Abstract:
An optical system for a solar energy device to produce electrical energy. The optical system includes an aplanatic optical imaging system, a non-imaging solar concentrator coupled to the aplanatic system and a multi-junction solar cell to receive highly concentrated light from the non-imaging solar concentrator.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     The present invention is concerned with a multi-junction solar cell employing an optical system which provides extremely high solar flux to produce very efficient electrical output. More particularly, the invention is directed to a solar energy system which combines a non-imaging light concentrator, or flux booster, with an aplanatic primary and secondary mirror subsystem wherein the non-imaging concentrator is efficiently coupled to the mirrors such that imaging conditions are achieved for high intensity light concentration onto a multi-junction solar cell.  
         [0002]     Solar cells for electrical energy production are very well known but have limited utility due to the very high Kwh cost of production. While substantial research has been ongoing for many years, the cost per Kwh still is about ten times that of conventional electric power production. In order to even compete with wind power or other alternative energy sources, the efficiency of production of electricity from solar cells must be drastically improved.  
       SUMMARY OF THE INVENTION  
       [0003]     Aplanatic optical imaging designs are combined with a non-imaging optical system to produce an ultra-compact light concentrator that performs at etendue limits. In a multi-junction solar cell system the aplanatic optics along with a coupled non-imaging concentrator produce electrical output with very high efficiency. In alternate embodiments a plurality of conventional solar cells can be used in place of a multi-junction cell.  
         [0004]     A variety of aplanatic and planar optical systems can provide the necessary components to deliver light to a non-imaging concentrator which forms a highly concentrated light output to a multi-junction solar cell. In one embodiment a secondary mirror is co-planar with the entrance aperture, and the exit aperture is co-planar with the vertex of the primary mirror. It is readily shown on general grounds that for the most compact imaging system with a primary and secondary mirror the ratio of depth to diameter is 1:4.  FIG. 1  exemplifies this relation. In a preferred embodiment the inter mirror space is filled with a dielectric with index of refraction, n, such that the numerical aperture (“NA”) is increased by a factor of n. A non-imaging light concentrator is disposed at the exit aperture of the primary mirror wherein the non-imaging concentrator is a θ 1 /θ 2  concentrator with θ 1 , chosen to match the NA of the imaging stage of the system (sin θ 1 =NA,/n) while θ 2  is chosen to satisfy a subsidiary condition, such as maintaining total internal reflection (“TIR”) or limiting the angle of irradiance on the multi-junction solar cell, or allowing radiation to emerge to accommodate a small air gap between the concentrator and the multi-junction solar cell (or the light source for the illuminator form of the invention described hereinafter).  
         [0005]     This system with its combination of elements enables employment of the highly efficient multi-junction solar cell such that a very intense solar flux can be input to the solar cell by the non-imaging light concentrator which is coupled to an aplanatic and planar optical subsystem. While multi-junction solar cells are about 100 times more expensive than conventional cells on an area basic, the system described herein can provide highly concentrated sunlight, such as at least about several thousand suns, so that the multi-junction cell cost becomes very attractive commercially. The optical system therefore provides the light intensity needed to achieve commercial effectiveness for solar cells. It should also be noted that the above-described optical system also can be employed as an illuminator with a light source disposed adjacent the light transformer.  
         [0006]     Objectives and advantages of the invention will become apparent from the following detailed description and drawings described hereinbelow.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]      FIG. 1  illustrates an aplanatic optical system with an associated non-imaging concentrator coupled to a multi-junction solar cell; and  
         [0008]      FIG. 2  is a detail of the non-imaging concentrator. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0009]     An optical system  10  constructed in accordance with one embodiment of the invention is shown in  FIG. 1 . A secondary mirror  14  is co-planar with an entrance aperture  12  of a primary mirror  20 . The focus of the combination of the primary mirror  20  and the secondary mirror  14  resides at the center of an entrance aperture  25  of a nonimaging concentrator  24  best seen in  FIG. 2  (described below in detail). The final flux output which may be considered the nominal “focus” of the optical system  10  of the primary mirror  20 , secondary mirror  12 , and the nonimaging concentrator  24  is produced at the exit aperture  16  which intersects the vertex  18  of the primary mirror  20 . The vertex  18  is a point located at the intersection of the primary mirror  20  and the optic axis  26 . The primary mirror  20  is interrupted to accommodate the concentrator  24 . In the preferred embodiment, the vertex  18  is also at the center of the exit aperture  32 . Solar radiation uniformly incident over angle 2θ 0  (the convolution of the solar disk with optical errors) is concentrated to the focal plane where it is distributed over angle 2θ 1 . If we fill intervening space with dielectric  22  of index of refraction (n), the numerical aperture (NA) is increased by n. For typical materials, this is a factor between about 1.4 and 1.5 which is significant since the corresponding concentration (for the same field of view) is increased by n 2 ˜2.25 (provided the absorber is optically coupled to a light transformer or a concentrator  24 ). In a preferred embodiment, the non-imaging concentrator  24  is disposed at the exit aperture  16  and has another entrance aperture  25 . This concentrator  24  is most preferably a θ 1 /θ 2  non-imaging concentrator where θ 1  is chosen to match the numerical aperture (NA 1 ) of the imaging stage portion of the optical system  10  with the primary mirror  20  and the secondary mirror  14  where (sin θ 1 )=NA 1 /n). The θ 2  is chosen to satisfy a subsidiary condition, such as maintaining total internal reflection (TIR) or limiting angles of irradiance onto a multi-junction cell  26 , or allowing radiation to emerge to accommodate a small air gap between the concentrator  24  and the multi-junction solar cell  26  (or the light source  30  for the illuminator form of the invention). The concentration or flux boost of the terminal stage approaches the fundamental limit of (sinθ 2 /sinθ 1 ) 2 . The overall concentration can approach the extendue limit of (n/sinθ 0 ) 2  where sinθ 0 =n sinθ 1 . In an alternate embodiment, the multi-junction cell  26  can be a conventional small solar cell. In another embodiment the non-imaging concentrator  24  can be a known tailored non-imaging concentrator.  
         [0010]     In the optical system  10 , both the entrance aperture  14  and the exit aperture  16  are substantially flat, making this a straightforward case to analyze. In fact, the preferred optical system  10  has a design which falls under the category of well-known θ 1 /θ 2  non-imaging concentrators. The condition for TIR is 
 
θ 1 +θ 2  ≦π−2θ c    (1) 
 
 where θ c  is the critical angle, arc sin (1/n). 
 
         [0011]     In many cases of practical importance the TIR condition is compatible with limiting the irradiance angle to reasonable prescribed values. Since the overall optical system  10  is near ideal, the overall NA is NA 2 =n sin (θ 2 )≃n when θ 2  is close to π/2. In an alternative embodiment a reflective surface  31  of the concentrator  24  need not be such that TIR occurs. In this alternative embodiment the exterior of the θ 1 /θ 2  concentrator, the reflective surface  31  can be a silvered surface, thereby not restricting θ 2  but incurring an optical loss of approximately one additional reflection (˜4%).  
         [0012]     The overall optical system  10  is near-ideal in that raytraces of both imaging and nonimaging forms of the concentrator  24  reveal that skew ray rejection does not exceed a few %. Co-planar designs can reach the minimum aspect ratio (f-number) of ¼ for the selected concentrator  24  that satisfies Fermat&#39;s principle of constant optical path length. By tracing paraxial rays from the two extremes of (1) the rim of the primary mirror  20  and (2) along optic axis  36 , and stipulating constant optical path length to the focus, it is straightforward to show that (a) the distance from the primary&#39;s vertex  18  to the entrance aperture  12  cannot be less than ¼ of the entry diameter, and (b) the compactness limit requires co-planarity. Because such high-flux devices will ultimately be constrained by dielectric thickness (volume), we can describe various embodiments for the preferred co-planar units.  
         [0013]     The design choice for θ 1  has considerable freedom despite the co-planarity constraint. The most practical design when accounting for fragility, cell attachment and heat sinking would appear to site the PV absorber at the vertex  18  of the primary mirror  20 . For a design so constrained, there is a tradeoff between increasing θ 1  and shading by the secondary mirror  14 . For example, for shading ≦3%, θ 1  ≦24°. Taking n≈1.5, we have θc≈42°. Then from Eq (1), θ 1 +θ 2 ≦96°. The illustrative case in  FIG. 1  has θ 1 =24°, θ 2 =72° and 3% shading, with (n sin(θ 2 )) 2  =2.0 being quite close to the étendue limit. Perhaps the simplest terminal concentrator  24  is a frustrum (truncated V-cone). However, the frustrum depth needed to realize the maximum concentration enhancement is substantially greater than the corresponding θ 1 /θ 2  design (for the parameter ranges considered here) if both light leakage and excessive ray rejection are to be avoided.  
         [0014]     Manufacturing simplicity and cost could militate against the optical coupling of the cell  26  to the concentrator  24 . In this case, light is extracted into air and then projected onto the cell  26 . The integral ultra-compact design of  FIG. 1  is still applicable, including siting the cell  26  at the vertex  18  of the primary mirror  20 . The terminal concentrator  24  must then have θ 2 &lt;θc in order to avoid ray rejection by TIR. Accommodating its relatively greater depth (i.e., retaining the same cell position) requires redesigning the imaging dielectric concentrator  24  with its focus closer to the secondary mirror  14 . The corresponding étendue limit for achievable concentration is reduced by a factor of n 2  to (1/sin(θ o )) 2 .  
         [0015]     All dielectrics that are transparent in some wavelength range will have dispersion, a consequent of absorption outside the transparent window. Even for glass or acrylic, where the dispersion is only a few percent, this significantly limits the solar flux concentration achievable by a well-designed Fresnel lens to ≈500 suns. For a planar dielectric form of the concentrator  24 , the only refracting interface is the entrance aperture  12 , normal to an incident beam  28 . At the interface (the entrance aperture  14 ) angular dispersion is, 
 
δθ=−tan(θ)δn/n   (2) 
 
 which is completely negligible since the angular spread of the incident beam  28  is &lt;&lt;1 radian. The dielectric optical system  10  is for practical purposes achromatic. In fact, Equation (2) indicates some flexibility in design. The dielectric/air interface (the entrance aperture  12 ) need not be strictly normal to the beam. A modest inclination is allowable, just as long as chromatic effects, as determined by Equation (2) are kept in bounds. 
 
         [0016]     Non-imaging devices, such as the concentrator  24 , can operate very well at the diffraction limit where the smallest aperture is comparable to the wavelength of light. This is well beyond what would be required for a photoelectric concentrator, but can be useful in detectors at sub-millimeter wavelengths, which is a plausible application for the embodiments herein. With the wide range of scales available, the power densities on the multi-junction cell  26  are about 1 watt (electric) per square mm, providing care is taken in designing the tunnel diode layers separating the junctions. This would imply a solar flux ≈3330 suns with a geometric concentration Cg ≈4600 (taking a 30% system efficiency to electricity from a nominally 40% efficient cell which accounts for losses from mirror absorption, Fresnel reflections, attenuation in the dielectric, shading, cell heating, a few % ray rejection, and a modest dilution of power density in order to accommodate the full flux map in the focal plane).  
         [0017]     With a 1 mm diameter cell  26 , the concentrator  24  of  FIG. 1  would be 68 mm in diameter with a maximum depth of 17 mm and a mass per unit area equivalent to a flat slab 8.5 mm thick. Clearly, considerably thinner forms of the concentrator  24  can be designed (for the same cell size) with lower concentration and commensurately reduced power generation densities. The corresponding angular field of view is 
 
θ o ≈Sin(θ o )=n sin(θ 2 )/√ C   g    (3) 
 
 which is ≈21 mrad for the above example, sufficient to accommodate the convolution of the inherent sun size (4.7 mrad) with liberal optical tolerances. A tighter optical tolerance would generate a smaller spot on the cell  26 . Fortunately, experiments have shown that cell performance can be relatively insensitive to such flux inhomogeneities even at flux levels of thousands of suns. Raytrace simulations of the air-filled concentrator  24  indicated that θ o  can reach 20 mrad before second-order aberrations start to reduce flux concentration noticeably. The corresponding threshold here would be nθ o ≈30 mrad. The cell  26  itself might be one or several mm 2 . Since the planar concentrator volume grows as the cube of the cell size, this is an engineering optimization. In any case, the heat rejection load of a few watts can be dissipated passively such that temperature increases do not exceed around 30 K. 
 
         [0018]     So far, the optical system  10  has been viewed as axisymmetric, with circular apertures and circular ones of the cell  26 . Given the relative ease of reaching high flux levels, maximizing collection efficiency is paramount, including concentrator packing within modules. Also, given that economic fabrication and cutting techniques yield square ones of the cell  26 , one could consider concentrating from a square entrance aperture onto a square target. Producing the same power density at no loss in collection or cell efficiency then ordains increasing geometric concentration by a factor of (4/π) 2 ≈1.62 (or one could dilute power density at fixed geometric concentration).  
         [0019]     High-NA 1  co-planar designs are possible, but only when the focus is well recessed within the primary. Eq (1)—and hence TIR—cannot be satisfied, so the terminal concentrator  24  would need to be externally silvered (and no terminal booster is required as NA 1 Δ1). The dielectric  22  in the central region can be removed while preserving the factor of n 2  amplification in concentration. Cell attachment and heat sinking would be considerably more problematic than in the design of  FIG. 1 .  
         [0020]     The planar all-dielectric optical system  10  presented here embodies inexpensive high-performance forms that should be capable of (a) generating about 1 W from advanced commercial 1 mm 2  solar cells  26  at flux levels up to several thousand suns, (b) incurring negligible chromatic aberration even at ultra-high concentration, (c) passive cooling of the cell  26 , (d) accommodating liberal optical tolerances, (e) mass production with existing glass and polymeric molding techniques, and (f) realizing the fundamental compactness limit of a ¼ aspect ratio.  
         [0021]     In addition to the embodiment described hereinbefore, in reverse the optical system  10  can be a compact collimator performing very near the etendue limit. A light source  30  (shown in phantom in  FIG. 2 ), positioned near the “exit” aperture  32  of the non-imaging concentrator  24 , can be a light emitting diode. In general the optical system  10  can be a light transformer, either collecting light for concentration downstream from the non-imaging concentrator  24  or generating a selected light output pattern in the case of the light source  30  dispersed near the “exit” aperture  32  of the non-imaging concentrator (now an “illuminator”)  24  which would then output light in the desired manner. Such collimators would find many applications in illumination systems to create a desired pattern.  
         [0022]     The following non-limiting examples are merely illustrative of the design of the system.  
       EXAMPLE 1  
       [0023]     The optical space is filled with the dielectric  22 , i.e., the planar non-imaging concentrator  24  resembles a slab of glass. The multi-junction technology lends itself to small solar cell sizes. This size relationship works better since the high current has a shorter distance to travel, mitigating internal resistance effects. Consequently, it is preferable that the cells  26  are in the one to several square mm sizes. The design choice for NA 1  has considerable freedom, a trade-off with shading by the secondary mirror  12 , but is typically in the range of about 0.3 to 0.4. Taking n≈1.5, a typical value for glasses (and plastics) we have θ c ≈42 0 . Then from Equation (1), (θ 1 +θ 2 )≦96 0 , we take NA 1 =0.4n, θ 1 ≈23.5 0  and θ 2  can be as large as 72 0 , a perfectly reasonable maximum irradiance angle on the multi-junction solar cell  26 . At the same time, NA 2 ≈0.95n, within 5% of the etendue limit.  
       EXAMPLE 2  
       [0024]     In another embodiment the non-imaging optical concentrator (or illuminator) is a cylinder with θ 1 =θ 2 . The angular restrictions imposed depend on the desired conditions. If TIR is desired and the solar cell is optically coupled to the multi-junction solar cell  26  (or the light source  30  for the illuminator), θ 1  should not exceed (90 0 −θ c ) ≈48 0 . If TIR is desired and there is a small air gap between the concentrator and the multi-junction solar cell  26  (or the light source  30  for the illuminator), θ 1  should not exceed θ c ≈42 0 . If the cylinder is silvered and the concentrator is optically coupled to the multi-junction solar cell  26  (or the light source  30  for the illuminator) there is no restriction. If the cylinder is silvered and there is a small air gap between the concentrator and the multi-junction solar cell  26  (or the light source  30  for the illuminator), θ 1  should not exceed θ c ≈42 0 .  
       EXAMPLE 3  
       [0025]     In another embodiment, radiation is allowed to emerge to accommodate a small air gap between the concentrator and the multi-junction solar cell  26  (or the light source  30  for the illuminator), then θ 1  should not exceed θ c ≈42 0 . Let θ 2 =39 0  and θ 1 =23.5 0  as before. Then NA 2 =n sin( 39   0 )=0.94, which is within 6% of the etendue limit.