Whispering Gallery Resonator Spans an Octave

Breck Hitz

White-light resonators are resonant across a broad, continuous swath of frequencies — perhaps as much as an octave — but still retain a high quality factor, or Q, at all of the resonant frequencies. Recently, scientists at California Institute of Technology’s Jet Propulsion Laboratory in Pasadena designed and demonstrated a white-light resonator based on a whispering gallery resonator. They developed the resonator with two primary applications in mind: cavity ringdown spectroscopy and electro-optic modulation.

A whispering gallery resonator, named after the acoustic effect that sometimes occurs in domed buildings, guides light by total internal reflection around the circumference of a circular optical structure. It can be relatively small, at hundreds of microns in diameter, and can have a Q on the order of 10¹⁰ or higher.

In cavity ringdown spectroscopy, the concentration of a substance is measured by placing it inside a resonator and injecting an optical pulse, with a wavelength absorbed by the substance, into the resonator. The concentration of the substance can be calculated from the time it takes the pulse to “ring down” as it circulates inside the resonator. One problem with the technique is that the resonant frequency of the resonator must correspond to the absorption frequency of the substance. This problem disappears with a white-light resonator.

One technique commonly employed in the past to overcome this problem is to inject the pulse so that it couples to a great many transverse and longitudinal modes of a nonconfocal resonator. The many modes overlap and result in a “whitened” spectrum, but the breadth of the spectrum is nonetheless limited by the typical nanometer reflectivity width of the dielectric resonator mirrors. The reflecting mechanism in a whispering gallery resonator, however, is total internal reflection, which is not wavelength-dependent.

Figure 1. By coupling light obliquely into the 5-mm-diameter, 500-μm-thick CaF₂ disk, the scientists excited many overlapping whispering cavity modes.

The scientists fabricated a 500-μm-thick, 5-mm-diameter whispering gallery resonator from optical quality CaF₂ (Figure 1). The thickness is crucial because it provides many angular degrees of freedom for light to propagate around the circumference with a slight tilt relative to the top of the resonator. There is a family of modes at any given tilt angle, each mode corresponding to an integral number of wavelengths around the circumference at that angle. The result is an extremely dense spectrum of modes, with neighboring modes separated from one another by less than their spectral width — in other words, a white-light spectrum (Figure 2).

To show that their resonator’s spectrum spanned a full octave, the researchers measured its ringdown time with light from three lasers: a frequency-doubled Nd:YAG at 532 nm from Oz Optics Ltd. of Ottawa, a diode laser at 780 nm from New Focus Inc. of San Jose, Calif., and an Nd:YAG at 1320 nm from the former Lightwave Electronics. The measured ringdown time of tens of nanoseconds varied by less than 50 percent across the spectrum and corresponded to a cavity Q of ~10⁸.