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. A method of manufacturing an optical element, the method comprising:
transferring a concave-convex shape formed in a master to a transfer material, thereby forming a first light transmissive layer that has a plurality of reflecting surfaces in a transfer surface thereof;
forming a plurality of elongated gaps into either of opposed first and second surfaces of a second light transmissive layer; and
joining the first light transmissive layer to the second light transmissive layer,
wherein the plurality of reflecting surfaces of the first light transmissive layer are arrayed along the elongated gaps in the second light transmissive layer, and
wherein the reflecting surfaces have a first length in a depth direction of the concave-convex shape of the transfer surface and are arrayed at a pitch in a second direction perpendicular to the depth direction of the concave-convex shape,
light incident on one principal surface of one of the first light transmissive layer and the second light transmissive layer is reflected by the reflecting surfaces toward one principal surface of the other layer, 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
ψ
sin
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 of the first light transmissive layer, 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. A method of manufacturing an optical element, the method comprising:
transferring a concave-convex shape formed in a master to a transfer material, thereby forming a first light transmissive layer that has a plurality of reflecting surfaces in a transfer surface thereof;
forming a plurality of elongated gaps into either of opposed first and second surfaces of a second light transmissive layer; and
joining the first light transmissive layer to the second light transmissive layer,
wherein the plurality of reflecting surfaces of the first light transmissive layer are arrayed along the elongated gaps in the second light transmissive layer, and
wherein the reflecting surfaces have a curvature in at least a portion thereof, have a first length in a depth direction of the concave-convex shape of the transfer surface, and are arrayed at a pitch in a second direction perpendicular to the depth direction of the concave-convex shape,
light incident on one principal surface of one of the first light transmissive layer and the second light transmissive layer is reflected by the reflecting surfaces toward one principal surface of the other layer, 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 of the first light transmissive layer, 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).
3. A method of manufacturing an optical element, the method comprising:
transferring a concave-convex shape formed in a master to a transfer material, thereby forming a first light transmissive layer that has a plurality of reflecting surfaces in a transfer surface thereof;
forming a plurality of elongated gaps into either of opposed first and second surfaces of a second light transmissive layer; and
joining the first light transmissive layer to the second light transmissive layer,
wherein the plurality of reflecting surfaces of the first light transmissive layer are arrayed along the elongated gaps in the second light transmissive layer, and
wherein the reflecting surfaces have fine ruggedness, have a first length in a depth direction of the concave-convex shape of the transfer surface, and are arrayed at a pitch in a second direction perpendicular to the depth direction of the concave-convex shape,
light incident on one principal surface of one of the first light transmissive layer and the second light transmissive layer is reflected by the reflecting surfaces toward one principal surface of the other layer, and
an energy distribution of the light reflected by the reflecting surfaces is a Gaussian distribution with a direction of specula reflection being a center,
a standard deviation of the Gaussian distribution is 5″ or less, and
a following formula (1) is 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).
4. The method of manufacturing the optical element according to claim 2 , wherein joining the first light transmissive layer to a second light transmissive layer includes embedding at least a part of a distal end of a convex portion on the transfer surface in an adhesive.
5. The method of manufacturing the optical element according to claim 2 , wherein joining the first light transmissive layer to a second light transmissive layer includes swelling a distal end of a convex portion on the transfer surface and press-bonding the swollen distal end to the second light transmissive layer such that a shape of the convex portion on the transfer surface is modified to be closer to a shape as per design values.
6. The method of manufacturing the optical element according to claim 2 , wherein joining the first light transmissive layer to a second light transmissive layer includes press-bonding a distal end of a convex portion on the transfer surface to the second light transmissive layer while applying heat to the distal end of the convex portion on the transfer surface such that a shape of the convex portion on the transfer surface is modified to be closer to a shape as per design values.