Projects in Scientific Computing

Download the PDF version of this article as it appeared in Projects in Scientific Computing, 2003.


For MIT physicist John Joannopoulos, success means defects and imperfections. His research draws on the vocabulary of post-apocalypse fantasy, with explorations of “degenerate bands” and “forbidden zones.” His findings, however, aren’t fiction. His work on innovative materials called “photonic crystals” presages an impending technological revolution — computing and communications at the speed of light.

Tiny, honeycomb-like, crafted from layers of silicon, photonic crystals have unprecedented ability to trap, guide and control light. Their promise is to manipulate photons, the tiniest lumps of energy in light, with the same precision that semiconductors make possible with electrons. To move from electronics to photonics — using photons rather than electrons as the markers of digital 0s and 1s — is the objective.

The result will be networks that move data at trillions of bits per second, a thousand times faster than today. For computing, along with a radical leap in processing speed, photonics should shrink by a thousand fold the size and power needs of circuitry. It's a rapidly emerging technology, burgeoning with promise, with likely impacts in many fields including medical and chemical scanning and sensing devices.

(l to r)
						Steven G. Johnson, John Joannopoulos, Michelle Povinelli,
						Elefterios Lidorikis.

(l to r) Steven G. Johnson, John Joannopoulos, Michelle Povinelli, Elefterios Lidorikis.

Over the last decade, Joannopoulos and his MIT colleagues have done much of the work that has generated a buzz about this new field, with several patents to their credit. They've developed software designed especially to simulate, predict and explain the remarkable properties of these materials, and they work closely with MIT laboratory researchers to fabricate their designs.


When LeMieux, Pittsburgh Supercomputing Center's terascale system, became available as a production resource in 2002, Joannopoulos tapped into this massive new supply of computational power. "This machine is a fantastic creation," he says. "It has enabled us to do calculations that weren't possible before. We've made great progress on several projects."

With LeMieux, Joannopoulos' group last year simulated a photonics crystal phenomenon called "superlensing," demonstrating that it's feasible in three-dimensional crystals. They had previously demonstrated superlensing in two dimensions, but until LeMieux were stymied with the more challenging 3D computation.

They've also applied LeMieux to an important problem with polarized light. Photonic crystal "waveguides" are able to guide a stream of photons like a canal channels water, but to date they've been selective in how they transmit light's two polarities, the horizontal and vertical component of the wave. In recent work, Joannopoulos and colleagues Elefterios Lidorikis, Michelle Povinelli and Steven G. Johnson appear to have solved this problem, and their new findings are a big step toward integrated photonic networks.

Bright Ideas

Photonic Crystal.
Click Image to Enlarge

Designed by Joannopoulos' group, this photonic crystal is made from alternating 2D layers, one with dielectric (silicon) rods in air, the other with air holes in the dielectric.

Fiber-optic cables have for years been the information-carrying medium of choice for high-performance networks, but fiber optics is inherently limited. Among other drawbacks, all the routers and switches that decode and sort the information are electronic; they convert photons to electrons and back again, creating bottlenecks.

Enter the photonic crystal, known also, more descriptively, as the photonic band-gap crystal. They’re built from clusters of material arrayed in a regular pattern with holes between the clusters. Think of microscopic Swiss cheese with precisely spaced holes.

The material, often silicon, is of a different refractive index than the holes, usually air. When this geometry is designed just right, it creates an environment where certain wavelengths of light can’t enter. Most frequencies along the light spectrum pass through freely, but for a forbidden few — called the band gap or forbidden zone — the crystal acts like a mirror. It’s the optical equivalent of a semiconductor, which controls electrons by way of built-in energy gaps.

Connoisseurs of Oriental carpets know that a flaw woven into the pattern is the weaver’s way to say that only God can create perfection. Somewhat similarly, the real beauty of photonic crystals is their deliberate defect. An enlarged hole, for instance, of just the right placement and dimension within the otherwise regularly patterned structure can trap band-gap photons. “Pretend you’re a photon in the defect,” says Joannopoulos. “You can see the perfect crystals, but you know better than to move there because if you do, you’ll cease to exist.”

Joannopoulos’ work has shown that with relative ease these defects can be fine tuned to trap desired wavelengths, such as, for instance, to capture the red light from a white beam. By lining up a series of defects, the crystal becomes a “waveguide.” Like traveling in a tunnel, photons have no choice except to stay on the path defined by the defects.

“We can do things with photonic crystals that we’ve never been able to do with light before,” says Joannopoulos, “and with that ability all sorts of possibilities arise, all new fields open up.”

Degenerate Light

Fishermen know that polarized sunglasses make it easier to see fish. The reason is that light vibrates both horizontally and vertically as it travels, and under some conditions takes on more of one or the other polarity. The sun’s glare off water’s surface tends to polarize horizontally. Vertically polarized glasses filter out this horizontal vibration, and the sea appears more transparent.

Schematic showing
						the polarization-independent waveguide bend and linear
Click Image to Enlarge

This schematic shows the polarization-independent waveguide bend (red) and linear waveguide (orange) structure simulated by Joannopoulos and colleagues. The blowups show the geometry of stacked layers, a layer of pillars alternating with a layer of "Swiss cheese" dielectric. The rightmost blowup shows the defects that create the waveguide: varying radii of holes and pillars. To gauge size, the distance from one hole to the next would be approximately half a micron, ten times thinner than an average human hair.

Joannopoulos’ group at MIT has demonstrated the feasibility of photonic crystal waveguides that provide tight cornering without energy loss, a significant advance over fiber optics. A common drawback for these photonic waveguides, however, has been that they are polarization selective; they transmit one polarization differently than the other.

Joannopoulos’ team set out to demonstrate that, by joining two different styles of photonic-crystal slabs into a single crystal, it should be possible to create waveguides that are polarization independent. To test their idea, without the prohibitive expense of trial-and-error fabrication in the laboratory, they turned to LeMieux. First, they worked on a linear waveguide, a straight-line tunnel through the crystal, analyzing various defect designs to find a combination that resulted in “degeneracy” — a condition in which the two polarizations behave in the same way.

They found a winning combination and went further, testing their design on a waveguide with a 60-degree bend. Because the curve disrupts the symmetrical arrangement of defects, the computational task is much more challenging. To realistically evaluate the light transmission requires clear separation between incident, reflected and transmitted pulses, which in turn requires a very large simulated structure.

Polarized Light Goes Around the Bend. Polarized Light Goes Around the Bend.
Click Images to Enlarge

Polarized Light Goes Around the Bend
These images from the simulations show the two polarizations (modes) of light in the waveguide, each in adjacent layers of the crystal. The left panels show lateral and vertical images of the TE (transverse electric) mode in the Swiss-cheese layer. The right panels show the TM (transverse magnetic) mode in the pillared layer. Color (red & blue) indicates positive and negative values for the magnetic and electric fields.

"Both modes are very well localized with the waveguide area," notes Lidorikis, "and share a similar mode profile. This is important for using the crystal as a component in an optical network."

Using 256 LeMieux processors, they simulated light pulses of different polarizations. With an extensive series of computations — each requiring about six hours — to completely map all possible wavelengths, the researchers found that, within a frequency range, light comes out of the bend with an efficiency of about 95 percent, maintaining virtually the same polarization over its entire journey. “This is proof of principle,” says Lidorikis. “With further tuning, it should be possible to achieve 100 percent degenerate transmission through sharp bends.”

It’s a breakthrough that marks the first optical-circuit design to control light to this degree. Miniaturization of optical components is a major goal, and photonic crystals present a promising choice. “Designers will have the opportunity to work with smaller components,” says Joannopoulos, “free from concerns about polarization.”

Polarized Light Goes Around the Bend.

Somewhere in a beam of sunlight in the Amazon basin, the three-inch wings of a morpho butterfly glow with deep blue iridescence. Then the morpho shifts its wings and, as if a switch flipped, shows its other self, dull brown.

Scientists have discovered that many creatures — including some beetles, birds and butterflies — owe their iridescent coloring to natural photonic crystals. Unlike pigments, which reflect light based on their chemical composition, photonic crystals reflect due to their structure, a periodic array of holes. Pigments look the same from any angle, but a photonic crystal may reflect light differently, and appear differently colored, depending on the angle of reflection. (MS)

John Joannopoulos, Steven G. Johnson, Elefterios Lidorikis, Michelle Povinelli, Massachusetts Institute of Technology.

Terascale Computing System.

User-developed code.

Related Material on the Web:
Photonic Crystal Research by the Joannopoulos Group at MIT.
Setting a Trap for Light, Projects in Scientific Computing, 2002.

E. Lidorikis, M. L. Povinelli, S. G. Johnson, & J.D. Joannopoulos, "Polarization-independent linear waveguides in 3D photonic crystals," preprint.

John D. Joannopoulos, Robert D. Meade & Joshua N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

Mary Megliola Franzen, ed. M. Schneider.

Web Design:
Sean Fulton, Pittsburgh Supercomputing Center

Revised: October 22, 2003