OPTICAL RESONATORS: Chaos theory optimizes resonator design

June 1, 1997
An asymmetrical optical resonator with highly directional light throughput has been designed by A. Douglas Stone and Jens Nöckel from Yale University (New Haven, CT).

An asymmetrical optical resonator with highly directional light throughput has been designed by A. Douglas Stone and Jens Nöckel from Yale University (New Haven, CT). Using quantum chaos equations, Stone and Nöckel developed a cavity design in which light can be trapped in a compact area with a radius anywhere from 5 to 100 µm. By departing from cylindrical symmetry, the design is potentially several orders of magnitude more efficient than symmetrical resonators of similar design.

"This is a new design that builds on an old idea," says Stone. Most conventional resonators rely on parallel mirrors to select light of a given frequency. The principles that determined resonator lifetime and emission directions for such Fabry-Perot resonators are well established. More recently, a cylindrical dielectric resonator was developed that traps light through total internal reflection, in so-called "whispering gallery modes."

In the early 1990s, Richard Slusher, of Lucent Technologies, Bell Labs (Murray Hill, NJ) employed this resonator in microdisk lasers. But the symmetrical design offers no predictability to the direction of emission. "Because it was intrinsically isotropic, this wasn`t good for lasers," says Stone. For almost all applications the light emission or detection needs to be directional. The idea for the asymmetric resonant cavity (ARC) arose from a collaboration with a colleague of Stone`s at Yale, Richard Chang, who was studying lasing liquid droplets. His group had observed for some time that these droplets would lase even when strongly deformed, but the light was no longer emitted equally in all directions. They wanted to understand why the light emerged where it did, a question to which conventional theory gave no answer.

"I`m a theorist, so my job was to understand the mathematics of the resonator when deformed. In principle, Maxwell`s equations tell us everything we need to know." But if the deformation is 10% or more, Maxwell`s equations are not easily solved and one needs a super computer. Even then, the results are often not of much use, says Stone. The modern branch of theoretical physics known as "quantum chaos" looks at exactly this sort of problemthe solution of wave equations with non-symmetrical boundaries. The term chaos here refers to the fact that the motion of a light ray bouncing within such a boundary is chaotic, that is, very sensitive to minute disturbances.

"A whimsical illustration of the chaos theory is the so-called `butterfly effect,`" says Stone. Because the short-term weather is a chaotic system, a butterfly fluttering its wings in Peking will change the weather two weeks later in New York.

The chaos in the ARC resonator makes possible the use of chaos theory to predict the three things one needs to know about a resonator: its frequency, its lifetime (the time light remains trapped inside), and the emission pattern or how light travels in and out, says Stone. Using computer simulations and indirect experiments, the researchers were able to predict the lifetime of the ARC resonator and its emission pattern. They predicted that, as the cavity is deformed, almost all of the light should escape from the far right and far left points, tangential to the surface of the cavity.

Stone says, "For a long time people have wanted to trap light in very small areas and move it around to make integrated optical `circuits.` This type of resonator could become an important component of such systems." Specifically the ARC may be useful for wavelength-division multiplexing, integrated optics, microlasers, and optical amplifiers.

Most of the researchers` knowledge of the properties of the ARC comes from theory and computer simulations. "Now we have to test the concept and work out the details in the lab," Stone says. Stone and Chang are principal investigators on a recent National Science Foundation grant to do just this, using prototype glass resonators supplied by Corning Inc. (Corning, NY).

"The ARC concept is really exciting from a basic optical physics point of view," says Stone. "But it is not yet a technology. Someone else will have to come up with the engineering ideas for how to incorporate this into existing or future systems, and that may be a few years away."

About the Author

Laurie Ann Peach | Assistant Editor, Technology

Laurie Ann Peach was Assistant Editor, Technology at Laser Focus World.

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