In nature, as in everyday life, we are surrounded by resonance. Vibra­tions near resonance cause strong impacts. Bridges collapse if soldiers march in unison; a kid can push themselves on a swing by moving their legs at the correct rate, and two pendulum clocks on the same table will synchronise. These examples show the enhanced sensi­tivity given to an object when it is provided with energy at a resonant frequency. It's no wonder then that physicists and engineers are always looking for ways to use resonance to trigger useful effects and strong responses by applying the smallest amount of energy. Now, a team of physicists from the University of Bath has found a way to use resonance to harness the energy of light more effectively inside micro­resonators.

For light, micro­resonators act as miniature racetracks, with photons zipping around the circle in loops. Photons of different colors correspond to waves oscillating at specific wave­lengths and frequencies. If the peaks of these waves reach the same point after a full loop is made around the resonator, then the energy storage capacity of the resonator hits a maximum when measured against frequency. In other words, the resonator and the light inside come to resonance. The ability of a resonator to store energy is charac­terized by the sharpness of the resonance, the finesse.

Physicists are caught in a race to maximize the finesses of resonators, so as to store as much energy as possible in a single resonator. The reason for this is not just bragging rights. When high light energy is circulating in a resonator, it starts to reveal interes­ting properties. For instance, the resonator begins to produce photons of light with new frequencies and therefore of different colours. A newly created rainbow of colors – a frequency comb – has many useful properties led to researchers working on the optical frequency comb technique winning the 2005 Nobel Prize in Physics. Unlike a sky rainbow, the one created in a resonator doesn't display a continuous spectrum of colors. Instead, it contains a regular and equally spaced pattern of colours, similar to the teeth on a comb. The regularity of these teeth allows these combs to be used for ultra-precise measure­ments – for instance, of distances and time.

The University of Bath study has found that boosting the strength of light matter inter­actions to make frequency combs is not the only reasons high-finesse micro­resonators are important. If finesse is relatively small, then tuning a laser around one of the resonances causes a given comb tooth to adjust its color conti­nuously. Reaching finesses of several thousands and into tens of thousands, however, starts to break this conti­nuity. When the conti­nuity is broken, a laser tuned to generate a pair of photons with two specific colors will need to pass through the idle interval before the next color becomes ignited. During this interval, there can be no conversion into new colors.

In the language of resonance theory, the interval creation is called Arnold tongues. Arnold tongues is a pheno­menon often found in networks of oscillators. The neurons in our brains work according to the rules of Arnold tongues to synchronize the transmission of signals. The micro­resonator tongues reported in the Bath study represent a map of the narrow tongue-like structures that shows how laser parameters should be tuned to either generate or not generate new colors.

The photon pair generation process is a key phen­omenon underpinning the development of tunable light sources for various appli­cations, and in particular for optical data processing and trans­mission. Discovering the connection between photon-pair generation and Arnold tongues is expected to boost the efficiency of this process. Further increasing of finesses is possible by freezing the micro­resonators to a temperature where the molecules it is made from stop vibrating. This is expected to trigger new ways to manipulate photons, and the Bath team plans to study these next.

Dmitry Skryabin from Bath's Centre for Photonics and Photonic Materials, said, “Since the 2005 Nobel Prize, the comb technology has rapidly downscaled to the size of computer chips. This means miniaturised frequency comb generators can have myriads of diverse appli­cations in for example pollution moni­toring, radar technology, and discovering of new planets.” (Source: U. Bath)

Reference: D. N. Puzyrev & D. V. Skryabin: Finesse and four-wave mixing in microresonators, Phys. Rev. A 103, 013508 (2021); DOI: 10.1103/PhysRevA.103.013508

Link: Centre for Photonics and Photonic Materials, Dept. of Physics, University of Bath, Bath, United Kingdom