Optical element, method of manufacturing optical element, illumination device, window member, and fitting
An optical element includes a first surface, a second surface positioned to face the first surface, and a plurality of reflecting surfaces arrayed in a first region defined by the first surface and the second surface, wherein the reflecting surfaces have a first length in a first direction vertical to the first surface and are arrayed at a pitch in a second direction perpendicular to the first direction, light incident on one of the first surface and the second surface is reflected by the reflecting surfaces toward the other surface, and predetermined parameters satisfy predetermined relational formulae representing conditions for ensuring total reflection at the reflecting surfaces and for avoiding total reflection at a light emergent surface.
1. An optical element comprising:
a planar first light transmissive layer having opposed first and second surfaces;
a second light transmissive layer having opposed first and second surfaces, the first surface of the second light transmissive layer being adhered to the second surface of the first light transmissive layer, a plurality of elongated gaps being formed into either of the first and second surfaces of the second light transmissive layer and extending partially in a thickness direction to an interior portion thereof,
wherein a plurality of reflecting surfaces are arrayed along the gaps in the second light transmissive layer,
wherein the reflecting surfaces have a first length in a first direction vertical to the first or second surface of the second light transmissive layer and are arrayed at a pitch in a second direction perpendicular to the first direction,
light incident on one of the first surface of the first light transmissive layer and the second surface of the second light transmissive layer is reflected by the reflecting surfaces toward the other surface, and
following formulae (1) and (9) are satisfied:
d
=
(
2
n
-
1
)
p
tan
β
(
n
∈
N
)
(
1
)
(
n
p
+
n
air
sin
α
)
(
n
p
-
n
air
sin
α
)
sin
2
2
ψ
≤
n
air
2
(
1
-
cos
2
ψs
in
α
)
2
(
9
)
(where d is the first length, n is a number of total reflections of the incident light at the same reflecting surface, p is an array pitch of the reflecting surfaces, β is an angle formed between a projection of the light impinging on the reflecting surface to a surface including the first and second directions and a tangential line at an arbitrary point on the reflecting surface (6.5°≦β≦87.5°), N is a set of natural numbers, n p is a refractive index inside the region defined by the first surface and the second surface, n air is a refractive index of air, α is an incidence angle of the light incident on the optical element, and ψ is an angle formed in the surface including the first and second directions between a tangential line at an arbitrary point on the reflecting surface and the first direction).
2. The optical element according to claim 1 , wherein the reflecting surfaces are formed by interfaces between a second region including the gaps and a first region including the second light transmissive layer into which the gaps are formed, the second region having a second length in the second direction and having a refractive index differing from the refractive index inside the first region, and the first region, and given that the second length is w, (p−w)/p≦0.2 is satisfied.
3. The optical element according to claim 2 , wherein the second region is an air layer.
4. The optical element according to claim 1 , further comprising a structure layer positioned outside the first region and having a periodic or aperiodic concave-convex shape with a light diffusing property.
5. The optical element according to claim 4 , wherein the concave-convex shape is provided by prisms having a ridgeline direction aligned with the second direction and arrayed at a pitch in a direction perpendicular to both the first direction and the second direction.
6. An illumination device including the optical element according to claim 1 .
7. A window member including the optical element according to claim 1 .
8. A fitting including, in a lighting portion thereof, the optical element according to claim 1 .
9. The optical element of claim 1 , wherein the first light transmissive layer and the second light transmissive layer are made from at least one of Triacetylcellulose (TAC), Polyester (Thermoplastic Polyester Elastomer (TPEE)), Polyethyleneterephtalate (PET), Polyimide (PI), Polyamide (PA), aramid, Polyethylene (PE), polyacrylate, polyethersulfone, polysulfone, Polypropylene (PP), diacetyl cellulose, polyvinyl chloride, acryl resin (Polymethylmethacrylate (PMMA), Poly carbonate (PC), epoxy resin, urea resin, urethane resin, and melamine resin.
10. The optical element of claim 1 , wherein the plurality of elongated gaps are formed using an ultraviolet curable resin, the ultraviolet curable resin further containing (meth)acrylate, comprising a monomer and/or an oligomer including urethane (meth)acrylate, epoxy (meth)acrylate, polyester (meth)acrylate, polyol (meth)acrylate, polyether (meth)acrylate, and melamine (meth)acrylate.
11. The optical element of claim 1 , wherein the plurality of elongated gaps are filled with a material having a lower refractive index than the second light transmissive layer.
12. The optical element of claim 1 , wherein the first length is a value between 10 um and 1000 um inclusively, and the array pitch is a value between 100 um and 800 um inclusively.
13. An optical element comprising:
a planar first light transmissive layer having opposed first and second surfaces;
a second light transmissive layer having opposed first and second surfaces, the first surface of the second light transmissive layer being adhered to the second surface of the first light transmissive layer, a plurality of elongated gaps being formed into either of the first and second surfaces of the second light transmissive layer and extending partially in a thickness direction to an interior portion thereof,
wherein a plurality of reflecting surfaces are arrayed along the gaps in the second light transmissive layer,
wherein the reflecting surfaces have a curvature in at least a portion thereof, have a first length in a first direction vertical to the first or second surface of the second light transmissive layer, and are arrayed at a pitch in a second direction perpendicular to the first direction,
light incident on one of the first surface of the first light transmissive layer and the second surface of the second light transmissive layer is reflected by the reflecting surfaces toward the other surface, and
following formulae (1) and (16) are satisfied:
d
=
(
2
n
-
1
)
p
tan
β
(
n
∈
N
)
(
1
)
(
β
+
ξ
)
≤
Arccos
(
-
n
air
n
p
)
(
16
)
(where d is the first length, n is a number of total reflections of the incident light at the same reflecting surface, p is an array pitch of the reflecting surfaces, β is an angle formed between a projection of the light impinging on the reflecting surface to a surface including the first and second directions and a tangential line at an arbitrary point on the reflecting surface (6.5°≦β≦87.5°), N is a set of natural numbers, n p is a refractive index inside the region defined by the first surface and the second surface, n air is a refractive index of air, and ξ is an angle of divergence of light diverging after being focused, the light impinging on the reflecting surface, when the portion of the reflecting surface having the curvature is regarded as a lens).
14. An optical element comprising:
a planar first light transmissive layer having opposed first and second surfaces;
a second light transmissive layer having opposed first and second surfaces, the first surface of the second light transmissive layer being adhered to the second surface of the first light transmissive layer, a plurality of elongated gaps being formed into either of the first and second surfaces of the second light transmissive layer and extending partially in a thickness direction to an interior portion thereof,
wherein a plurality of reflecting surfaces are arrayed along the gaps in the second light transmissive layer,
wherein the reflecting surfaces have fine ruggedness, have a first length in a first direction vertical to the first or second surface of the second light transmissive layer, and are arrayed at a pitch in a second direction perpendicular to the first direction,
light incident on one of the first surface of the first light transmissive layer and the second surface of the second light transmissive layer is reflected by the reflecting surfaces toward the other surface,
an energy distribution of the light reflected by the reflecting surfaces is a Gaussian distribution with a direction of specular reflection being a center,
a standard deviation of the Gaussian distribution is 5° or less, and
a following formula (1is satisfied:
d
=
(
2
n
-
1
)
p
tan
β
(
n
∈
N
)
(
1
)
(where d is the first length, n is a number of total reflections of the incident light at the same reflecting surface, p is an array pitch of the reflecting surfaces, β is an angle formed between a projection of the light impinging on the reflecting surface to a surface including the first and second directions and a tangential line at an arbitrary point on the reflecting surface (6.5°≦β≦87.5°), and N is a set of natural numbers).