14 Label-Free Super-Resolution Imaging with Hyperbolic Materials
351
(Sapphire)
-
(a)
(b)
Fig. 14.3 Permittivities of two naturally occurring hyperbolic materials: a sapphire (Al 2 O 3 ) [30]
and b hexagonal boron nitride (h-BN) [31]. Note the presence of substantial material loss in the
hyperbolic bands (where Re [ τ ] Re [ n ] < 0)
Fig. 14.4 Metamaterial realizations of hyperbolic medium: a layered structure and b nanorod array
multilayer geometry, when the metal and dielectric components with the permittivities m and d , have the corresponding thickness values of h m and h d , the effective
medium theory [38] yields
τ = m ·
h m
h m + h d
+ d ·
h d
h m + h d
,
(14.5)
1
n
=
1
m
·
h m
h m + h d
+
1
d
·
h d
h m + h d
.
(14.6)
In Fig. 14.5, we show the resulting permittivities for a silver-silica-layered structure,
with equal thicknesses of the metal and dielectric components of the composite. Note
the relatively small amount of loss in this structure.
351
(Sapphire)
-
(a)
(b)
Fig. 14.3 Permittivities of two naturally occurring hyperbolic materials: a sapphire (Al 2 O 3 ) [30]
and b hexagonal boron nitride (h-BN) [31]. Note the presence of substantial material loss in the
hyperbolic bands (where Re [ τ ] Re [ n ] < 0)
Fig. 14.4 Metamaterial realizations of hyperbolic medium: a layered structure and b nanorod array
multilayer geometry, when the metal and dielectric components with the permittivities m and d , have the corresponding thickness values of h m and h d , the effective
medium theory [38] yields
τ = m ·
h m
h m + h d
+ d ·
h d
h m + h d
,
(14.5)
1
n
=
1
m
·
h m
h m + h d
+
1
d
·
h d
h m + h d
.
(14.6)
In Fig. 14.5, we show the resulting permittivities for a silver-silica-layered structure,
with equal thicknesses of the metal and dielectric components of the composite. Note
the relatively small amount of loss in this structure.