Multi-layer photonic structures having omni-directional reflectivity and coatings incorporating the same
A multi-layer photonic structure may include alternating layers of high index material and low index material having a form [H(LH) N ] where, H is a layer of high index material, L is a layer of low index material and N is a number of pairs of layers of high index material and layers of low index material. N may be an integer ≧1. The low index dielectric material may have an index of refraction n L from about 1.3 to about 2.5. The high index dielectric material may have an index of refraction n H from about 1.8 to about 3.5, wherein n H >n L and the multi-layer photonic structure comprises a reflectivity band of greater than about 200 nm for light having angles of incidence from about 0 degrees to about 80 degrees relative to the multi-layer photonic structure. The multi-layer photonic structure may be incorporated into a paint or coating system thereby forming an omni-directional reflective paint or coating.
1. A multi-layer photonic structure comprising alternating layers of high index material and low index material having a form [0.5 L H (LH) N 0.5 L] where H is a layer of high index material, L is a layer of low index material, 0.5 L are half layers of low index dielectric material positioned on a top and a bottom of the multilayer photonic structure, and N is a number of pairs of layers of high index material and layers of low index material, wherein:
N is an integer≧1;
the low index dielectric material has an index of refraction n L from about 1.3 to about 2.5;
the high index dielectric material has an index of refraction n H of greater than or equal to about 3.0, wherein n H >n L , and the half layers of low index dielectric material pass visible wavelengths of light and reflect UV and IR wavelengths of light such that the multilayer photonic structure is substantially transparent to visible wavelengths of light and has an IR reflectivity band and a UV reflectivity band, wherein a reflectance of the multilayer photonic structure is about 100% within the IR reflectivity band and within the UV reflectivity band for light having angles of incidence from about 0 degrees to about 80 degrees relative to the multi-layer photonic structure; and
the multi-layer photonic structure has a range to mid-range ratio greater than about 20% in a transverse electric mode and a transverse magnetic mode, and wherein the range to mid-range ratio for the transverse electric mode is determined by
η
TE
=
2
λ
long
TE
(
θ
0
=
90
°
)
-
λ
Short
TE
(
θ
0
=
0
°
)
λ
long
TE
(
θ
0
=
90
°
)
+
θ
Short
TE
(
θ
0
=
0
°
)
,
where λ long TE is a first band edge for a first long wavelength in the transverse electric mode and A λ short TE is a second band edge for a first short wavelength in the transverse electric mode, and the range to mid-range ratio for the transverse magnetic mode is determined by
η
TM
=
2
λ
long
TM
(
θ
0
=
90
°
)
-
λ
Short
TM
(
θ
0
=
0
°
)
λ
long
TM
(
θ
0
=
90
°
)
+
θ
Short
TM
(
θ
0
=
0
°
)
,
where λ long TM is a third band edge for a second long wavelength in the transverse magnetic mode and λ short TM is a fourth band edge for a second short wavelength in the transverse magnetic mode.
2. The multi-layer photonic structure of claim 1 wherein the IR reflectivity band is greater than about 250 nm and the UV reflectivity band is greater than about 100 nm for light having angles of incidence from about 0 degrees to about 45 degrees relative to the multi-layer photonic structure.
3. The coating of claim 2 wherein at least one wavelength of visible light is reflected for visible light with an angle of incidence greater than about 15 degrees.
4. The multi-layer photonic structure of claim 1 wherein an index contrast between the high index material and the low index material is from about 0.5 to about 2.0.
5. The multi-layer photonic structure of claim 1 wherein the high index material and the low index material are non-metallic materials.
6. The multi-layer photonic structure of claim 1 wherein the range to mid-range ratio in the transverse electric mode or the transverse magnetic mode is from about 20% to about 50%.
7. The multi-layer photonic structure of claim 1 , wherein the multi-layer photonic structure is a flake comprising an average thickness from about 0.5 microns to about 10 microns and an average diameter from about 10 microns to about 50 microns.
8. The multi-layer photonic structure of claim 1 wherein the high index dielectric material has an index of refraction n H of less than or equal to about 5.0.
9. A UV-IR reflective multilayer photonic structure comprising layers of high index material and low index material having a form [0.5 L H (LH) N 0.5 L] where H is a layer of high index dielectric material, L is a layer of the low index dielectric material, 0.5 L are half layers of low index dielectric material positioned on a top and a bottom of the multilayer photonic structure, and N is the number pairs of layers of high index material and layers of low index materials, wherein:
N is an integer≧1;
the low index dielectric material has an index of refraction n L from about 1.3 to about 2.5;
the high index dielectric material has an index of refraction n H of greater than or equal to about 3.0 , wherein n H >n L and, for angles of incidence from about 0 degrees to about 80 degrees, the half layers of low index dielectric material reflect wavelengths of light in an infrared spectrum and an ultraviolet spectrum such that the multi-layer photonic structure comprises a reflectivity band greater than about 300 nm for light in the infrared spectrum, a reflectivity band greater than about 50 nm for light in the ultraviolet spectrum, and the half layers of low index dielectric material pass wavelengths of light in a visible spectrum such that the multi-layer photonic structure is substantially transparent to visible light for angles of incidence from about 0 degrees to about 15degrees; and
the multi-layer photonic structure has a range to mid-range ratio greater than about 20% in a transverse electric mode and a transverse magnetic mode, and wherein the range to mid-range ratio for the transverse electric mode is determined by
η
TE
=
2
λ
long
TE
(
θ
0
=
90
°
)
-
λ
Short
TE
(
θ
0
=
0
°
)
λ
long
TE
(
θ
0
=
90
°
)
+
θ
Short
TE
(
θ
0
=
0
°
)
,
where λ long TE is a first band edge for a first long wavelength in the transverse electric mode and A λ short TE is a second band edge for a first short wavelength in the transverse electric mode, and the range to mid-range ratio for the transverse magnetic mode is determined by
η
TM
=
2
λ
long
TM
(
θ
0
=
90
°
)
-
λ
Short
TM
(
θ
0
=
0
°
)
λ
long
TM
(
θ
0
=
90
°
)
+
θ
Short
TM
(
θ
0
=
0
°
)
,
where λ long TM is a third band edge for a second long wavelength in the transverse magnetic mode and λ short TM is a fourth band edge for a second short wavelength in the transverse magnetic mode.
10. The multi-layer photonic structure of claim 9 wherein the multi-layer photonic structure comprises a reflectivity band greater than about 450 nm for light in the infrared spectrum having an angle of incidence from about 0 degrees to about 45 degrees.
11. The multi-layer photonic structure of claim 9 wherein an index contrast between the high index material and the low index material is from about 0.5 to about 2.0.
12. The multi-layer photonic structure of claim 9 wherein the range to mid-range ratio in the transverse electric mode or the transverse magnetic mode is from about 20% to about 50%.
13. The multi-layer photonic structure of claim 9 wherein the multi-layer photonic structure is a flake.
14. The multi-layer photonic structure of claim 13 wherein the flake has an average thickness from about 0.5 microns to about 10 microns.
15. The multilayer photonic structure of claim 13 wherein the flake has an average diameter from about 10 microns to about 50 microns.
16. The multi-layer photonic structure of claim 9 wherein the high index dielectric material has an index of refraction n H of less than or equal to about 5.0.
17. An article of manufacture comprising a broadband omni-directionally reflective coating with at least one reflectivity band comprising a bandwidth greater than about 250 nm for angles of light incident on the coating from about 0° to about 80° , the coating comprising:
a binder and a plurality of multi-layer photonic structures dispersed in the binder, wherein the multi-layer photonic structures have a range to mid-range value in a transverse electric mode and a transverse magnetic mode from about 20% to about 50% and at least one reflectivity band having a bandwidth greater than about 250 nm for angles of light incident on the multilayer photonic structure from about 0° to at least about 45° , wherein the multilayer photonic structure comprises layers of high index material and low index material having a form [0.5 L H(LH) N 0.5 L] where H is a layer of high index dielectric material, L is a layer of the low index dielectric material, N is the number of pairs of layers of high index material and layers of low index materials, 0.5 L are half layers of low index dielectric material positioned on a top and a bottom of the multilayer photonic structure, wherein:
N is an integer≧1;
the low index dielectric material has an index of refraction n L from about 1.3 to about 2.5;
the high index dielectric material has an index of refraction n H of greater than or equal to about 3.0 and n H >n L ;
the half layers of low index dielectric material pass wavelengths of light in a visible spectrum and reflect wavelengths of light in an infrared spectrum and an ultraviolet spectrum such that the at least one reflectivity band comprises a first reflectivity band having a bandwidth greater than about 300 nm for light in the infrared spectrum, a second reflectivity band greater than about 50 nm for light in the ultraviolet spectrum, and the multi-layer photonic structure is substantially transparent to visible light;
and the range to mid-range ratio for the transverse electric mode is determined by
η
TE
=
2
λ
long
TE
(
θ
0
=
90
°
)
-
λ
Short
TE
(
θ
0
=
0
°
)
λ
long
TE
(
θ
0
=
90
°
)
+
θ
Short
TE
(
θ
0
=
0
°
)
,
where λ long TE is a first band edge for a first long wavelength in the transverse electric mode and λ short TE is a second band edge for a first short wavelength in the transverse electric mode, and the range to mid-range ratio for the transverse magnetic mode is determined by
η
TM
=
2
λ
long
TM
(
θ
0
=
90
°
)
-
λ
Short
TM
(
θ
0
=
0
°
)
λ
long
TM
(
θ
0
=
90
°
)
+
θ
Short
TM
(
θ
0
=
0
°
)
,
where λ long TM is a third band edge for a second long wavelength in the transverse magnetic mode and λ short TM is a fourth band edge for a second short wavelength in the transverse magnetic mode.
18. The article of manufacture of claim 17 wherein the multi-layer photonic structures are flakes comprising an average thickness from about 0.5 microns to about 10 microns and an average diameter from about 10 microns to about 50 microns.
19. The article of manufacture of claim 17 wherein the high index dielectric material has an index of refraction n H of less than or equal to about 5.0.