Null-field radiationless sources: even more invisible than invisible?

I spend a lot of time talking about invisibility on this blog, as it is a subject near and dear to me: I did my PhD work, completed in 2001, on early historical forms of invisibility.  I like to tell people that I’m an invisibility hipster, and that I worked on invisibility “before it was cool.”

The field has progressed dramatically since I first did my work, and in recent years I’ve been playing a bit of “catch up” with my own invisibility work, trying both to build on the newest insights as well as apply knowledge from the old theories.

This past fall, my student Elisa and I used this approach to ask and answer a curious question: can something be more invisible than invisible?

Our answer was published in a paper titled “Null-field radiationless sources,” that appeared in November in Optics Letters.*  Ordinary invisible objects, including cloaking devices, are objects that don’t scatter any light outside the domain of the object; a potential null-field object will potentially not scatter light inside, as well!

Getting to null-field scatterers is a goal that has not yet been achieved; in our paper, Elisa and I focused on sources of radiation, things like radio and cell phone antennas.  Such sources produce electromagnetic waves by making electrical charges accelerate, and such “wiggling” charges typically produce electromagnetic waves.  This connection is used in an extreme way, for instance, at circular particle accelerators known as synchrotrons.  The charged particles, constantly being accelerated in a circle around the track, produce high energy x-rays that can be used in imaging experiments.

The Advanced Photon Source at Argonne National Laboratory.

The Advanced Photon Source synchrotron at Argonne National Laboratory.  Photo from APS website.

This link between accelerating charges and radiation is so strong that most physics students take it as a given; however, it has been known now for over a century that it is possible to construct, theoretically at least, oscillating charge distributions that produce no radiation at all.  This appears to have been first discussed by Paul Ehrenfest in 1910, in the context of atomic theory.  At the time, it was a big mystery how electrons could circulate around in an atom without radiating; Ehrenfest suggested that radiationless charge distributions could explain it.

I’ve talked in detail about Ehrenfest’s work in a previous blog post and won’t repeat that discussion here.  He produced several simple examples of radiationless sources, but then went further and provided a general mathematical description for “designing” a wide variety of such sources.

What caught my attention when I first read this paper, years ago, is one big condition Ehrenfest imposed in order to find his solution.  No only did he design his sources to have no electric field (labelled E) and no magnetic field (labelled H) outside the source, i.e. no electromagnetic waves, he also imposed a requirement that there be no magnetic field inside the source, as well!  This is roughly illustrated below.


This in itself is weird!  The laws of electromagnetism explicitly indicate that an oscillating electric field should produce a magnetic field, and vice versa.  Ehrenfest inadvertently showed that, when one is within the region of oscillating charges, this is not necessarily true.

This made Elisa and me wonder: does it work the other way?  Is it possible to make a source with a magnetic field, but no electric field?  And can we take it further — is it possible to make multiple fields exactly zero in the source region?

There are, in fact, four possible fields to attempt to set to zero in the source region.  In physics, we typically talk about two different types of electric fields: the microscopic electric field E, and the macroscopic electric displacement D.  Similarly, there are two different types of magnetic fields: the microscopic magnetic induction B, and the macroscopic magnetic field H.  The “macroscopic” fields are mathematical constructs designed to automatically incorporate the response of matter to electromagnetism, while the “microscopic” fields are the fundamental physical fields.  In calculations and applications, both types of fields are important.

A few other researchers have investigated null fields over the years, but none seem to have studied all the possible null conditions, as we did.

Through a handy bit of pen-and-paper work (which turned out to be much harder than we first thought), we demonstrated that it is possible to construct radiationless sources for which any of the four fields — EDB, or H — are identically zero inside the source.  The zero field is, in essence, “nulled” by the source properties itself.

Even stranger, and quite surprising, we found that it is possible to null both the electric field E and the magnetic field H simultaneously!  An example of a source that does this, from our paper, is shown below.

The source structure of a null field source. (a) the x-component of polarization, (b), the y-component of magnetization, and (c) the z-component of magnetization.  After our Opt. Lett. paper.

The source structure of a null field source. (a) the x-component of polarization, (b), the y-component of magnetization, and (c) the z-component of magnetization. After our Opt. Lett. paper.

The colors show the electric and magnetic properties of the source that result in a null field.  Part (a) shows the electric oscillations of the source, while (b) and (c) show two components of the magnetic oscillations of the source.

There are two things to learn from these images.  First, it turns out that it is not possible to make a source completely null-E and null-H everywhere within the source.  A boundary region with at least one nonzero must surround the null region; a hint of this region can be seen in image (c) above.

Second, this is the first time that we have mentioned that the source must include both electric and magnetic oscillations!  The latter observation suggests that such sources, or truly invisible objects derived from them, must use specially constructed metamaterials, such as those which can produce negative refraction.

So what is the significance of such “more invisible than invisible” sources?  The source problem is, for us, a stepping stone to seeing if a similar effect can be produced in “invisible” objects.  Such an invisible object would, at least for one electromagnetic field associated with it, totally unperturb any illuminating field, both inside and out.

To be honest, I’m not quite sure what benefit that would be, yet!  However, such scattering objects do not seem to be possible using the usual invisibility cloak design techniques such as transformation optics, in which a material is designed to effectively “warp” space around a region.  Our work therefore gives a hint that still stranger invisibility effects may still exist that lie outside the domain of existing design techniques.

Thanks to David “Why Sharks Matter” Shiffman for suggesting that I write more about my own research! I will hopefully discuss more of my work in the future.


* E. Hurwitz and G. Gbur, “Null-field radiationless sources,” Opt. Lett. 39 (2014), 6529.

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