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Photonic crystals have been one of the hottest topics in optics in the last 10 years. This research is born out of a desire to have precise control over light—similar to the semiconductor industry's control over electrons. The current favorite way to do this is to construct devices that have a refractive index that varies on the scale of the wavelength of light.
These metamaterials are made by combining two different materials in a very precise way, leading to all sorts of fabrication headaches. This may change in the near future because a pair of researchers have shown that you might be able to create temporary photonic crystals in a single material simply by shining a couple of light fields on it.
As a starting point, the researchers noted that the refractive index experienced by light changes dramatically when the material it's passing through can absorb the light—that is, the light frequency is coincident with an atomic resonance. So, if you choose a light field that has a frequency that is slightly higher than an atomic resonance frequency, it will experience a lower refractive index.
On the other hand, if you choose light with a frequency slightly lower than the atomic resonance, it will experience a larger refractive index and some absorption. This doesn't appear to help though—to get a useful difference between the two refractive indices, the light field has to be very nearly resonant with the atomic resonance. Over very short distances, the light is lost to absorption.
In a fit of creativity, and, seemingly, ignoring reality, the researchers asked themselves what would happen if a light field were simultaneously at a frequency that was both higher and lower than an atomic resonance? Of course, this can't be the same atomic resonance, that would be too bizarre. Instead, the light is sandwiched between two neighboring resonances. One atomic resonance provides gain and the other absorption, with the two balancing exactly. Under these circumstances, the refractive index could be made to vary strongly.
So, the refractive index can be varied, and the loss is nearly zero. That sounds like the perfect photonic crystal. But how to make it so?
First, find an atom with two excited states that have a separation such that the frequency to get from the ground state to the first excited state is slightly lower than the energy required to get from the first excited state to the second excited state. Then, choose a light frequency slightly larger than that required to get from the ground state to the excited state, but, just too small to get from the first excited state to the second. We have now met the condition of having a light frequency that is simultaneously lower and higher than an atomic resonance.
Getting that part to work as advertised requires a rather detailed setup, especially once you start considering real atoms. However, once it is working, you get a photonic crystal that has nearly perfect boundaries between high and low refractive index areas.
It has, in principle, no loss, which is almost the complete opposite of any real photonic crystals. And, with an even more complicated optical arrangement, this can be extended from 1D to 2 and 3D (the researchers don't actually consider more than a single dimension). Even better, the 2 and 3D photonic crystals, could, conceivably, be big. Much bigger than fabricated photonic crystal, which might have an area of 1 square centimeter and a depth of a hundred micrometers.
So, will it work? Yes, but probably not very well. The problem is that, to get a high refractive index contrast, the light field has to sit very close to the atomic resonance. And, thanks to those lovely, perfect interfaces, the light field will be reflected back and forth beautifully, building up quite a high intensity inside the photonic crystal. The result is that the light field will start modifying the photonic crystal in such a way as to reduce the refractive index contrast.
Eventually, some sort of equilibrium will be reached where the photonic crystal kinda-sorta still exists, but it hasn't got the contrast that you really want anymore. There are also more complicated problems that arise when you consider some of the simplifications that seem to be implicit in the model.
The researchers will probably argue that this photonic crystal should only be used with very weak light fields. That is all well and good, but the better the photonic crystal, the weaker the light field need to be, and that seems like a bad direction to go. Nevertheless, I think this is a very cool idea, and, certainly, if I had the equipment, I would put a student on this immediately.
Physical Review Letters, 2011, DOI:10.1103/PhysRevLett.107.137401
Making it work in theory
The photonic crystal won't work if there are no atoms in the first excited state. To make it more difficult, you want to excite atoms into the excited state in such a way that in some places they are all excited, and in others, none are excited. The researchers suggest that this can be achieved by placing the atoms in an optical cavity and shining a very strong light field (lets call it the pump) that is resonant with the first excited state into the cavity.
In an optical cavity, the pump field will form a standing wave. This means that in some places, the intensity of the light is zero—it is always dark—while in other places, the intensity is maximum—it is always bright.
If the pump field is really powerful, then you get very sharp transitions between areas where all the atoms are in the first excited state and areas where none of the atoms are in the first excited state. Thus, a periodic structure with a high refractive index is obtained. This is also where the loss compensation comes from. In areas of the crystal where the atoms are in the ground state, the light field experiences strong absorption because it is very nearly resonant with the transition. On the other hand, when the light field hits the part of the crystal where all the atoms are excited, it stimulates emission, regaining its original intensity.
What about real atoms?
One of the problems that the researchers explicitly considered was that real atoms very rarely have such a convenient arrangement of resonances. They suggest that you could make use of the Stark shift. This is the phenomena where an electric field will shift an atomic resonance frequency. Light fields happen to be made of electric fields, so, by choosing light fields that are near atomic resonances and tuning the intensity of the light field appropriately, one can shift the atomic resonances so that the energy separation is exactly right.
So, in a real system, you need one laser to set the atomic resonances to the right frequencies, another laser and an optical cavity to get the spatial variation in the refractive index, and, finally, the light you actually want to put through the crystal. Seems kind of complicated, but not out of reach.
Some of the other problems
Aside from the rather complicated setup, there is a contradiction hidden in the physics used in the researcher's model. To get gain in the parts of the crystal where the atoms are in the excited state, we need more than half of the atoms to be in the excited state. But, if the pump field is directly exciting this transition, we have only two possibilities: the system is coherent and exhibits Rabi oscillations, or the system is incoherent and the maximum population is half the total number of atoms.
If the first is true, the entire atomic population cycles periodically between the excited state and the ground state, meaning that the photonic crystal is only present for a fraction of the time. If the second option is true, there can't be any gain, and the photonic crystal has catastrophic losses.
To overcome that particular problem, we are forced to choose an atomic system that looks very much like a laser. In this case, we tune our pump laser to a different excited state and let the population naturally decay into the first excited state. This will, with luck, allow us to get the majority of the population into the state that allows the photonics crystal to function, while also avoiding population oscillations. But, this is now looking like a really special atomic system, and I really doubt that all the conditions can be met.