Aplanatic optics were invented over a century ago, motivated principally to achieve high-fidelity imaging in telescopes, microscopes and cameras. Aplanats are designed to completely eliminate the two leading orders of geometric aberration - spherical and comatic - and the simplest designs comprise two contours that can be reflective and/or refractive. Aplanats of high radiative efficiency can also approach the thermodynamic limit to flux concentration and light collimation - of particular value in nonimaging applications such as solar energy collection, light-emitting-diode collimation, and infrared technology. Recently, it was discovered that the original aplanatic mirrors and lenses cover only a small spot in a rich landscape of fundamental categories of optical devices, which opened a broad spectrum of powerful new designs. In this presentation we review these advances, and summarize the complete classification schemes that have now been elucidated for aplanats. They include examples of practical designs for achieving radiative transfer near the thermodynamic limit in flux concentration and irradiation applications, based on dual-mirror, dual-contour lens and lens-mirror combinations. The representative designs that are illustrated also include the most recent progress in Fresnel (faceted) aplanats, motivated by the quest for progressively more compact optical systems, as well as examples of hybrid designs – combining aplanats of different classifications for enhanced performance.
We identify fundamentally new classes of aplanatic lenses where the focus resides inside the lens. These new aplanatic designs comprise a primary contoured dielectric entry, and a secondary contoured profile that, in general, is mirrored, but also admit solutions satisfying total internal reflection. We show that these aplanatic lenses engender 8 basic, distinct design categories, of which 6 yield physically admissible solutions. Flux concentration for far-field small-angle sources such as the sun and, conversely, narrow-field collimation of wide-angle emitting light sources such as LEDs can approach the thermodynamic limit. Losses due to chromatic aberration are smaller than in conventional lenses of comparable f-number, primarily due to the focus being in the lens. By the same token, exit numerical aperture can be increased by a factor of n (the dielectric's refractive index) - and hence flux concentration can be increased by a factor of n2 - relative to common lenses where the focus resides outside the lens.
We identify and evaluate a variety of efficient and feasible micro-optics for confining the radiative emission of solar cells. The key criteria used for assessing viable designs are (1) high optical efficiency for both the transmission of impinging solar beam radiation and the external recycling of isotropic cell luminescent emission; (2) liberal optical tolerance; (3) compactness; and (4) being amenable to fabrication from existing materials and manufacturing processes. Both imaging and nonimaging candidate designs are presented, and their superiority to previous proposals is quantified. The strategy of angular confinement for boosting cell open-circuit voltage—thereby enhancing conversion efficiency—is limited to cells where radiative recombination is the dominant carrier recombination pathway. Optical systems that restrict the angular range for emission of cell luminescence must, by reciprocity, commensurately restrict the angular range for the collection of solar radiation. This, in turn, mandates the introduction of concentrators, but not for the objective of delivering concentrated flux onto the cell. Rather, the optical system must project an acceptably uniform spatial distribution of solar flux onto the cell surface at a nominal averaged irradiance of 1 sun.
Solar rectifying antennas constitute a distinct solar power conversion paradigm where sunlight’s spatial coherence is a basic constraining factor. In this presentation, we derive the fundamental thermodynamic limit for coherence-limited blackbody (principally solar) power conversion. Our results represent a natural extension of the eponymous Landsberg limit, originally derived for converters that are not constrained by the radiation’s coherence, and are irradiated at maximum concentration (i.e., with a view factor of unity to the solar disk). We proceed by first expanding Landsberg’s results to arbitrary solar view factor (i.e., arbitrary concentration and/or angular confinement), and then demonstrate how the results are modified when the converter can only process coherent radiation. The results are independent of the specific power conversion mechanism, and hence are valid for diffraction-limited as well as quantum converters (and not just classical heat engines or in the geometric optics regime). The derived upper bounds bode favorably for the potential of rectifying antennas as potentially high-efficiency solar converters.
Enhancing solar cell conversion efficiency by angular confinement of radiative emission (photoluminescence) requires a combination of (1) high external luminescent efficiency, and (2) optics that can substantially and efficiently limit the angular range of cell luminescence. After covering the basic principles and recent proposals for suitable micro-optics, we investigate an assortment of alternative micro-optical designs that can improve device compactness considerably, which would reduce the amount of material required and would ease micro-fabrication, while offering liberal optical tolerance and high collection efficiency.
The spatial coherence of solar beam radiation is a key constraint in solar rectenna conversion. Here, we present a derivation of the thermodynamic limit for coherence-limited solar power conversion – an expansion of Landsberg’s elegant basic bound, originally limited to incoherent converters at maximum flux concentration. First, we generalize Landsberg’s work to arbitrary concentration and angular confinement. Then we derive how the values are further lowered for coherence-limited converters. The results do not depend on a particular conversion strategy. As such, they pertain to systems that span geometric to physical optics, as well as classical to quantum physics. Our findings indicate promising potential for solar rectenna conversion.
Efficiency bounds for the rectification (AC to DC conversion) efficiency of non-coherent broadband radiation are derived, motivated by determining a basic limit for solar rectifying antennas. The limit is shown to be 2/π for a single full-wave rectifier. We also derive the increase in rectification efficiency that is possible by cascading multiple rectifiers. The approach for deriving the broadband limit follows from an analysis of sinusoidal signals of random phase. This analysis is also germane for harvesting ambient radio-frequency radiation from multiple uncorrelated sources.
We report the first direct measurement of the spatial coherence of solar beam radiation. Although often perceived as
incoherent, direct sunlight exhibits spatial coherence at a sufficiently small scale. These dimensions were recently
derived theoretically to be around two orders of magnitude greater than the wavelength. The partial coherence of
sunlight raises tantalizing prospects for a new paradigm for solar power conversion via the antenna effect exploited so
successfully in radio-frequency and microwave technologies (albeit at frequencies of order 1 PHz for solar). After
reviewing the equal-time mutual coherence function of sunlight, we explain the particular suitability of a lateral cyclicshearing interferometer wherein the solar beam is split into two parts that are subsequently recombined with a relative
lateral displacement. The method is relatively uncomplicated, inexpensive and obviates the problem of component
dispersion (potentially problematic for a light source as broadband as sunlight). The experimental results are in good
agreement with the recent theoretical predictions.
The tantalizing prospect of using antennae for solar power conversion received preliminary consideration, but was not
pursued in earnest due to the daunting challenges in suitable materials, fabrication procedures, and the rectification
(conversion to DC power) of frequencies approaching 1 PHz (1015 s-1). Recent advances in nano-materials and nano-fabrication
technologies have prompted revisiting the solar antenna strategy. Coherence theory informs us that even
ostensibly incoherent radiation is partially coherent on a sufficiently small scale. Based on a generalized broadband
analysis, we show how the partial coherence of sunlight, exhibiting transverse partial coherence on a scale of two orders
of magnitude larger than its characteristic wavelengths, impacts the potential of harvesting solar energy with aperture
antennae (coherent detectors), and establish a fundamental bound. These results quantify the tradeoff between
intercepted power and averaged intensity with which the effect of increasing antenna size (and hence greater system
simplicity) can be evaluated.