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 high-frequency 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 (10^{15}s^{−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 65μm for quasi-monochromatic (QM) light of wavelength *λ*=0.5*μ*m.^{2, 3} Since the QM assumption is not valid for broadband sunlight, this result was recently generalized using a spectrum-integrated version of the van Cittert-Zernike theorem. The proper coherence radius was found to be ∼200*μ*m (see Figure 1).^{4}

The distinct solar conversion mechanisms of solar cells (photonic detectors) vs. rectennas sharpen the role of coherence. Solar cells are insensitive to the phase distribution of the incident radiation field. Their power output is proportional to the integration of the irradiance over their aperture. Conversely, aperture antennas are sensitive to the phase distribution, and their output power is proportional to the integration of the field over their aperture.

**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 ∼200μm.

**Figure 2. **Intercepted power (normalized to the asymptotic quasi-monochromatic value for λ=0.5μm) as a function of antenna radius. (The overall spectral power is equal for all cases.) At small radii, all curves converge to the geometric optics limit, independent of λ, whereas at large radii each curve asymptotes to an area-independent value. The intercepted solar power undergoes a transition from 3D to 1D blackbody radiation as the radius increases from zero to asymptotically large.

**Figure 3.** Coherence efficiency (intercepted power relative to its value in the pure-coherence limit) as a function of antenna radius for broadband solar radiation.

We evaluated the trade-off between the size of an ideal antenna and its intercepted power for both QM and broadband solar radiation (see Figure 2). For the coherent (small-area) limit, the antenna resides within the coherence area, and the intercepted power is given by geometric optics (proportional to area and projected solid angle). For the incoherent (large-area) limit, the antenna is large relative to the coherence area, and the intercepted power is independent of antenna area. Another measure of coherence efficiency is the ratio of the intercepted power to its pure-coherence limit (see Figure 3).

These results help quantify the feasibility of a small number of large-aperture rectennas sized near the spatial coherence area of sunlight, versus the common approach of using many independent sub-wavelength rectennas.^{4} The large-aperture rectenna approach offers massive reductions in the number of antennas, rectifiers, and peripherals needed, as well as a more subtle but significant boost to rectification efficiency as a consequence of the non-linear rectifier response to the higher antenna voltage.

We are currently working on the first-ever experimental measurement of the spatial coherence of direct solar radiation. More ambitious future research will focus on the major challenges of designing and fabricating solar (nano-)antennae, finding optical concentrators that could reduce the number of solar rectennae needed by about a factor of 10,000, and establishing materials and nanostructures able to rectify solar frequencies.

Heylal Mashaal, Jeffrey M. Gordon

Ben-Gurion University of the Negev

Sede Boqer Campus, Israel

Heylal Mashaal is completing his MSc on the rectenna harvesting of sunlight. The principal theoretical results were published elsewhere,^{4} and he is now concluding an attempt at the first direct measurement of the coherence area of sunlight.

Jeffrey Gordon is a professor of energy and environmental physics in the Jacob Blaustein Institute for Desert Research. His research and teaching focus on solar concentrator optics, photovoltaic physics, gradient-index optics, nanomaterial synthesis, and biomedical optics.

References:

1. R. L. Bailey, A proposed new concept for a solar energy converter, *J. Eng. Power* 94, pp. 73-77, 1972.

2. M. Born, E. Wolf,* Principles of Optics*, Cambridge University Press, Cambridge, UK, 2002.

3. J. W. Goodman, *Statistical Optics*, Wiley, New York, 1985.

4. H. Mashaal, J. M. Gordon, Fundamental bounds for antenna harvesting of sunlight, *Opt. Lett.* 36, pp. 900-902, 2011.