Heylal Mashaal

Fundamental bounds for antenna harvesting of sunlight

We evaluate fundamental bounds for using aperture antennas to harvest sunlight based on a generalized analysis of the partial coherence of solar radiation.

First direct measurement of the spatial coherence of sunlight.

Direct sunlight is often deemed incoherent, hence unsuitable for antenna power conversion. However, all radiation exhibits spatial coherence when detected on a sufficiently small scale. We report the first direct measurement of the spatial coherence of solar beam radiation, achieved with a customized tabletop cyclic-shearing interferometer. Good agreement is found between experiment and theory, with promising ramifications for solar aperture antennas.

Basic limit for the efficiency of coherence-limited solar power conversion.

A basic upper bound for the efficiency of solar power conversion (generally, from any blackbody source) is derived, generalizing the Landsberg limit to arbitrary solar and sky view factors (e.g., arbitrary concentration or angular confinement), and to coherence-limited devices such as rectifying aperture antennas.

Rectenna harvesting of sunlight

A novel paradigm for converting solar radiation to electrical power using optical rectifying antennas, or ‘rectennas,’ was first proposed by Robert Bailey in 1972.1 An antenna is a device that converts electromagnetic waves propagating in free space into guided waves propagating in transmission lines. A rectifier is coupled to the antenna to provide conversion from highfrequency AC to usable DC. Limitations of materials and efficiency prevented solar energy pioneers from using rectennas. But the recent confluence of microwave conversion efficiencies exceeding 90% with recent advances in nanomaterials and nanofabrication technologies prompt revisiting the prospect of optical rectennas. We hope eventually to mimic the analogous familiar radio and microwave antenna and rectification processes. But there are prodigious, unsolved challenges related to the nominal lack of coherence of solar radiation, as well as a lack of rectification materials for the frequencies of visible light. Such frequencies approach 1PHz (1015s 1). To date, no one has developed feasible rectification for 0.1PHz. Even 0.01PHz is a struggle for which there are only inefficient, benchtop results. Rectification around 1PHz still constitutes a daunting challenge in materials science. The potential payoff would be a fundamentally new solar power conversion technology that could use relatively simple materials, at efficiencies rivaling or exceeding those of photovoltaic cells. In this article we examine the partial coherence of sunlight and what limitations that coherence sets on the potential of rectenna harvesting of solar energy. Sunlight (or blackbody radiation in general) is commonly viewed as incoherent, meaning the individual lightwaves in sunlight have no particular phase relationship with each other. But in fact sunlight exhibits partial spatial coherence on a sufficiently small scale, as predicted by the van Cittert-Zernike theorem. The coherence area is usually defined as the first null of the equal-time mutual coherence function between points on the aperture antenna, corresponding to a radius of 65 m for quasimonochromatic (QM) light of wavelength D 0:5 m.2, 3 Since the QM assumption is not valid for broadband sunlight, this Figure 1. Equal-time mutual coherence function (EMCF), normalized to its maximum value at zero radius, for individual wavelengths (broken colored curves) and broadband sunlight (solid black curve). For the latter, the oscillations are essentially averaged out, and the first null is at a radius of 200 m.

New types of refractive-reflective aplanats for maximal flux concentration and collimation.

We identify and evaluate new categories of dual-contour refractive-reflective aplanatic lenses, some of which can satisfy total internal reflection at the secondary surface. Raytrace simulations for a representative design in both solar concentrator and collimator (illumination) mode reveal high efficiency while approaching the thermodynamic limit for radiative transfer.

Micro-optical designs for angular confinement in solar cells

Abstract. 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.

Efficiency limits for the rectification of solar radiation

Efficiency limits for rectifying (converting AC to DC) incoherent broadband radiation are presented, prompted by establishing a fundamental bound for solar rectennas. For an individual full-wave rectifier, the bound is 2/π. The efficiency boosts attainable with cascaded rectifiers are also derived. The derivation of the broadband limit follows from the analysis of an arbitrary number of random-phase sinusoidal signals, which is also relevant for harvesting ambient radio-frequency radiation from a discrete number of uncorrelated sources.

Basic categories of dual-contour reflective-refractive aplanats.

We derive, illustrate, and analyze previously unrecognized basic categories of dual-contour reflective-refractive aplanats, evaluated for solar concentration.

Solar and Thermal Aperture Antenna Coherence Performance Limits

Although direct sunlight is commonly viewed as incoherent—and therefore ostensibly not suitable for antenna collection—all radiation exhibits spatial coherence when collected on a sufficiently small scale. A first step in evaluating the potential of solar aperture antennas for light harvesting is establishing basic performance bounds based on a generalized analysis of the partial coherence of broadband solar radiation, which comprises a substantial part of this chapter. Indeed, direct sunlight exhibits spatial coherence on a scale that is two orders of magnitude larger than its characteristic wavelengths. This in turn indicates the feasibility of using optical concentrators that can effectively replace antenna and rectifier elements by as much as a factor of 10,000. Our theoretical results quantify the fundamental tradeoff between aperture antenna size and intercepted power, which provides a measure of coherence efficiency. They also illustrate why applying the notion of aperture antennas for collecting radiation from conventional thermal sources is not feasible. Our analytic computations are followed by details of the first direct measurement of the spatial coherence of solar beam radiation, with a novel cyclic-shearing interferometer. These experimental results validate the theoretical predictions, with promising consequences for solar aperture antennas.

Aplanatic lenses revisited: the full landscape

The full scope of solutions for dual-contour aplanatic lenses that can approach the basic limit for radiation transfer are identified, analyzed, and illustrated. Complementary solutions are shown to yield lenses that are either monolithic or have two refractive contours separated by an air gap. The performance of a promising representative design for LED collimation is presented.