Research Profile

June 3, 2008. People don’t like to hear about their limitations, but it’s a real time-saver to know what’s impossible in advance. That’s why electrical engineering Professor David Miller is beaming, so to speak, about discovering the following fact about the nanoscale optical components needed for future telecommunications and computing technologies: there is an exact, calculable limit on how well each component can perform. For example, a nanoscale crystal can separate out different wavelengths of light—and therefore different channels of data—with only so much precision.

“No matter what design you have, it can’t get any better than a certain limit, and I can give you that limit,” says Miller, whose intricate mathematical proof of these limits was published last fall in the Journal of the Optical Society of America B. “Design is very difficult, so you want to know when to stop.”

The kind of devices Miller’s discovery pertains to intricately machined pieces of glass and more exotic materials that manipulate light. These “nanophotonic” devices either slow different colors to different speeds, separate them out in space like a prism, sort out light pulses based on their shape, or filter out errors in optical transmissions. Shrunk down to the nanoscale, such components could help improve the capacity of future computer chips to share data at faster rates than they can today.

For example, within the next decade, even home computers could have scores of processors. To route their output back and forth around the computer (to memory, disks, etc.) most efficiently, the chips could emit optical pulses into fiber optic cables, much like telecommunications hardware does to transmit phone calls and Internet traffic today. But photonics can only increase data throughput if devices like the ones Miller studied can unblend these light signals at their destination with great precision. Essentially, these devices act like a TV tuner—finding the right channel within a broader band of signals.

The devices have to be pretty small, but engineers have never known for sure how small a device can be and still accomplish a particular task. Now they will. For example, Miller calculates, a one-dimensional structure of air and glass, must be at least 41.7 millionths of a meter (µm) thick to separate light pulses of 32 different frequencies around 1.55 µm center wavelength. Trying anything thinner is a losing proposition.

In general, the performance limits Miller has found depend only on a component’s size, shape, and an electromagnetic property of the component’s material known as its dielectric constant. Component designers will now know to bring those parameters in to line first, before sweating over more advanced design decisions such as how to etch or machine a device with the slots, holes, and ridges characteristic of various optical gizmos.

The path to discovery

It was more than a decade ago, during in the process of trying to make advanced nanoscale optical components, that Miller began to realize a fundamental limit might exist.

“I had started wondering what would be the most compact form in which we could do optical wiring,” Miller says. “Then we were trying to make very compact wavelength splitters. As we started looking at it, we started getting a limit out of it empirically.”

In fact over the years, Miller and his students have made or designed more than 600 structures to split wavelengths of light and all of them seemed to be bumping up against a particular performance curve.

Miller literally set out with a clean sheet of paper and a pencil to determine whether there was indeed a fundamental mathematical rule at play. Quite a few 0.3 mm pencil leads and dead-end approaches later, Miller had discovered and proved a new theorem that applies to a variety of wave phenomena in space and time including acoustic waves, all frequencies of light (including radio waves), and other quantum mechanical waves.

The response to the paper has been enthusiastic—earning Miller recognition for publishing the journal’s “most downloaded article,” and a related paper on slowing light has won him an invited talk at a conference this summer—but it has also confounded many of its readers, Miller acknowledges.

“It’s a difficult paper to read and I’m not proud of that,” he says. “But that’s because it starts from the bottom and goes through three or four levels of argument. Also, the approach I have here is not like any one that people are used to using in optics. It takes people a while to get used to it.”

Ultimately, regardless of whether component makers understand how Miller found the limits, they can certainly use the guidance it gives them. That, in turn, should make it easier for them to advance photonics technology. Knowing what’s impossible could help them make new things possible sooner.