Photonic Crystals: the story they tell us of light

Photonic crystals are lattices of molecules that have special light properties. They occur in nature (peacock feathers) but in the lab are used in such sci-fi sounding ways as invisibility, entangled photons, and logic gates. Also, they are a good example of what in organic chemistry is called “symphony,” which is when outcomes happen only when multiple circumstances come together in just the right way. (To switch our metaphors, we might think of it as “a perfect storm”). And they are another example (as I have been discussing) of how groups of things can have properties different from those found in the individuals that comprise the group (which is of philosophical interest because it messes up hierarchical thinking, since the group traits higher in the hierarchy do not encompass those traits in the lower).

So what are photonic crystals? (Or perhaps I should rephrase with a proper amount of gee-whiz incredulity, “What are these guys?”).

A photonic crystal is made of repeating units of dielectric media, and here the operative word is “periodicity.” Periodicity (a pattern happening over and over) is a property of the whole; it does not exist in just one unit by itself.

What happens is that, as light travels through the crystal, the light bends (refracts) as it passes through one medium to the next. It is the same way that light changes direction as it goes through water except that now it is doing that periodically as it moves through various sections of the crystal. But more than that (and thinking now of light as a wave), one wave can combine with another (be superimposed in an interference pattern) in a way that amplifies or diminishes the waves as they combine. A peak of a wave can combine with the peals of other waves to make even higher peaks, or troughs can combine with troughs to make lower troughs. Also, peaks can combine with troughs to cancel each other out into flatness. So that is happening throughout the crystal. And this way of having areas of extreme peaks and flatness is what creates the sparkling iridescence that we see, for instance, in opals, seashells, and in the “eyes” of peacock feathers.

But in nature, the repeating pattern occurs only in one direction of the crystal. So, what happens if we make the periodicity occur in two or even three dimensions?

“Wow” is what happens

The places of superposition can become so intense that, where the light is canceled, it completely stops the flow of light, meaning that the crystal can be used as a switch to turn on or off the light flow as conditions change. In other words, it is a logic gate which can be used in the same way as a transistor. What a transistor does for electrons (let them pass or not, in a way that depends on the circumstances which we can control), a photonic crystal does for light.

But secondly, the places of extreme cancellation of light can also function like a cavity with light flowing back and forth through it (which is the description of a laser). So a photonic crustal can itself laze (although there are easier ways of making a laser).

Thirdly, the photons can become entangled while traveling back and forth in the crystal, which again lets us do with light what had previously been thought to require electrons or neutrons.

And finally, overall the crystals can generate negative indices of refraction, which is a first step to one way of producing invisibility. Because the crystals can be used to change what usually happens when light interacts with a material, they are said to be “metamaterials.” And they can be put into a coating of an object to cloak it in the sense that the light incident on the object will not reflect it in the usual way back to an observer.

All four applications depend on how the spacing of things in the crystal lines up with the spacing of the wavelength of the light. It is when they are the same (or multiples of) one another that the situation gets interesting.. (And of course it also depends on the composition of the crystals and on what else the crystals are connected with, to achieve each of these applications).

Since in past posts I have been trying to introduce what it might look like to have a philosophy of chemistry (see also my earlier post on MRI’s “When Logic Says It Is Impossible”), I will here add a few curious details.

It is possible to take an idealized approach to describing the spacing of the points in a crystal—to see it as being perfect (without flaws)—so as to describe it mathematically. In a photonic crystal, that becomes especially rewarding because the waves of light are themselves already routinely described with math. Then in this idealized approach, we can use tensor algebra to combine the two mathematical formulas (of light and of crystal) and describe what happens when the spacing among points in the crystal equals the spacing among the peaks in the light waves. That can be especially helpful in showing how “gaps” (or places of complete nullification of light travel) are to be expected in the crystal.

But we should also not be afraid of reality, either —we can afford to take a realistic approach in addition to an idealized one—because what makes crystals of any kind exciting is the way that inevitably they do have to have impurities in them, but the impurities give them added properties such as color. It is similar to alloys and to how with steel we deliberately add impurities to make it stronger.

And more to the point, that is the case with transistors. The silicon used to make semiconductors is deliberately “doped” with impurities which give it the capacity to allow electrons to pass or not and so be made into transistors. And it is likewise with the impurities in photonic crystals.

I personally like the theory that what happens in photonic crystals is that the light congregates at the site of the impurities which is then where the superposition of the waves occurs to create the gaps and cavities. That can be described in terms of just total energy and the way that the setup is going together. In typical quantum fashion, the light does not travel in a predictable manner (it moves unpredictably until it happens to reach a point of impurity), but we can still tell what will happen in the larger scheme of things by looking at what the photons do altogether. It is like in chemistry where we do not know what each molecule in a reaction is doing (other than that it is moving randomly), but we can still say much about what is happening altogether to make an overall outcome. Likewise, we can still talk about the light in an overall way.

Both approaches (idealized and realistic) combine to make an interesting story. Both are needed. But the point might be to a philosopher of chemistry that the world does not have to be perfect in order for it to work. It is not, as per Plato, that the world is trying and failing to act perfect.ly. A crystal or a semiconductor can be messy, impure, and only imperfectly periodic and still it can function as a logic gate. In fact, it needs to be impure in order to work.

It is not that everything acts by following orders in a deterministic way. Rather, here is another example of how complex features can be made out of random actions. (So the unpredictability in quantum mechanics need not seem so paradoxical, after all, if we can see how it can lead to complexity).

I was making a similar point in my posts on the development of functionality in biology. The world can be messy (as in not deterministic) and still get things done. (I know that many people will disagree with me, but that is okay. Such disagreements make the world more interesting).

Then the only remaining issue is how to fabricate a photonic crystal with all its periodic patterns.

Imagine trying to fill in every square of a Scrabble board is such a way that each square follows a pattern up and down as well as left to right. And that is only in two dimensions. Now try to do that in three dimensions, and you see the difficulty.

One solution is literally to drill tiny holes (now there’s some impurities) into a crystal, which is possible to do if the holes are not too close together. But that limits how small the wavelength of light can be. And pity the poor slob trying to drill the tiny holes.

A better solution is to call in your local friendly chemist who will do it with self-organization. Let the molecules themselves arrange themselves into the appropriate formation.

Chemistry is sometimes defined as the science of the creation of new materials exhibiting new properties, and photonic crystals would seem to quality.

In the next post, I will describe self-organization. Only a generation ago, self-organization was a hot new idea of somewhat dubious reputation. Today, it is in standard use in chemistry, even as still (on the face of it) it seems to defy the second law of thermodynamics.

Yet in the brave new world of today, self-organization is good for making photonic crystals.

ACKNOWLEDGEMENT

The title of this post borrows from a book of poems “The Story They Told Us of Light” by Rodney Jones. My highest recommendation. Even of you consider most poetry to be on the order of the Vogons’ in “The Hitchhiker’s Guide to the Galaxy,” get this book (one of only two I so recommend).

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