19.1 Photonic Band Gap Materials
491
Fig. 19.5 Reflectance of various Bragg mirrors from YSZ/Al 2 O 3 grown by pulsed laser deposition on sapphire. The
different layer thicknesses result in the design energies 0.43 eV (N = 10.5, R max = 0.9812, red), 1.19 eV (N = 10.5,
R max = 0.9779, orange), 2.11 eV (N = 15.5, R max = 0.99953, green), 3.39 eV (N = 15.5, R max = 0.99946, blue) and
4.54 eV (N = 15.5, R max = 0.99989, purple)
(a)
(b)
Fig. 19.6 a Index of refraction of YSZ and Al 2 O 3 as a function of photon energy. b Reflectance spectra of the 2.11 eV
(green), 3.39 eV (blue) and 4.54 eV (purple) Bragg mirrors of Fig. 19.5 replotted as a function of the scaled frequency
˜
ω = ω/ω 0
The principle of the quarter-wave stack is scalable to frequencies other than visible light.
1 In Fig. 19.5
the reflectance of various quarter-wave stacks from yttria-stabilized zirconia (YSZ [1590], high index
material, Fig. 19.6a) and Al 2 O 3 are shown [1591]. The different design wavelengths have been achieved
solely by varying the layer thicknesses.
In Fig. 19.6b the three Bragg mirrors from Fig. 19.5 with N = 15.5 pairs are replotted in relative
frequency units ˜
ω. The spectra look very similar; subtle differences in the width of the reflectance band
are due to slightly larger index contrast at higher design energy (cmp. Fig. 19.6a). The width of the gap
is approximately ˜
ω ≈ 0.18 in agreement with (19.30).
As further example, a Mo/Si Bragg mirror with a period of 6.7 nm is shown in Fig. 19.7. Such a
mirror works in the extreme UV and is used for soft X-ray optics, possibly in advanced lithography
1 This is a general property of Maxwell’s equations which do not contain a specific length scale.
491
Fig. 19.5 Reflectance of various Bragg mirrors from YSZ/Al 2 O 3 grown by pulsed laser deposition on sapphire. The
different layer thicknesses result in the design energies 0.43 eV (N = 10.5, R max = 0.9812, red), 1.19 eV (N = 10.5,
R max = 0.9779, orange), 2.11 eV (N = 15.5, R max = 0.99953, green), 3.39 eV (N = 15.5, R max = 0.99946, blue) and
4.54 eV (N = 15.5, R max = 0.99989, purple)
(a)
(b)
Fig. 19.6 a Index of refraction of YSZ and Al 2 O 3 as a function of photon energy. b Reflectance spectra of the 2.11 eV
(green), 3.39 eV (blue) and 4.54 eV (purple) Bragg mirrors of Fig. 19.5 replotted as a function of the scaled frequency
˜
ω = ω/ω 0
The principle of the quarter-wave stack is scalable to frequencies other than visible light.
1 In Fig. 19.5
the reflectance of various quarter-wave stacks from yttria-stabilized zirconia (YSZ [1590], high index
material, Fig. 19.6a) and Al 2 O 3 are shown [1591]. The different design wavelengths have been achieved
solely by varying the layer thicknesses.
In Fig. 19.6b the three Bragg mirrors from Fig. 19.5 with N = 15.5 pairs are replotted in relative
frequency units ˜
ω. The spectra look very similar; subtle differences in the width of the reflectance band
are due to slightly larger index contrast at higher design energy (cmp. Fig. 19.6a). The width of the gap
is approximately ˜
ω ≈ 0.18 in agreement with (19.30).
As further example, a Mo/Si Bragg mirror with a period of 6.7 nm is shown in Fig. 19.7. Such a
mirror works in the extreme UV and is used for soft X-ray optics, possibly in advanced lithography
1 This is a general property of Maxwell’s equations which do not contain a specific length scale.