# Optical rectennas are not a promising clean energy technology

“Optical rectennas” (or sometimes “nantennas”) are a technology that is sometimes advertised as a path towards converting solar energy to electricity with higher efficiency than normal solar cells. I looked into them extensively as a postdoc a decade ago, wound up concluding that they were extremely unpromising, and moved on to other things. Every year or two since then, I run into someone who is very enthusiastic about the potential of optical rectennas, and I try to talk them out of it. After this happened yet again yesterday, I figured I'd share my spiel publicly!

(For some relevant background context, check out my write-ups [on the fundamental efficiency limit of single-junction solar cells](https://github.com/sbyrnes321/SolarCellEfficiencyLimits/blob/master/sq.ipynb), and [on the thermodynamic efficiency limit of any solar energy conversion technology whatsoever](https://github.com/sbyrnes321/SolarCellEfficiencyLimits/blob/master/ultimate_PV.ipynb).)

1\. What is a rectenna?
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Rectenna is short for “rectifying antenna”, i.e. a combination of an antenna (a thing that can transfer electromagnetic waves from free space into a wire or vice-versa) and a rectifier (a.k.a. diode).

Rectennas are an old and established technology for radio-frequency (RF) electromagnetic waves. For example, if you have a very-low-power gadget, you can power it with a rectenna that scavenges energy from nearby commercial radio stations.

Basically, the commercial radio station emits an electromagnetic wave in free space, and the antenna converts that into an RF signal in a wire (“waveguide”). However, this signal is “AC”—its voltage cycles between positive and negative, at megahertz frequencies, averaging to zero. You can’t recharge a battery with such a signal; it would slightly charge the battery one nanosecond, then slightly discharge it a few nanoseconds later, etc. Hence the diode, which converts (part of) that energy to DC, allowing it to usefully charge batteries or power any other electrical component.

2\. If RF rectennas can turn RF electromagnetic waves into electrical energy, why can’t optical rectennas turn sunlight into electrical energy?
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Well, they can! That is, they can if you’re OK with very low power conversion efficiency. Very, very, very low. Like, 0.00…1% power conversion efficiency. I don't even remember how many zeros there were.

Are higher efficiencies possible for an optical rectenna? Yes! That is, if you’re collecting energy from an intense focused high-power laser, rather than from sunlight.

Why do I say this? There are two problems.

3\. The easy problem: antennas
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The easy problem is scaling down the antenna until it is nano-scale, such that the antenna is sized to absorb and emit sunlight-appropriate electromagnetic waves (e.g. 500 nm wavelength), instead of RF waves (e.g. 500,000,000 nm wavelength).

Making this nano-scale device, and making it inexpensive to mass-produce such that it covers an inexpensive sheet, and getting the antennas to absorb lots of sunlight, constitute the easy problem. This is tractable. It's not trivial, but if this were the only problem, I would expect commercial optical rectennas in short order.

Absorbing lots of sunlight was never the problem! If you want a surface to absorb lots of sunlight, just paint it black!

The hard part is getting useful electrical energy out of that absorbed sunlight. Which brings us to…

4\. The hard problem: diodes
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The hard problem is finding a diode which will rectify that energy. I claim that there is no commercially-available diode, nor any prototype diode, nor any computer-simulation-of-a-diode, *nor even a whiteboard sketch of a possible diode*, that is on track to rectify these electromagnetic waves and turn them into useful energy.

There are actually two problems: speed and voltage.

**The speed problem** is that almost all diodes stop rectifying signals if the frequency of those signals is too high. If memory serves, one common problem is that the diode has too high a capacitance, and another is that electrons can only move so fast. Remember, the sun emits electromagnetic waves with a frequency of around 500 THz = 500,000,000 MHz. This rules out almost all types of diodes.

And that's actually the *less* thorny problem, compared to:

**The voltage problem** is that, for the small wavelength of sunlight, you need a small antenna, and a small antenna has a small absorption cross-section with which it can collect light. So you wind up with very very little sunlight energy getting absorbed by any given antenna, and thus very little voltage in the attached circuit—if memory serves, well under a millivolt.

Alas, diodes stop being diodes if the voltage of the signal is extremely small. Just look at the IV curves:

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/2e7d51c89dc4da8877f8e89482766d20e542910608a143e1.png)

Just like in Calculus 101, if you take a curve and zoom into a very narrow range of x-values, it looks like a line. Hence, if you take a device which functions as a diode for ±1V signals (left), that same device probably functions as a resistor for ±1mV signals (right). 

If the diode doesn’t actually rectify, then the power is absorbed instead of converted to usable energy.

**Taking these together,** it turns out that there are diodes which are fast enough for optical frequencies (metal-insulator-metal “MIM” diodes), but they do not turn on sharply at ultra-low voltage. There are diodes which turn on sharper than usual at low voltage (“backwards diodes”), but I don’t think they can support such high frequencies. And even if they could, even these diodes are not remotely close to being sharp *enough* for our (IIRC sub-millivolt) signal.

There is no diode, to my knowledge, that can work for this device. During this little postdoc project, I spent quite a while scouring the literature, and even trying to invent my own crazy new device concepts, but failed to find anything remotely close to meeting these specs.

5\. But what if we combine the power collected by many antennas into a single waveguide, to increase the voltage?
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Alas, the second law of thermodynamics mandates a fundamental tradeoff between the absorption cross-section and the collection angle, of any antenna (or antenna array) whatsoever.[^t5gwqhbz0ak] If you make a bigger antenna, it will collect more light, but only when the sun is in exactly the right spot in the sky.

6\. But what if we track the sun?
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Well, then you lose ~100% of the light on cloudy days, and you lose 15% of the light even on clear days (e.g. the light from the blue sky). Worse, you need very accurate 2-axis mechanical tracking as the sun moves across the sky, which is expensive. More importantly, if you’re willing to bear those costs (of precise two-axis mechanical tracking and losing the diffuse light), then you might as well just use a big lens and a tiny solar cell, and then the solar cell can be one of those super-expensive multi-junction cells, which incidentally is already getting pretty close to the theoretical efficiency limit on solar energy conversion.

Anyway, we shouldn’t compare with the theoretical efficiency limit, but rather with a rectenna, which I very much doubt would exceed 1% efficiency even at the theoretical limit of maximum possible absorption cross-section. (Why is there a limit, as opposed to being able to track ever-more-accurately? Because the sun is a disc, not a point. So there’s only so much that you can cut down the light collection angle.)

7\. But what if we track the sun virtually, with a phased array?
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That only solves one of the many problems above, and anyway phased arrays don’t work because sunlight is broadband.

8\. But what if we use an impedance converter?
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I glossed over this above, but to translate from “there is only so much electrical energy in the waveguide at any given time” to “there is only so much voltage across the diode”, you also need to know the relevant *impedance*. If the impedance is high enough, you can get a higher voltage for the same electrical energy.

Alas…

**Problem 1** is that high impedance makes the diode speed problem even worse, by effectively increasing the RC time constant.

**Problem 2** is that there seems to be a tradeoff between how much you increase impedance, and how broadband your impedance converter is. And sunlight is rather broadband.

I say “seems to be a tradeoff”, in that I am unaware of a law of physics demanding such a tradeoff. But it seems to be the case for all the impedance-conversion techniques that I know of, or at least for the techniques that work for these kinds of very high frequency waves (e.g. things like [quarter-wave impedance transformers](https://en.wikipedia.org/wiki/Quarter-wave_impedance_transformer)).

9\. But is this even the right way to think about optical rectennas?
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In this whole post, I've been invoking electrical engineering (EE) abstractions: waveguides, antennas, diodes, impedance transformers, and so on. Meanwhile across campus, optical physicists think about the conversion of light to useful energy via a very different set of mental pictures, involving an *individual electron* getting excited by an *individual photon*, and then this particular electron does something. That latter picture, of course, is how everybody thinks about solar cells: an individual electron absorbs an individual photon, thus jumping from the valence band to the conduction band, then the resulting electron and hole go in their opposite directions, then blissfully reunite across the load and live happily ever after in our renewable energy abundance future.

These two pictures (EE versus optical physics) are superficially quite different, and the story of how one can smoothly transition from one picture to the other picture is an elegant and fascinating physics lesson that does not fit in the margin of this blog post (i.e., I used to know it but I forget). Oh well.

Anyway, when you take the high-frequency picture (photons interacting with electrons) and apply it to rectennas, you get “**photon-assisted tunneling**”, a different perspective on MIM diodes where now we think of individual electrons absorbing photons and tunneling across the insulator. Insofar as this new picture is accurate, what are the consequences? Well, for one thing, it means that the efficiency ceiling for our rectenna is down from the thermodynamic limit (55%, assuming no light concentration) to the single-junction solar cell limit (32%). But really, commercial silicon solar cells get impressively close to that ceiling (up to 22%ish, i.e. 70% of the ceiling), whereas I am not optimistic about photon-assisted tunneling getting anywhere close.

Consider: In photon-assisted tunneling, an electron absorbs a photon, and then we hope that it will tunnel across the insulator before it rapidly dissipates its energy in collisions etc. I mean, I'm sure that will happen sometimes, but not more than 70% of the time, right? (Maybe 10% of the time? 1%? Even less?) Like, shouldn't at least half of such electrons randomly zip away from the insulator instead of towards it? Shouldn't a substantial fraction of light get absorbed by the wrong metal? Shouldn't another substantial fraction of light get absorbed by the right metal, but far enough away from the interface that the electron will lose its energy before tunneling?

Anyway, for all these reasons, I am not optimistic about photon-assisted tunneling devices getting anywhere close to the efficiency of today's solar cells.

10\. But what if … something else?
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Hey, what do I know? Maybe there’s a solution. Maybe the numbers I threw out above are misremembered, or maybe I flubbed the math during my postdoc project.

I am very happy when I see people working on or excited about optical rectennas, as long as they are grappling with these problems, proposing solutions, and doing back-of-the-envelope calculations.

Instead, what I often see is people going on and on about the “easy problem” (i.e. the antenna), and how they’re making such great progress on it, *without even mentioning* the “hard problem” (i.e. the diode).

[^t5gwqhbz0ak]: This theorem has a nice little stat-mech proof: basically, you assume that there is a 3D blackbody distribution of electromagnetic waves bouncing around free space, and that there is also a 1D blackbody distribution of electromagnetic waves bouncing around the wire / waveguide, with the same temperature. Then the second law of thermodynamics requires that the power emitted by the antenna has to equal the power collected by the antenna. You wind up with a tradeoff between an antenna’s “directivity” and its “effective area”. This tradeoff depends on wavelength squared, ultimately thanks to different wavelength-dependence of the 1D versus 3D blackboy formulas. And that explains why going down to tiny optical wavelengths is so brutal, if you want a single antenna to collect a lot of power.