In 2018, it was ten years since I stumbled upon the opportunity to write my Bachelor's thesis on the subject of photonic crystals. Photonic crystals are a metamaterial, an artificial material created by putting together small pieces of ordinary materials to get something with unusual properties. A photonic crystal can for example efficiently block electromagnetic radiation (light, microwaves etc.) in a specific frequency band, while frequencies outside the band get through with relatively little loss. Materials with this property could have many interesting applications, but the application that caught the attention of popular science publications at the time was that metamaterials could maybe, maybe be used to make things invisible. The obvious question is then, have we gotten any closer to having invisibility cloaks over the last 10 years?
Ten years ago it was photonic crystals specifically that people were talking about. A photonic crystal consists of at least two materials that have different optical properties - usually materials that are not electrically conducting and that have different refractive indices. It could for example be two different types of plastic or plastic and glass. The two materials are placed in a periodic structure, which for example could mean a stack of thin slabs where every other is plastic and every other is glass (Wikipedia has some excellent figures that shows what this can look like). The thickness of the slabs should correspond roughly to about half the wavelength of the electromagnetic radiation that you want to stop from propagating in the material.
Just stopping radiation of a specific frequency from propagating is, however, not enough to make something invisible. Preferably, we would like to lead the light around the object that we want to render invisible, so that the eye of people looking at it only receive light from whatever is behind the object. Theoretically this is possible with photonic crystals, due to something called effective negative refractive index.
When light passes from one material to the other, for example from air to glass, it does not continue in a straight line but changes direction with a specific angle. The angle depends on the difference in speed of light between the two materials, and this difference is expressed in terms of the refractive index. In normal materials the refractive index is positive, but in metamaterials radiation at some frequencies can change direction with a much larger angle than is ever possible in a normal material (see figure). This is expressed as the metamaterial having an effective negative refractive index. By adjusting the metamaterial to get a specific value of the refractive index it is possible to use this to control the path of light, for example to lead it around an object you want to conceal.
However, there are two problems with this. Firstly, the frequecy range where photonic crystals have a negative refractive index is usually very narrow, so a given metamaterial will only work for a small number of frequencies (say for example you would be invisible in green light but not in red or blue). Secondly, even if every layer in the photonic crystal is very thin you need a lot of layers to get a good effect. This means that even for visible light, with wavelengths below one micron, an invisibility cloak based on photonic crystals would be quite unwieldy.
Since my first contact with this field, another type of metamaterial has become more popular. Instead of mostly using non-conducting materials, the materials are built up from metallic elements or even small electric circuits. This category of metamaterials mostly builds on various resonance phenomena that can occur in metallic materials that are exposed to electromagnetic radiation. A common example is so-called split-ring resonators, that consist of to rings of metallic material where one is smaller and placed inside the other one. The rings both have an opening and they are placed so that the openings are opposite of each other. When this structure is exposed to electromagnetic radiation, this causes an electric current in the rings (induction) and electromagnetic charge will build up around the openings (capacitance). These currents and charges in turn affect surrounding electric and magnetic fields, i.e. the radiation.
A difference between traditional photonic crystals and metamaterials with metallic components is that with the metallic components the individual elements in the metamaterial, like the ring resonators for example, should be much smaller than the wavelength of the radiation that is to be stopped or controlled. This is a good thing if you want to make an "invisibility cloak" for lower frequencies (i.e. where the the wavelengths are larger) but for visible light you might run into the problem that it is still fairly difficult to make large quantities of components that are just a few tens of nanometres in size, especially since they need to be manufactured with high precision. In addition, the metallic metamaterials also only work in a limited frequency band that depends on the size of the elements. The frequency band is a bit wider than for photonic crystals, but from what I have been able to find it would still be difficult to cover for example the entire visible range. Thus, no invisibility cloak à la Harry Potter yet.
As a final note, I should probably mention that even if an invisibility cloak for the visible spectrum would be cool, that is not really what drives research in this area. Most papers I have found deal with electromagnetic radiation with wavelengths from a few millimetres up to several centimetres, which are used for e.g. radar and communication. In this frequency range metallic metamaterials work fairly well and have given applications for those who for example want to make airplanes harder to detect with radar.
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