High-Q Cavity

When optics researchers get together over coffee to discuss their favorite cavities, attention turns to microtoroids, tiny glass spheres, and photonic crystals with defects. These cavities all have a few things in common: they are all really good at storing light, and they are high-precision devices.

Physicists use a number, called Q, to characterize how well an optical cavity stores light: the higher the Q, the longer light stays confined in the cavity. You do not, it turns out, go blithely into your local fab and turn out a high-Q cavity. It takes a lot of practice and trial and error to create a high-Q optical cavity.

But, it turns out that it doesn't have to be as complicated as previously thought. Writing in Advanced Photonics, Andrey Bogdanov and colleagues have reported a new take on high(ish) Q cavities. Their approach draws inspiration from the physics of bound states in the continuum. But, perhaps a simpler way to envision this is to think about interference between loss channels.

The short summary of their finding is that a cavity may leak light in different ways, called channels. But, if the light waves from different channels destructively interfere, then no light leaks from any of the channels. Hence, a high-Q cavity is born.

Powered by interference

Bogdanov and colleagues considered a simple cylinder modeled as two different cavities. Light is stored by reflecting back and forth between the end facets, called a Fabry-Perot mode. At each facet, some light leaks from the cylinder. Light can also be stored by reflecting around the perimeter of the cylinder in a mode called a Mie mode. As with the Fabry-Perot mode, light leaks out of the Mie mode at each reflection.

Light shined on the cylinder will be stored in the Fabry-Perot and Mie modes. Left to its own devices, the light in both modes will quickly be lost: neither mode stores light very well. These are cavities with a Q so low we usually don't even think of them as cavities.

Strong coupling of modes in a dielectric resonator.

However, Bogdanov and colleagues noted that the light emitted from the cylinder via the Fabry-Perot mode can interfere with the radiation emitted from the Mie mode. This may not sound special, but often the properties of different modes prohibit this from happening.

So, how do you make a high-Q cavity from a cylinder? The key is to ensure that the radiation from the two modes destructively interferes with each other. When that happens, the light stored by the cylinder in the two modes cannot easily be emitted.

The result is a mode with a Q of a few thousand. Eventually, light leaks from the cylinder anyway, but that happens in a completely different way. Essentially, the light has to be scattered out via some imperfection in the cylinder.

Not content with only calculating the properties of their new cavity, the researchers also performed an experiment using a cylinder of water and microwaves. They obtained remarkably good agreement between their calculations and experimental results.

A picky cylinder

An interesting facet of the research is something called the mode spacing. In a normal optical cavity, the modes are determined by the relationship between the dimension of the cavity and the wavelength of light. The result is a regularly spaced set of wavelengths that match the cavity. Light with these wavelengths will be stored in the cavity.

But, in order for the light to be stored, destructive interference between the two different cavities is required. The wavelength has to have the right relationship with the length of the cylinder and with the perimeter of the cylinder. This thins out the regularly spaced set of wavelengths, leaving only a few lonely leftovers that match the combined cavities.

Why does any of this matter? High-Q cavities are great for many applications: think of lasers with really sharply defined wavelengths, very sensitive sensors, or high-precision filters. The simple cylinder described in this paper isn't ready for any of these applications yet, but it is headed in that direction.

Of course, this is only a light summary of the paper. Dig in and you will find the joys of avoided crossings, mode patterns, and perturbation theory. What more could you ask for with your morning coffee?

Read the article in Advanced Photonics on the SPIE Digital Library: doi.org/10.1117/1.AP.1.1.016001

Read a technical commentary from S. I. Azzam and A. V. Kildishev:  doi.org/10.1117/1.AP.1.1.010503