US20060174867A1 - Nonimaging solar collector/concentrator - Google Patents

Abstract

A non-imaging solar collecting and concentrating apparatus for use in i.e., passive lighting and solar power applications that is relatively immune from optical incidence angle(s) and therefore does not need to track the movement of the sun to efficiently collect and concentrate solar energy. The apparatus includes a non-planar support structure having a sun-facing entrance and an energy-outputting exit. An interior surface of the structure includes a graded-index structure(s) and/or diffraction grating(s) to enhance the collection and concentration efficiency.

Description

CROSS REFERENCE TO RELATED APPLICATIONS
• This application claims the benefit of U.S. Provisional Patent Application No. 60/639,272 filed Dec. 28, 2005.
FIELD OF THE INVENTION
• This invention relates generally to the field of solar energy and in particular to an apparatus that efficiently collects and concentrates incident optical energy without the use of imaging devices.
BACKGROUND OF THE INVENTION
• The efficient collection, concentration and distribution of solar energy remain some of the most significant, yet long-unfulfilled problems of contemporary society. Its importance cannot be overstated. As fossil fuels continue to dwindle in supply and contribute to undesirable environmental effects, the importance of solar energy will only increase. Efforts to realize the potential(s) of solar energy—and in particular efforts directed toward the efficient collection and concentration of solar energy—are therefore of great significance.
• The prior art has produced a variety of solar energy collectors and concentrators having a solar energy receiver upon which solar energy to be collected is directed, where only a portion of the receiver surface has solar energy directed upon it at a particular instant. Losses result from those portions of the receiver surface(s) which do not have solar radiation directed thereupon.
• For example, one type of solar collector is the familiar parabolic mirror which directs radiant energy incident theron to a particular point or focus. Such a mirror is usually stationary and—due to the motion of the sun—the focus will move over a particular path each day. As a result, the prior art positioned receivers to cover the particular focus path(s), and only those portions of the receiver(s) upon which the focus was incident would actually be affected by the incident energy.
• U.S. Pat. No. 4,052,976 which describes a Non-Tracking Solar Concentrator With a High Concentration Ratio attempted to address a number of the problems inherent in the art by providing a plurality of energy absorbers at the focus of a parabolic reflector. The absorbers were position so that the focus, which moved as the sun moved, was incident on at least one, and ideally no more than two, of the absorbers at any one instant.
• U.S. Pat. No. 4,267,824 describes a Solar Concentrator constructed from relatively thin, flexible material inflatable to an upright position in which it is generally conical in shape, convergent from its upper to lower end. The inflated device includes a transparent top and a highly reflective inner conical surface which reflects downwardly and thereby concentrates radiant energy.
• Axially-Graded Index Couplers for Solar Concentrators were disclosed in U.S. Pat. No. 5,936,777 which issued to Joseph Dempewolf on Aug. 10, 1999. The coupler(s) disclosed therein included a single lens component, comprising two axially-graded index of refraction elements, each having a low refractive index surface and a high refractive index surface and joined along their respective high refractive index surfaces. As disclosed, the optical coupler(s) so constructed are useful as solar concentrators for concentrating solar radiation onto a solar sell or other solar-receptive medium.
• More recently, somewhat complex arrangements have been described, such as the Solar Radiation Concentrator and Method of Concentration Solar Radiation which was disclosed in U.S. Pat. No. 6,820,611 which issued to M. Kinoshita on Nov. 23, 2004. In particular, the patentee therein describes a plurality of reflectors disposed on reflector arrangement surfaces and a plurality of reflector vertical bars, connected to the plurality of reflectors in addition to a number of motion members that perform motions along various routes according to variations in the incident angle of the incident solar radiation.
• Finally, G. A. Rosenberg discloses a Device For Concentrating Optical Radiation in U.S. Pat. No. 6,274,860 which issued on Aug. 14, 2001. More specifically, the optical radiation concentrating device comprises a holographic planar concentrator including a planar, highly transparent plate and at least one multiplexed holographic optical surface mounted on a surface thereof. The multiplexed holographic optical film has recorded thereon a plurality of diffractive structures having one or more regions which are angularly and spectrally multiplexed. The recording of the diffractive structures is tailored to the intended orientation of the holographic planar concentrator and at least one solar energy collecting device is mounted along at least one edge of the holographic planar concentrator.
• Despite these developments however, there exists a continuing need for solar collecting and concentrating structures providing high efficiency, while eliminating the need to track the source of the solar energy. Such structures would represent a significant advance in the art.
SUMMARY OF THE INVENTION
• I have developed, in accordance with the principles of the invention, a solar collecting and concentrating apparatus for use in i.e., passive lighting and solar power applications. In sharp contrast to prior art devices, my inventive collector and concentrator is a non-imaging device. Consequently it is relatively immune from solar incidence angle(s) and therefore does not need to track the movement of the sun to efficiently collect and concentrate solar energy.
BRIEF DESCRIPTION OF THE DRAWING
• A more complete understanding of the present invention may be realized by reference to the accompanying drawing in which:
• FIG. 1 shows a perspective view of a passive lighting system including a gradient index device constructed according to the teachings of the present invention;
• FIG. 2a,2band2cis a schematic diagram showing the gradient index device ofFIG. 1 collecting incident solar energy at various azimuth angles of the sun;
• FIG. 3 is a schematic diagram showing light traversing the gradient index structure such as that ofFIG. 2, and its subsequent collection and coupling;
• FIG. 4 is a schematic diagram depicting the preferential reflection of light from a diffracting grating;
• FIG. 5 is a schematic diagram of a gradient index structure including diffraction grating(s), according to the present invention;
• FIG. 6 is a schematic of an alternative embodiment of the present invention including diffraction grating(s) inscribed on an interior surface of a conical structure;
• FIG. 7 is a schematic depicting diffraction principles according to the present invention;
• FIG. 8 is a graph showing the simulated optical efficiency of a diffractive solar concentrator according to the present invention as compared with a reflective concentrator;
• FIG. 9 is a cross section of a grating depicting various design parameters according to the present invention;
• FIG. 10 is a cross section of another grating according to the present invention;
• FIG. 11 is graph depicting concentrator length to diameter ratio/efficiencies;
• FIG. 12 is a series of graphs depicting length-to-diameter ratio results with non-zero loss values;
• FIG. 13 is a graphs depicting concentrator efficiency as a function of grating diffraction efficiency;
• FIG. 14 shows schematics of alternative concentrator geometries including a paraboloid and exponential conic;
• FIG. 15 is a cross sectional view of a concentrator depicting rays of light being concentrated on a representative structue;
• FIG. 16ais cross sectional view a concentrator having a mixed geometry structure where the;
• FIG. 16bis a cross sectional view of the concentrator of16bwith a chirp introduced in a straight portion;
• FIG. 17 is a cross sectional view of a concentrator having both CEC and straight cone characteristics;
• FIG. 18 is a cross sectional view depicting the incidence of light upon combined cone;
• FIG. 19ais graph depicting incidence vs.loss 2%;
• FIG. 19bis a graph depicting incidence vs. loss 7%;
• FIG. 20 is a cross sectional view of a concentrator having a “box” top; and
• FIG. 21 is a cross sectional view of a concentrator having a hexagon shape;
DETAILED DESCRIPTION
• FIG. 1 shows a perspective view of a passive solar lighting system constructed according to the present invention. More specificallycollector cone10 includes a gradedindex medium12 disposed therein. It is noted that thelens12 provides a radial and longitudinal asymmetry to the cone interior index of refraction and acts in a manner substantially the same as a Graded Index (GRIN) Lens.
• Overlying the open top of thecone10 is anoptional lens14 which serves to further direct incident light into thecone10. As a result, incident light passes through thelens14 and is directed into the graded index interior of thecone10 where it is further directed to an output of thecone10 and into a light pipe orfiber bundle18 where it is directed to diffuser20 from which it emanates. Cone output andfiber bundle18 may be made integral or optionally coupled bycoupler18, which provides a suitable opto-mechanical coupling betweenfiber bundle18 and output ofcone10.
• While thisFIG. 1 depicts aconvex overlying lens14, those skilled in the art will readily appreciate that a Fresnel lens structure(s) or others, would suffice as well. In addition, the interior sides ofcone10 are treated/applied/prepared such that they exhibit diffractive orreflective elements22. Consequently, incident light that is not directly directed to output is redirected such that it eventually does exit output where it is coupled intofiber bundle18.
• When integrated into an overall passive lighting system such as that shown inFIG. 1, a mountingfixture24 may be constructed from material having predictable coefficient of thermal expansion such that thecone10 somewhat tracks the motion of thesun26, to further improve its overall effectiveness.
• Turning now to FIGS.2(a) and2(b) it can be seen that for low-angle incidence, a properly-structured gradedindex12 will have the effect of bendinglight rays32 and34 toward the central axis of a GRIN cone. Advantageously, this bending will track with solar motion so that most of the sunlight captured will continue to fall on an aperture at the base of theGRIN cone10, where it may be coupled into a collection mechanism such as afiber bundle18.
• FIGS.2(a) and2(b) also show but one method I have employed to increase the collection efficiency of my inventive GRIN structure. In particular, areflective coating40, is added to the interior sides of theGRIN cone10. Consequently, as light circulates around the interior of theGRIN cone10, light rays reflect from the sides of thecone10 and back towards the center, thereby resulting in a greater bending of the light rays due to the shape of thecone10. Accordingly, a gradual evolution of the angle of an incident ray is changed such that it becomes closer to the acceptance angle of afiber18 or similar optical coupler disposed at an exit of thecone10.
• Through the use of molded plastics and novel manufacturing methods such as photonic bandgap structures where the index variation in the cone is achieved by creating very small voids in the host plastic, various GRIN profiles may be achieved, thereby allowing a greater range of design to accommodate wider collection angles, better peak efficiency, and other desirable performance parameters. Such index profiles might include for example, linear, Gaussian, parabolic or other power series, or other functional index gradients that cannot be achieved through conventional glass manufacturing methods. Similarly, the index profile may be functionally graded along the radius of the cone as well as along its length and around its circumference (azimuthal index variation).
• That said, one skilled in the art will nevertheless readily appreciate that the net effect of my inventiveGRIN cone structure10 will transmit a greater amount of sunlight to a fixed aperture orfiber bundle18 than a stationary lens or reflector such as those used in the prior art. For overhead sun (direct rays36) aGRIN cone10 creates a poor image of the sun (i.e. larger circle of confusion and greater chromatic aberration). Fortunately, such aberration is of little consequence, since the image of the sun is not of interest, but rather just the light from it.
• In fact, and as can be appreciated by those skilled in the art, there is an obvious disadvantage in focusing the sun too tightly on a plastic fiber or fiber bundle or a solar photovoltaic cell, so this built-in aberration provides a failsafe mechanism—namely preventing overheating of the fiber bundle or non-uniform illumination of a solar cell. Furthermore—and of significant advantage—aGRIN cone structure10 such as that shown also allows much greater first surface curvature than with conventional collectors where strong focus is a consideration. As can be appreciated, the greater curvature possible by my inventive GRIN structures offers several advantages, such as a greater profile to capture low incidence rays and greater focal symmetry (e.g. a ball lens vs. a bi-convex lens).
• While the GRIN cone structure is efficient over a wider range of angles than conventional reflective concentrators, there are nevertheless situations in which further improvements may be made. More specifically, at very high incidence angles (i.e., early morning or late afternoon sun), some rays may miss the exit aperture and escape the GRIN cone, as indicated inFIG. 3.
• Of course, though applying areflective coating40 to the sides of theGRIN cone10 is advantageously simple, it nevertheless requires that the angle of theGRIN cone10 must be properly designed to take advantage of the multiple pass focusing of the GRIN structure. As can be readily appreciated, if the angle of theGRIN cone10 is too low (making the sides closer to vertical), then fewer (and perhaps an insufficient number of) reflections will occur. Conversely, if the angle of theGRIN cone10 is too wide, then an undesirable amount of light will reflect out of theGRIN cone10.
• One solution to this problem—according to the present invention—is to make the sides of the cone reflect preferentially at a given angle. This can be achieved by inscribing the sides of a GRIN cone with reflective diffraction gratings. Advantageously, such reflective gratings may be constructed to preferentially reflect incident light at a particular angle(s), thereby ensuring that more light will be coupled into a fiber bundle or similar collector or coupler positioned at an output of the GRIN cone.
• A further improvement of the present invention is to inscribe reflective diffraction gratings in a hollow cone structure such as indicated inFIG. 4. This allows the diffractive effect of the gratings to be compounded every time a light ray strikes the interior surface of the cone. This innovative geometry results in an “integrated diffraction” effect which further directs incoming light over a broad range of angles toward the output of the cone by successive diffractive events.
• By way of some theoretical background, a simple model of a diffraction grating is the grating equation$\begin{array}{cc}\frac{m\lambda }{d}=\sin \alpha +\sin \beta ,& \left(1\right)\end{array}$
  where m is the diffraction order, λ is the wavelength of the incident light beam, d is the groove spacing of the grating, α is the incident angle of the light in the plane perpendicular to the grating, and β is the diffracted angle of the light after it strikes the grating surface.
• As illustrated inFIG. 5, when diffraction occurs, a strong reflection will occur at a larger angle β than the angle α at which a ray is incident. Importantly, one can learn fromrelationship 1 that the reflected maximum does not occur at the angle of incidence to the grating planes, but at an angle where the rays reflected from the grating planes are in phase.
• The quantity$\begin{array}{cc}\frac{m\lambda }{d}=\mathrm{Gm}\lambda =K_g,& \left(2\right)\end{array}$
  is often referred to as the grating vector since the ray vector for the diffracted beam may be computed from the incident vector and this quantity directed perpendicular to the grooves or planes of the grating. This formulation makes clear that in order to induce a preference for diffraction toward the exit aperture of the conic concentrator, a structure similar to a blazed grating, where the grooves have a sawtooth pattern canted in a direction toward the exit of the cone, is preferable to a symmetric structure such as a holographic grating, where the grooves have a sinusoidal profile. The blazed structure of a ruled grating induces an asymmetric diffraction where light incident from the entrance of the cone will be diffracted into an order that lies distal of the specular ray, and light incident from the bottom of the cone will be diffracted into an order which lies proximal to the incident ray relative to the specular reflection, as shown inFIG. 5. This type of diffraction will then lead to the integrated diffraction effect of the cone as described previously.
• Further refinements on this simple picture are also possible. It is known that the general solution to the interaction of light with a diffractive structure is the method of rigorous coupled wave analysis, wherein Maxwell's equations at the diffractive surface are reduced to their time-invariant counterparts, resulting in the Helmholtz equation$\begin{array}{cc}\left(\frac{\partial }{\partial x^2}+\frac{\partial }{\partial y^2}+{\mathrm{<figure-callout\; label="k"\; filenames="US20060174867A1-20060810-D00008.png,US20060174867A1-20060810-D00011.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^2\varepsilon \left(x,y\right)\right)E\left(x,y\right)=0,& \left(3\right)\end{array}$
  where x and y are the spatial coordinates transverse to the propagation of the ray, k₀is the free space wavenumber, ε(x,y) is the spatially-varying dielectric constant of the grating, and E(x,y) is the electric field of the incident light. Typically, the dielectric function has some periodic spatial variation which can be represented mathematically by a series of component functions (such as Tschebyshev or Legendre polynomials), and it is assumed that the field solution may be similarly expanded. The solutions to the diffracted field can then be found by finding solutions to the set of coupled differential equations that result. This is the essence of rigorous coupled wave analysis (RCWA).
• The RCWA formulation allows the construction of solutions to the grating equation where the intensities of the diffracted orders may be designed to favor certain diffraction angles over others, as described in the simple case of the blazed grating above. Other variants include binary amplitude or phase gratings, variably spaced gratings, chirped gratings, apodized gratings, spectrally-selective gratings, grating superstructures, and variable blaze gratings, where the blaze angle is varied while the pitch remains constant. Another such example is a grating structure designed for optimal coupling only in the visible radiation band (400-700 nm), which is at the same time designed for poor performance in the infrared so as to discard incident radiation in the form of heat. Since a purely reflective cone structure (whether a straight conic, paraboloid, or exponential) has poor angular acceptance, the disadvantage of the reflective structure may be used as a selective feature in a diffractive structure of similar geometry.
• Turning our attention now toFIG. 6, there is shown a preferred embodiment of my inventive solar collector/concentrator, which builds upon the concepts and/or principles presented so far. More specifically, the solar collector/concentrator includes acone10, which may advantageously be constructed form a curved diffraction grating such that the rules or lines of the grating12 lie in planes that are substantially perpendicular to theaxis14 of thecone10. Positioned at a base (exit) of thecone10 is asolar cell18, or optical light guide. As can be appreciated, the shape of the concentrator need not be conical, rather it may be made parabolic, hyperbolic, exponential or exhibit another similar geometry.
• FIG. 7 is a schematic depicting the diffraction principles applied in the present embodiment of my invention. In particular, and in sharp contrast to the purely reflective devices of the prior art, my inventive diffractive collector/concentrator employs diffractive surfaces, whereby alight ray40, striking the interior surface of thecone10, will be diffracted into a higher order such that theangle beta42, between the surface normal of thecone10 and correspondinglight ray40. As can be readily appreciated by those skilled in the art—and as noted before—the diffraction has the effect of directing light rays preferentially toward anoutput50 of thecone10.
• Turning now toFIG. 8, there is shown a graph depicting the calculated efficiencies of a diffractive collector/concentrator constructed according to my inventive teachings, and a purely reflective device. As can be observed from that graph, the diurnal efficiency (or angular acceptance) of a concentrator constructed according to my inventive teachings is greatly improved.
• More specifically, using a relatively simple diffraction grating (1000 lines/mm with 70% diffraction efficiency into non-zero orders) in a cone-shaped collector extends the angular cutoff for 70% efficiency to over 80 degrees, versus a standard reflective concentrator for which the 70% cutoff is approximately 10 degrees. As can be readily understood by those skilled in the art, various methods and techniques exist for producing such gratings with engineered diffraction efficiencies in selected orders, including a number which use holographic or embossing techniques that are particularly amenable to scaling for large area manufacture.
• With reference now toFIG. 9, there is shown a cross-sectional view of a grating, along with several design aspects pertinent to blazed ruled gratings that are important to the present invention. Specifically, ruled gratings are typically classified in several categories according to their blaze angle. Low blaze angle gratings usually have very little polarization dispersion but narrow spectral response. High blaze angle gratings have broad spectral response for light polarized perpendicular to the grooves (s-plane) and narrower response for the opposite polarization (p-plane).
• In a preferred embodiment of the present invention, we use low blaze angle gratings to reduce polarization sensitivity and to design a chirp (variation in pitch) in the grating to achieve broader spectral coverage. Generally, triangular or sawtooth blaze gratings have highest efficiency when the blaze angle matches the diffraction angle shift determined by the grating equation (i.e. as a function only of pitch, wavelength, and incident angle), so by modulating the pitch of the grating, the efficiency at any given incident angle can be spread over a wider wavelength band. This type of pitch or blaze variation is a simple matter for a computer-controlled ruling engine.
• A further embodiment of the type of preferential grating used to another preferred embodiment of the invention is illustrated inFIG. 10. This binary grating features a set of step variations where the spacing of adjacent steps a as well as the width of each step b is varied, though the period of the repeating step pattern A is constant across the grating surface. Other variations using the basic model of a step grating such as variation in step height may also be used to obtain the desired diffractive response.
• Such a grating design may be used in the present invention to engineer very specific solutions to the RCWA problem and to produce more desirable diffraction results. One general example of such engineering might be the elimination of negative order diffraction at the expense of more positive orders or greater scattered light in the positive direction. Since the conic geometry is highly tolerant of a wide range of incident angle, the conventional concerns with low stray light and low aberrations (such as ghosts) in grating design are of much lesser importance in this case. In the present teaching, one may learn that the coupling of the conic geometries described herein with unconventional grating design methods may be used to produce a highly efficient collecting and concentrating device.
• At this point we are able to apply my inventive teachings to alternative configurations, and particular different cone-shaped concentrators. Ray tracing models of various “conic” concentrator geometries have been performed to ascertain the angular acceptance, efficiency, and optimal configuration of a solar concentrator based on a multi-pass diffractive technique.
• Perhaps the simplest geometry that may advantageously employ my inventive teachings, is a straight-sided cone having an opening diameter (d_max) to exit diameter (d_min) ratio given by the square root of the desired concentration factor. As an example, for photovoltaic (PV) applications, the maximal loading of standard silicon PV cells is in the range of 25 suns (AM25), which corresponds to an opening/exit ratio of 5.
• When constructing a conical concentrator according to my inventive principles, some of the important construction parameters are the length to opening diameter ratio (D=L/d_max), and the grating parameters including pitch (G), peak diffraction efficiency into specific orders m (η_max(m)), and loss (l). A standard set of these values for commercially available gratings is given in Table 1. From these, other values for different G may be interpolated in order to ascertain the influence of grating pitch on the overall efficiency of the concentrator. The pitch of the grating influences the diffraction angle and therefore the direction of the diffracted ray relative to the exit aperture of the cone. Furthermore, it can be seen fromrelationship 1 that only solutions to the grating equation where K_g≦2 will correspond to physically-realizable diffraction orders, thus limiting the range of incident angles α over which diffraction will occur. Basic optics therefore leads us to suspect that the grating pitch may be the most important parameter in designing a particular concentrator according to my inventive principles, and that there may be a strong optimum or narrow range for grating pitch over which the concentrator will perform efficiently.

  	TABLE 1
  	Pitch (l/mm)	ηmax(typ)	Blaze peak (deg)	ABW (deg)

  	300	90%	5	65
  	600	90%	9	50
  	900	80%	14	60
  	1200	70%	19	60

• In fact, this optimum is only apparent in the presence of loss in the diffractive surface of the device. For a lossless concentrator, lower grating pitch simply results in a requirement for a longer device to reach efficiency near 100%. This effect is illustrated inFIG. 11. At higher grating pitch, the efficiency of the device drops due to the incidence angle cutoff described above. Though not physically realizable, the lossless case illustrates the underlying physics of the impact of grating design on the present invention.
• The effect of loss in the diffractive surface (as may be due to absorption in a reflective coating or backscatter from negative diffraction orders) is to make longer devices and therefore lower grating pitch impractical, so that an optimum range of grating pitch does emerge for a given concentrator geometry. For a simple cone, with modest loss values of 2, 3, 5, and 7% per pass (representative of ideal metallic coatings, such as silver and aluminum), this optimum lies in the range from about 800 l/mm to 1200 l/mm, as shown inFIG. 12. These data represent a weighted average that compensates for the aperture correction of a fixed collection system, proportional to the solar zenith angle. It should be noted that this average does not represent a diurnal average for any given latitude. One feature of interest in all the data sets is that while gratings with higher groove density do tend to have the quickest rise to high efficiency, the highest peak value may shift to gratings of lower pitch as the loss increases. This is due to the geometric relationship between the diffraction angle, diffraction cutoff, and average number of reflections required to transit the cone. The effect of loss is consistent with results known from hollow waveguide manufacture, where coating loss affects the total throughput and effective NA of the guide, however, the diffractive surface improves the coupling efficiency by a significant margin over the state of the art of conventional hollow waveguides.
• Another important parameter is the peak diffraction efficiency, η_max. In a simple model for a blazed grating, the diffraction efficiency into low orders as a function of incident angle may be represented as a Gaussian model for η_m(α), where the peak of the distribution occurs at the incident angle specified by Table 1, with an angular spread as given. These values (along with peak unpolarized efficiencies) are consistent with published data on commercial gratings and with efficiency results obtained from RCWA modeling. The effect of diffraction efficiency and modest loss values is to shorten the length of concentrator required to reach peak efficiency. As an example for a straight cone concentrator with G=1000 l/mm and 2% loss, the dependence of angle-averaged concentrator efficiency on peak grating diffraction efficiency and concentrator D ratio is shown inFIG. 13.
• It is of note that while higher average diffraction efficiency (above about 75%) is desirable, if the loss of the film is low enough, then all of the higher diffraction efficiency values converge to approximately the same value as the length of the cone increases. This illustrates the utility of the present invention in that the various construction parameters of the device such as diffraction efficiency, film loss, and concentrator geometry may be optimized independently in order to compensate for lower than desirable values in one or more of these parameters. This independent optimization is possible with the non-planar geometries specified herein in a way that is not possible with the prior art and which prior publications in this area do not teach.
• A further illustration of this effect may be observed through the study of alternate geometries such as paraboloid or exponential conics, as illustrated inFIG. 14. It is known from previous literature that the conic parabolic concentrator (CPC) is the most efficient reflective concentrator device. The radial profile r(z) of such a device may be described by functions of the form$\begin{array}{cc}r\left(z\right)=r_0-\left(\frac{r_0-r_1}{{\left(L-z_0\right)}^2}\right){\left(z-z_0\right)}^2,& \left(4\right)\end{array}$
  where r₀is the entrance aperture radius, r₁is the exit aperture radius, z is the axial coordinate, z₀is the position of the entrance aperture, and L is the length of the CPC. A three-dimensional conic can be made from this type of function simply by rotating the line described by r(z) through 360 degrees to generate a surface, or by convolving the rotation with an ellipse or other non-circular rotation to generate an azimuthally-asymmetric shape, or by adding an azimuthal asymmetry only to the entrance aperture shape (e.g. r₀(θ) but r₁constant).
• Again, previous teachings may lead skilled practitioners to suspect that a diffractive CPC might be preferable to a comparable straight sided cone, but the interdependence of geometry and diffractive effects in the present invention is more subtle. A straightforward comparison of a symmetric diffractive CPC similar to the conic structure discussed above shows that the CPC requires a longer length to opening diameter ratio to achieve full efficiency and has stronger dependence on the grating pitch.
• FIG. 15 illustrates the reason for this difference in performance. In this case, the reflective efficiency of the CPC, which arises from its parabolic shape in a manner analogous to the optical focusing characteristics of parabolic lamp reflectors (such as automobile headlights), dominates when the incidence angle to the concentrator is low, and when the gratings do not have much effect. The first surface that oblique rays will strike is near the top of the CPC or cone and unlike the straight cone, the CPC has a surface in this region oriented with a normal closer to perpendicular with the cone axis. This means that for a monotonic grating, the angular range over which the first contact surface will have the greatest diffractive effect will occur at higher angles for the CPC than for the straight cone. In the middle range of incident angles, the CPC makes up for the lower diffractive efficiency near the top by having surfaces whose normals are directed substantially more upward (toward parallel with the cone axis) than the straight cone. This means that the monotonic diffractive CPC relies primarily on its reflective characteristics near the top and, particularly for oblique incidence, on its diffractive characteristics near the bottom. In light of this, one would expect the monotonic diffractive CPC not to have significant advantage over a monotonic straight cone, which is indeed the case.
• A comparison of optimal values for a straight cone of length-to-diameter ratio of 2.5 and a diffractive CPC with length-to-diameter ratio of 2.5, shows that the straight cone is roughly at 76% efficient with 5% film loss while the CPC is only 68% efficient with the same loss. In the case of the diffractive CPC, as may be surmised from the foregoing discussion, the grating may be more optimally designed to work with the surface, for example by designing a grating whose pitch and therefore diffracted angles vary continuously along the length of the CPC in proportion to the tilt of the surface normal, resulting in a parabolically-variable grating pitch. Other examples include using a periodically-variable pitch near the top of the CPC to give greater diffraction for the first incident rays over a greater range of angles, along with some other functional gradient designed to take advantage of the CPC curvature near the bottom of the cone. Similar analyses apply to higher powers of the axial coordinate in the radial function, r˜zⁿ, such as cubic (n=3), quartic (n=4), or quintic (n=5) concentrators. Those skilled in the art will appreciate that these are but a few examples of the range of variation possible using my inventive method.
• A second type of device known in the literature is the conic exponential concentrator (CEC), for which the reflective embodiment is of little interest since its angular acceptance and on-axis efficiency are both very poor, typically less than 10 degrees and 50%, respectively. Such a device may be described by mathematical relationships such as
  r(z)=r₀e^{−(z−z0)/b},  (5)
  and
  r(z)=r_a−ae^{−(z−z0)/b},  (6)
  where a and b are constants used to scale the CEC to the desired shape.
• The diffractive CEC, in contrast to the reflective, has very high angular acceptance. As with the diffractive CPC, the interaction of geometric construction and diffractive characteristics leads to new effects in the diffractive CEC that are not obvious from prior art. In this case, the curvature of the inner surface of the CEC is opposite in character to that of the CPC, so that the surface normal near the top of the cone is tilted upward farther than is the case for any point along the CPC or straight cone. This surface tilt in turn lowers the incident angle at which the grating will have strong effect on the first incident rays, at the expense of higher oblique rays, which at very high angles may strike the first surface on the opposite side of the normal vector and therefore will be diffracted out of the concentrator.
• Another embodiment could use a mixed geometry structure, such as a tube and a cone, where the entrance to the concentrator is a straight-sided tube and the bottom a straight-tapered cone, as shown inFIG. 16(a). High incidence angle rays would then diffract at an angle closer to the axis of the cone when striking the flat surface and would be “funneled” as normal by the cone. It will be apparent that this configuration is a very crude approximation to the diffractive CPC, showing the concepts discussed above in greater distinction.
• This configuration also provides a simple example of the mesoscopic grating design that can be used with a simple design such as this. By introducing a chirp in just the top (straight) portion as shown inFIG. 16(b), a greater percentage of incident rays over a greater range of angles will be diffracted when they first strike the cone. Since this primary diffraction event can have a strong influence on the overall efficiency of the device at a given angle, a simple design modification such as this, which combines the shape, dispersive, and coherent properties of the surface, can lead to very useful and novel combinations which are not obvious from prior art.
• Another efficient possibility is that where the dominant effect of the exponential curvature occurs near the top of the cone and the long taper near the exit does little to increase the capture efficiency and increases vulnerability to loss. In this case, a mixture of a CEC with a straight cone as shown inFIG. 17 can be used to both shorten the overall length requirement and improve resistance to loss. As an example, D=3 straight cone performance can be nearly replicated with a mixed CEC-cone of D=2.3.
• Yet another evolution of cone geometry is the bulb shape, wherein a concave structure is built into the side of the cone, as illustrated inFIG. 18. There is a wide range of mathematical expressions which can describe this type of shape, but the three studied herein are as follows.
• Type 1:
  r₁(z)=(a+z)e^−(z−b)/d,  (7)
• Type 2:
  r₂(z)=r₀−k·z+p·z·e^{−[(ƒz−b)2/d2]},  (8)
• Type 3:
  r₃(z)=r₀−k·z+p·e^{−[(ƒz−b)2/d2]}.  (9)
• Clearly, these three equations alone represent a very large parameter space and some of these parameters (such as the offset b and the damping d) may have strong features in their dispersion. Several random permutations of these parameter sets with monotonic gratings have not yielded significantly better overall performance than the straight sided cone, but it is likely that the grating parameters must be designed to take advantage of the different curvatures, as the results given above have shown.
• The angular efficiency profile for different cone geometries is of some interest in evaluating how the total efficiency is distributed and in determining how the shape can be modified to optimize collection throughout the day for different applications.FIG. 19aand19bshow the comparison of angular data for a straight cone, a diffractive CPC, and a diffractive CEC-cone, with comparable D, G, and loss values, all with monotonic grating profiles. The telling features of the combined effect of geometry and diffraction are evident in the comparison of features between the 2% loss curves ofFIG. 19aand the 7% loss values ofFIG. 19b.The straight cone and the CPC have similar performance characteristics (though the CPC is slightly longer) save for the increase in efficiency for oblique incidence in the CPC which is indicative of the grating effect.
• For the CEC-cone, there is a marked difference in the central peak (α near 0, or when the sun is nearly overhead), for which the maximum value is lower than for the CPC or straight cone, but the width is larger (i.e. does not fall as rapidly to lower efficiencies with increasing incidence). There is also a distinct improvement at higher angles due to the grating effect, though at lower incident angles than for the CPC device. At very high angles, the CEC efficiency falls off faster than either the straight cone or the CPC. These effects all serve to illustrate the range of possibilities achievable when a concentrating device is designed according to the principles described in the present invention.
• It is apparent that different combinations of geometry and diffractive effects can produce different diurnal efficiency profiles. For example, the higher central maximum for the straight cone or the CPC may be most suitable for power generation applications where the overall efficiency is optimized for a non-tracking system or the angular acceptance and diffuse solar collection are improved for a quasi-tracking system (increasing the tracking error to a margin of over 20 degrees, compared with conventional imaging dish tracking systems where a 2 degree margin is more often the case).
• On the other hand, the oblique efficiency may be improved at very high incidence angles when the sun is lowest in the sky and least intense using a diffractive CPC device, in order to compensate for low light conditions in a passive lighting system, for example. Angular efficiency may be well controlled over a wide range using a diffractive CEC structure to enhance certain solar incidence ranges, or the broader central maximum may be advantageous in non-tracking applications.
• Since the use of different pitch gratings along the length of the conic concentrator has a decided advantage as discussed above, it is reasonable to ponder whether this may have some effect in a simple straight sided cone. Those skilled in the art might suspect that either a higher or lower grating pitch at the bottom of the cone would help to either ensure that oblique rays hit the exit aperture (in the case of higher pitch) or that a greater percentage of rays would be diffracted at the bottom of the cone in the case of lower pitch.
• In fact, for the straight cone geometry, simple large-scale variations do not have significant effect. Since basic diffraction physics tells us that rays incident at the same angle on different pitch gratings will diffract at different angles, this result has the important implication that even a simple diffractive cone geometry is very efficient at collecting scattered light. As noted previously, a similar design variation applied to a different geometry such as a diffractive CEC could be used to design a broader central acceptance peak with lower oblique efficiency.
• This again illustrates the inventive principle embodied herein that a broad range of geometries, comprising the macroscopic or incoherent part of the optical effect of the device, can be coupled with a range of grating surfaces, comprising the mesoscopic part of the device which determines local optical parameters such as diffraction cutoffs and angles, and with various grating structure designs, comprising the microscopic or coherent part of the optical effect of the device, to produce very different results for different applications. This combination of macroscopic, mesoscopic, and microscopic properties is a key feature in what distinguishes this invention from prior art.
• Since circles and ellipses have a very poor fill factor, it is desirable for power generation applications to look at other surface of rotation geometries such as rectangles and hexagons. Since much of the analysis given above applies to two dimensional problems or three-dimensional problems with full azimuthal symmetry, it may be expected that these geometries will behave very similarly to the round conics.
• In fact, there may be some subtle differences. While the straight-sided “box” concentrator (FIG. 20) does not show significant differences from the straight sides circular cone concentrator in optimal length, the peak efficiencies are slightly lower. These peak are attributable to geometry factors, as the two-dimensional diffraction picture discussed above evolves into a three-dimensional one.
• A simple interpolation would lead knowledgeable practitioners to deduce that a hexagon (FIG. 21) should lie somewhere between a square and a circle. In fact, the reality may be more complex, since the circulation of rays around the hexagon has a different geometric progression than a square or a circle. In this case, it is important to remember that only the component of a ray incident on a diffractive surface that likes the grating perpendicular plane will diffract. This effect can be observed in a marked increase in optimal D ratio for a comparable hex conic versus its circular counterpart. Thus it is also necessary to account for these factors in grating design, potentially by slanting the grating vector (i.e. aligning the grooves at an angle substantially not perpendicular to the cone axis). This again stresses the importance of coupled design of macroscopic and microscopic features of the diffractive concentrator device.
• At this point, while I have discussed and described my invention using some specific examples, those skilled in the art will recognize that my teachings are not so limited. Accordingly, my invention should be only limited by the scope of the claims attached hereto.

Claims (20)

1. An apparatus for collecting solar or other optical radiation comprising:

a curved support structure, defining an interior surface; and

a graded-index medium, disposed throughout the interior of the curved support structure;

such that light rays striking the interior surface of the curved support structure are directed to a common point, said common point being substantially a focal point of the curved surface.

2. The apparatus ofclaim 1, further comprising:

a substantially reflective surface, surrounding the graded-index medium and disposed on the interior surface of the curved support structure.

3. The optical apparatus ofclaim 2, wherein the interior surface comprises a diffractive grating.

4. The optical apparatus ofclaim 3, wherein the diffraction grating has between 100 and 2000 grating lines/mm.

5. The optical apparatus ofclaim 3 where the diffraction grating is blazed or otherwise engineered such that the diffraction to the common point is enhanced.

6. The optical apparatus ofclaim 4 wherein the diffraction grating is a binary or step grating having a set of step width, height, and/or spacing variations.

7. The optical apparatus ofclaim 2 further comprising a lens or transmission grating, overlying the curved support structure.

8. The optical apparatus ofclaim 3 wherein the curved support structure is one selected from the group consisting of: a conic parabolic concentrator (CPC), a simple power series concentrator including cubic, quartic, or quintic; a conic exponential concentrator (CEC), a conical shaped concentrator, a straight cone shaped concentrator, a bulb shaped concentrator, and mixed-geometry shaped concentrators.

9. The optical apparatus ofclaim 3 wherein the concentrator exhibits a radial profile defined by:

r(z)=a+bzⁿ

where a and b are constants determining the entrance aperture radius and the exit aperture radius, z is the axial coordinate, and n is a real number.

10. The optical apparatus ofclaim 4 wherein the diffraction grating is a grating superstructure or quasi-regular array of optical scatterers.

11. A method of collecting solar or other optical energy comprising the steps of:

receiving the optical energy on a substantially non-planar structure having a diffractive surface for receiving the optical energy;

diffracting the optical energy to a collecting point; and

collecting the optical energy into a collector positioned at the collecting point.

12. The method of claim further comprising the steps of reflecting a portion of the solar energy toward the collecting point.

13. The method ofclaim 11 wherein said diffracting step is performed through the effect of a diffractive grating.

14. The method ofclaim 13 wherein said diffractive grating has between 100 and 2000 grating lines/mm.

15. The method ofclaim 11 wherein said diffractive grating is a blazed grating or otherwise engineered such that the diffraction to the common point is enhanced.

16. The method ofclaim 11 wherein said diffractive grating is a binary or step grating having a set of step width, height, and/or spacing variations.

17. The method ofclaim 11 wherein the diffraction grating is a grating superstructure or quasi-regular array of optical scatterers.

18. The method ofclaim 11 further comprising the steps of focusing or directing, through the effect of a lens or transmission grating positioned between the non-planar structure and the optical energy, the optical energy into/onto the diffractive surface.

19. The method ofclaim 11 wherein the curved support structure is one selected from the group consisting of: a conic parabolic concentrator (CPC), a simple power series concentrator including cubic, quartic, or quintic; a conic exponential concentrator (CEC), a conical shaped concentrator, a straight cone shaped concentrator, a bulb shaped concencentrator, and a mixed-geometry shaped concentrator.

20. An optical collector/concentrator comprising:

a curved, means for supporting a diffractive surface wherein said curved supporting means defines an interior surface; and

a means for diffracting light rays, disposed upon the supporting means of the curved support structure;

such that light rays striking the interior surface of the curved support means are directed to a common point, said common point being substantially a focal point of the curved support means

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