gap structure of a fcc dielectric structure composed of air spheres in a dielectric
background of refractive index n = 3.5. The filling ratio is 86% air and 14% dielectric material. Dotted and solid lines
represent coupling to s- and p-polarized light, respectively. b Density of states for the band structure of part (a). Reprinted
from [1598] with permission, ©1990 APS
(a)
(b)
Fig. 19.10 a Calculated photonic band structure for a diamond dielectric structure consisting of overlapping air spheres
in a dielectric material with n = 3.6. Filling ratio of air is 81%. The frequency is given in units of c/a, a being the
cubic lattice constant of the diamond lattice and c being the velocity of light. The gap is indicated as grayed rectangle.
b Gap-to-midgap frequency ratio for the diamond structure as a function of filling ratio for dielectric spheres n = 3.6 in
air (solid circles) and air spheres in dielectric n (open circles). Optimal case: air spheres with 82% filling ratio. Adapted
from [1598], reprinted with permission, ©1990 APS
19.1.6 Disorder
A real photonic band gap structure deviates from the ideal, perfectly periodic system by slight variations of the position and possibly also the size of the dielectric ‘atoms’. This is schematically shown
in Fig. 19.13a. The difference between the real and ideal structure is a (bipolar) spatial distribution
of which acts as a source of scattering and hence exponential attenuation of coherent beams
propagating through photonic crystals over lengths l, named the ‘(extinction) mean free path’. After
propagating over such distance l, a light beam is converted to a diffuse glow that corrupts the functionality of any photonic integrated circuit. Experimentally for opals a mean free path consistent with
5% fabrication accuracy has been found (Fig. 19.13b). For such disorder and a lattice constant a ≈ λ,
the mean free path is about only 10 wavelengths, l ≈ 10λ.
19.1.7 Defect Modes
Similar to a perfect periodic atomic arrangement leading to the formation of the electronic band
structure, a perfectly periodic dielectric structure leads to the photonic band structure. As we know