Compact concentrator for microscale space photovoltaic systems
An exemplary’ embodiment of the present disclosure provides a device for concentrating light and methods of making and using such device. The device comprising a substantially cone-shaped optical body comprising a first side and an opposing second side extending along a central axis, the second side larger than the first side, a receiver positioned near the first side of the optical body and oriented towards the second side, and a reflector proximate the second side of the optical body, wherein a cross section of the reflector about the central axis comprises at least two substantially parabolic curves extending along a length of the second side of the optical body and converging at the central axis.
1 . A device for concentrating light, the device comprising:
a substantially cone-shaped optical body comprising a first side, an opposing second side extending along a central axis, and a conical surface extending from the first side to the second side such that the second side is larger than the first side;
a receiver positioned near the first side of the optical body and oriented towards the second side, the receiver comprising a photovoltaic cell that is optically bonded to at least a portion of the first side of the optical body; and
a reflector proximate the second side of the optical body, wherein a cross section of the reflector about the central axis comprises at least two substantially parabolic curves extending along a length of the second side of the optical body and converging at the central axis;
wherein the at least two substantially parabolic curves are oriented relative to the conical surface and the central axis such that incident light within an acceptance half angle of the central axis is refracted through the conical surface and reflected by at least the reflector to the receiver.
2 . The device of claim 1 , wherein the second side of the optical body comprises a curved surface.
3 . The device of claim 1 , wherein the reflector comprises a first parabolic curve and a second parabolic curve, and wherein each respective parabolic curve of the reflector is symmetric about a respective internal axis.
4 . The device of claim 3 , wherein a peripheral edge of the respective parabolic curve of the reflector is positioned at an approximately uniform height from a central point of the parabolic curve such that the internal axis of each respective parabolic curve of the reflector is parallel to the central axis.
5 . The device of claim 3 , wherein a peripheral edge of the respective parabolic curve of the reflector is positioned at an increased height from a central point of the parabolic curve such that the internal axis of each respective parabolic curve of the reflector is directed towards the receiver.
6 . The device of claim 3 , wherein a peripheral edge of the respective parabolic curve of the reflector is positioned at a decreased height from a central point of the parabolic curve such that the internal axis of each respective parabolic curve of the reflector is directed away from the receiver.
7 . The device of claim 3 , wherein each parabolic curve is tilted by an angle with respect to the central axis that satisfies the following equation:
β
=
δ
-
sin
-
1
(
1
n
sin
(
δ
-
θ
)
)
,
wherein β is the angle with respect to the central axis, δ is an angle with respect to a plane of the first side to the optical body, n is a refractive index of the optical body, and θ is the acceptance half-angle.
8 . The device of claim 1 , wherein the optical body is constructed of a material comprising a refractive index equal to or greater than about 1.3.
9 . The device of claim 1 , wherein the optical body comprises a dimension from the first side to the second side equal to or less than 1 cm.
10 . The device of claim 1 , wherein the device is configured to achieve an optical efficiency of at least 37%.
11 . The device of claim 7 , wherein the device is configured to achieve at least 37% power conversion efficiency with a concentration ratio greater than approximately 110 and the acceptance half-angle greater than approximately 5 degrees.
12 . The device of claim 7 , wherein the device is configured to decrease light rejection losses by at least 35% compared to a comparative device having a reflector comprising only one parabolic curve.
13 . A device for concentrating light, the device comprising:
an optical element comprising a first side, an opposing second side, and a conical surface extending from the first side to the second side defining an internal volume of the optical element;
a photovoltaic cell positioned on the first side of the optical element; and
a reflector positioned on the second side of the optical element;
wherein the optical element is configured to refract light entering the internal volume through the conical surface, and
wherein the reflector comprises two curved surfaces, each respective curved surface extending along a length of the second side of the optical element and converging at a central axis of the device such that the refracted light focuses on the photovoltaic cell.
14 . The device of claim 13 , wherein the two curved surfaces of the reflector are tilted by an angle with respect to the central axis in such a way that the reflector reflects the focused light to the photovoltaic cell, and wherein the angle of tilt satisfies the following equation:
β
=
δ
-
sin
-
1
(
1
n
sin
(
δ
-
θ
)
)
,
wherein β is the angle, δ is an angle with respect to a plane of the first side to the optical body, n is a refractive index of the optical element, and θ is an acceptance half-angle.
15 . A method of concentrating light, the method comprising:
exposing a device comprising a reflector and an optical body having a conical surface to incident light rays such that the light rays enter the optical body through the conical surface and reflect off the reflector, wherein the reflector comprises a curved surface comprising a cross section about a central axis of the device comprising at least two substantially parabolic curves; and
collecting the reflected light rays at a receiver positioned on an opposing side of the optical body from the reflector, wherein the receiver is a photovoltaic cell and covers at least a portion of a first side of the optical body.
16 . The method of any of claims 15 , wherein the two curves of the reflector are tilted by an angle with respect to the central axis in such a way that the reflector reflects the light rays to the receiver, and wherein the angle of tilt satisfies the following equation:
β
=
δ
-
sin
-
1
(
1
n
sin
(
δ
-
θ
)
)
,
wherein β is the angle, δ is an angle with respect to a plane of the first side to the optical body, n is a refractive index of the optical body, and θ is an acceptance half-angle; and
wherein the light rays in the optical body are subject to total internal reflection.
17 . A method of making a device for concentrating light, the method comprising:
aligning a receiver normal to a central axis on a first side of an optical body;
positioning a reflector proximal to an opposing second side of the optical body, wherein the second side of the optical body comprises a curved surface having a cross section comprising a plurality of substantially parabolic curves extending along a length of the second side of the optical body and converging at the central axis,
wherein optical body comprises a conical surface extending from the first side to the second side such that the second side is larger than the first side and wherein the plurality of substantially parabolic curves are oriented relative to the conical surface and the central axis such that incident light within an acceptance half angle of the central axis is refracted through the conical surface and reflected by at least the reflector to the receiver.
18 . The method of claim 17 , further comprising filling the optical body with a dielectric material.
19 . The method of claim 17 , wherein the curved surface of the optical body comprises a first parabolic curve and a second parabolic curve, and wherein each respective parabolic curve is symmetric about a respective internal axis.
20 . The method of claim 19 , further comprising tilting each parabolic curve at an angle that satisfies the following equation:
β
=
δ
-
sin
-
1
(
1
n
sin
(
δ
-
θ
)
)
,
wherein β is the angle, δ is an angle with respect to a plane of the first side to the optical body, n is a refractive index of the optical body, and θ is an acceptance half-angle.
21 . A device for concentrating light, the device comprising:
a substantially cone-shaped optical body comprising a first side, an opposing second side extending along a central axis, and a conical surface extending from the first side to the second side such that the second side is larger than the first side;
a photovoltaic cell positioned near the first side of the optical body and oriented towards the second side; and
a Fresnel reflector proximate the second side of the optical body, wherein the Fresnel reflector is configured to reflect light, such that incident light within an acceptance half angle of the central axis is refracted through the conical surface and reflected by the Fresnel reflector towards the photovoltaic cell.
22 . The device of claim 21 , wherein the Fresnel reflector is formed by coating a surface of the second side with a reflective material; and
wherein the surface of the second side comprises a plurality of angled faces.
23 . The device of claim 22 , wherein each of the plurality of angled faces is tilted by an angle with respect to the central axis that satisfies the following equation:
α
=
90
°
+
sin
-
1
(
1
n
(
δ
-
θ
)
)
-
[
δ
+
tan
-
1
(
A
1
G
+
X
Ui
)
]
wherein α is the tilt angle, δ is an angle with respect to a plane of the first side to the optical body, n is a refractive index of the optical body, θ is the acceptance half-angle, A is an aspect ratio of the optical body equal to a length of the optical body from the first side to the second side and divided by a width of the second side of the optical body, G is a geometric gain of the optical body equal to the width of the first side of the optical body divided by the width of the second side of the optical body, Ui is half the width of the first side of the optical body, and X is a distance from the central axis to a center of each respective angled face.