Optical-fiber microcavities reach angstrom-scale precision

A long-standing goal of optical science is the development of devices such as miniature buffers, microlasers, optical switches, and filters that can be assembled into an all-optical computer—no electrons needed. The fundamental structure required for all of those circuit elements is the microresonator, whose highly reflecting walls can confine a light signal in a tiny volume for up to hundreds of microseconds.

If fashioned into dielectric toroids, disks, or spheres a few tens of microns in diameter, the resonators store the light in the form of whispering-gallery modes, so called because the optical waves circulate by total internal reflection around a perimeter just as acoustic waves do around the dome of Saint Paul’s Cathedral in London. The resonance condition occurs whenever the roundtrip distance is an integral number of wavelengths.

The appeal of such whispering-gallery-mode resonators, particularly those made of silica, lies in their extremely high Q factor. A measure of light’s survival time, the Q factor is the ratio of the resonance wavelength to its spectral width and can, in such resonators, reach up to 10¹⁰. That’s at least two orders of magnitude higher than is achievable from state-of-the-art lithographically etched resonators such as those in photonic crystals. The higher the Q, the longer the circulation of light, the sharper the resonance spectrum, and the more sensitive to refractive-index variations is each resonator in a circuit.

Getting individual resonators in series to efficiently pass signals between them, however, requires matching the resonance wavelengths in each one. But precise tuning has proven difficult because the resonances are determined by a microcavity’s shape and size. In one promising approach developed over the past decade, researchers locally heat a glass fiber using a flame or carbon dioxide laser and pull it so that a bulge forms between tapered sections. In 2009 Arno Rauschenbeutel and colleagues from Johannes Gutenberg University used the technique to create a bottle-shaped microresonator whose local curvature axially confined whispering-gallery modes and could be accurately reproduced to within 2 μm. ¹

Misha Sumetsky and his colleagues at OFS Laboratories (a former branch of Bell Labs) now report an improvement in that precision to an astonishing 2 Å by modifying the approach in a way that could hardly be simpler: They opted not to stretch the fiber but merely to heat it locally to anneal away residual stresses. ² Mode-confining bulges still appeared but with surprising fidelity. As proof of principle, the group fabricated a series of five nearly identical resonators that are each separated, like beads on a string, by 100 μm of ordinary silica fiber. ³ 1 panel a illustrates the concept.

It’s a SNAP

Sumetsky hit on the method last year after trying to determine the natural variations in the diameter of an optical fiber. University of Bath physicists Tim Birks, Jonathan Knight, and Tim Dimmick had proposed an experiment a decade earlier to resolve the issue: ⁴ Light sent through a thin, tapered microfiber perpendicular to the main fiber will evanescently couple to that fiber and excite modes at wavelengths that satisfy the resonance condition. The radius can thus be inferred from the microfiber’s transmission spectrum, whose dips in intensity reveal the resonance wavelengths. Shifts in the radius are directly proportional to shifts in the wavelengths.

As Sumetsky and colleagues translated the microfiber along the main fiber’s axis a few microns at a time, they noticed only exceedingly subtle shifts in the resonance wavelengths, an indication that even standard, off-the-shelf silica fiber could be uniform to within a few angstroms over millimeter lengths. Armed with that insight, they set out to fabricate extremely shallow bulges—a change in diameter of a few nanometers—to deliberately confine the resonant modes.

As hot glass is drawn under a known tension into fiber, it preserves that tension as it cools, an effect discovered at OFS Labs several years ago. The researchers found that they could incrementally release the frozen stress by locally heating the fiber for just five seconds to a few hundred degrees—well below silica’s melting point. As the fiber got hotter with increases in laser power, the concomitant additional relaxation increased the fiber’s “effective radius”—a parameter capturing the combined effect of changes in actual radius and refractive index. That the fiber relaxed in so reproducible a way for a given laser power was, Sumetsky admits, “just our luck and completely unexpected.” The simple, quick, inexpensive, and reproducible nature of the technology prompted the researchers to coin the name “surface nanoscale axial photonics,” or SNAP.

The OFS researchers exposed ordinary 36-μm-diameter fiber to five separate laser bursts, each generating a 2.5-nm modulation in effective radius. Altogether, the exposures produced a chain of quantum-well microresonators spanning close to a half-millimeter of fiber, as shown in 1 panel b. Although the quantum wells are three-dimensional, the slow axial propagation of light through the chain follows a one-dimensional Schrödinger equation, whose potential is given by the shallow radius variation. The potential barriers between wells turned out to be low enough that the resonators coupled together, evidenced in the splitting of one band of modes and their tunneling from one resonator to the next.

To measure how well the radius variations—and thus the resonance wavelengths—of each resonator matched those of its neighbors, the researchers took transmission spectra every 10 μm along the microfiber axis. Birks’s earlier prescription for equating a shift in radius with a shift in a resonance wavelength works ideally outside a microcavity. But inside, resonant modes oscillate back and forth axially as helices between two turning points. Accordingly, the resonance dips don’t shift in wavelength with radius but remain nearly constant as the microfiber is scanned across each potential well. The widths of the resonances, however, narrow abruptly at the barrier regions, where coupling to the microfiber is weakest. So to gauge the tuning across different resonators, the researchers had to directly compare wavelengths of their narrowest resonances. The variation in those wavelengths showed that the radii were identical to within 2 Å.

Chalcogenides

Heat isn’t the only process that can reproducibly vary the effective radius of silica fiber so subtly. Sumetsky and company found that control over the change in effective radius was even finer—to within 1 Å—when they exposed photosensitive germanium-doped silica to UV light.

And silica isn’t the only glass fiber that can be formed into microresonators using laser light. Benjamin Eggleton and colleagues at the University of Sydney have demonstrated a similarly subtle localization of electromagnetic modes in a cavity they created from a half-millimeter strip of arsenic trisulfide fiber. ⁵

As part of the chalcogenide class of amorphous semiconductors, As₂S₃ forms weak interatomic bonds—at least compared with those in oxides like silica—which makes it transparent into the mid-IR region of the spectrum. And like doped silica, the chemical bonding changes when the material is exposed to light with a wavelength near the band edge. That photosensitivity has led to applications in solar cells, IR sensors, and phase-change memories in compact disks. ⁶ The material is also highly polarizable, its refractive index a hundred times more nonlinear than that of doped silica.

Like Sumetsky’s team, Eggleton and company exploited that photosensitivity using green laser light and monitored the resonance wavelengths of circulating whispering-gallery modes. As in silica, the change in the effective radius of As₂S₃ was dramatic and quick. But it was reversed in sign: The University of Sydney researchers measured a change of −0.24 nm/min, large enough that a single 12-minute light exposure created a mode-trapping microcavity. (The negative sign meant they had to irradiate outside the developing cavity.) Moreover, because the material remained cool during the exposure, Eggleton was able to dynamically monitor changes in the transmission spectra.

How the effective radius of a chalcogenide fiber may change with heat and ion doping remains an interesting and open question.