# Why don't we use lenses for RF?

Radio waves are a class of electromagnetic waves. Light also is a class of electromagnetic waves.

By shaping a material in which the speed of light changes, we can bend the propagation direction of light, we call this a lens, and we call the speed change rate refractive index $$\n\$$.

Also for RF we can define a speed change rate as $$\\frac{1}{\sqrt{LC}}\$$ or $$\\frac{1}{\sqrt{\epsilon_r\mu_r}}\$$.

We also use the exact same destructive interference in the same way for radomes and Anti reflective coatings.

So here comes the question: why don't we use lenses and ̶m̶i̶r̶r̶o̶r̶s̶ for RF, for example for focusing RF beams instead of using complicated directive antennas?

EDIT: yes, we actually use mirrors

• We do. A simple case of a "mirror" would be a satellite disc. we can also make solid wave-guides which take advantage of the difference in refractive index between the medium and the surrounding air, that is kind of equivalent to a lens. What I am saying is that there are plenty of applications which rely on the common properties of RF-waves and light. – Vinzent Jun 28 '20 at 16:39
• Consider how big they'd have to be for ordinary frequencies, and not just in two dimensions but three. With the exception of the special case of (effectively complete) reflectors, mostly the "rf lenses" that are encountered at traditional "radio" frequencies are unintended ones people are trying to overcome, though ionospheric behavior can sometimes be useful. – Chris Stratton Jun 28 '20 at 16:50
• @valerio_new Astronomers use RF lenses. I've used steel lids from 55 gallon drums for the purpose, in fact, pounding them out into shape. I'm an amateur astronomer. (Steel is quite transparent in the right micron ranges.) But here is a link describing a Luneberg system, for example. Or here at the square kilometer array. At times at Arecibo in Brazil, too. I didn't mention reflectors. – jonk Jun 28 '20 at 19:21
• @valerio_new You've plenty of sufficient answers here. I'd love to write a long discussion about it -- but then, per my own standards, I'd need to re-check everything I say with references I'd need to go find again. Too much to do, right now, especially given the answers at hand. Personal note: after building three optical telescopes from raw materials (and their lenses) and all the fine testing required for them, I found using steel as a lens a relief. Getting $\frac1{20}^\text{th}\,\lambda$ precision in optical is hard -- thousands of hours hard. At RF, it's really easy. – jonk Jun 28 '20 at 19:35
• Also, over on Physics.SE: Can a lens be used at radio frequency? – Andrew Morton Jun 29 '20 at 13:41

## 8 Answers

In optical engineering, the choice between lenses and mirrors often comes down to aperture diameter: less than a few inches and lenses can be made cheaply and with high accuracy. Larger and costs increase exponentially, so even 6" diameter systems usually work better reflective.

At RF frequencies, a 6 inch lens is on the order of a wavelength, and so not useful for focusing. It isn't until you get towards the edge of the microwave spectrum that the wavelength gets short enough for lenses to start to become practical.

Of course if you don't care about cost, and you don't mind it being extremely heavy, you could build a lens to use with a WiFi antenna. It just doesn't make much practical sense.

• RF frequencies span orders of magnitude. 150mm (6") is on the order of a 2GHz wavelength (a lens would need to be about 1.5m to actually work for this wavelength), but if you're talking about VHF then a wave is like 3m, and your lens would need to have a diameter about the size of a 15 storey building to function. Over most of the RF wavelength range the scale of construction required to build a refractive optic is simply ridiculously impractical. – J... Jun 29 '20 at 14:01
• In computer science, the choice comes down to between smoke and mirrors. – Kaz Jun 30 '20 at 3:59

i don't know of any rf lens usage case

That can be changed. They are quite common for ku-band and up. Think satellite communications, radar, point-to-point links where you want high but can't use a dish, e.g. for weather reasons.

Look at this nice lens antenna:

Or these nice insets to convert an open waveguide to an actual antenna

• I like this answer, but why don't we use them also for lower frequency bands? – valerio_new Jun 28 '20 at 17:16
• @valerio_new Others have explained pointed that (and multiple times!) in comments and other answers to your question. You will need to have to read them. – Marcus Müller Jun 28 '20 at 17:18
• Found it! A lens has to be an order of magnitude bigger than the wavelenght! :) – valerio_new Jun 28 '20 at 17:21

There is the Luneburg Lens, which can be used for various applications, from optical to RF. Luneburg Lenses are generally spherical, made of concentric shells of material with a stepped refractive index for practical purposes, but ideally the refractive index should be continously varying.

(image from www.rfwireless-world.com)

Applications are radar reflectors, microwave antennas and laser collimation.

You can make lenses out of metamaterials - see this Phys.org story

A three-dimensional self-supporting low loss microwave lens with a negative refractive index Journal of Applied Physics 112, 073114 (2012); https://doi.org/10.1063/1.4757577 Isaac M. Ehrenberg, Sanjay E. Sarma, and Bae-Ian Wu

• love the fact this has negative refraction index. – Marcus Müller Jun 29 '20 at 18:08
• POSITIVE index metamaterial: the "directors" of a yagi/uda antenna slow down the waves, forcing them to turn towards the active dipole. Heh, yagis have "len" elements and "reflector" elements. – wbeaty Jun 29 '20 at 18:15
• In fact a lot of metamaterial stuff is developed in the microwave spectral region, because mm-precision is much easier to prototype and test than nm-precision (especially in 3D) – Chris H Jun 30 '20 at 20:41

Heinrich Hertz used paraffin wedges, in the 1890s, as part of his 60MHz RF communication link. The wedges were crucial to proving WAVES were being emitted and collected and detected.

RF mirrors are quite common.

RF lenses are possible but much less common.

The short explanation is cost. Cost is almost always part of engineering. If there are two ways to do something, and one costs less for adequate performance, then that is the better engineering solution to the problem.

An array of wires to form a directive or reflective antenna element is cheaper to build and maintain than a solid lens structure for most applications.

• If engineering is costly, why even bother inventing a whole different field of wires sticking out of wires while we could have used an already well established knowledge as the optics field? – valerio_new Jun 28 '20 at 16:48
• @valerio_new, because the cost of the engineering work isn't the only cost that matters. The cost to build and maintain the RF system is also important. – The Photon Jun 28 '20 at 16:52
• @valerio_new, also consider that radio technology predates the widespread availability of plastics that we have today, which would have severely limited the practicality of RF lenses in the early days. Imagine how heavy a several-meter diameter glass lens would be. – The Photon Jun 28 '20 at 17:03

Another well-known example of RF lenses are Fresnel zone antennas. They are based on the same principle as the optical Fresnel lenses: The focusing effect is achieved via the phase shifting property of its surface rather than volume, which allows for compact or arbitrarily sized antennas (e.g. built into a curved surface).

Lenses can be used in the millimeter wave region. See, for example, https://doi.org/10.1007/BF01014036

Which describes use of Rexolite lenses for 90GHz military applications.