Devices called optical resonators confine light, but for only a limited time because of unavoidable light emission. Writing in Nature, Jin et al.1 report that such emission can be greatly reduced by using the interference of light waves known as bound states in the continuum. Such waves are akin to exotic electron waves that were introduced in the theory of quantum mechanics almost a century ago2. The authors’ finding could have many technological implications for nanophotonics, quantum optics and nonlinear optics — the study of how intense light interacts with matter.
Interference is a common wave phenomenon in physics, whereby two or more waves pass through one another to produce a combined waveform. Consider the case in which these waves are correlated with one another, either because they come from the same source or because they have almost the same frequency. If the crest of one wave coincides with the crest of another wave, the combined amplitude will be the sum of the individual amplitudes. And if the crest of one wave meets the trough of another wave, the combined amplitude will be the difference in the individual amplitudes. These two scenarios are called constructive and destructive interference, respectively.
The effects of interference can be observed for all waves, but interference associated with bound states in the continuum (BICs) has attracted much attention in photonics over the past few years3. BICs are formed by the destructive interference of several ordinary light waves that have a similar wavevector — a quantity that describes a wave’s velocity and direction of propagation. This interference provides a means of achieving strong confinement of light and of increasing its amplitude through a phenomenon known as optical resonance. It can also be used to tune an optical resonator into the ‘supercavity’ regime, in which emission of light from the resonator is restrained4. Several approaches to realizing BICs have been suggested for waves in electronic, electromagnetic and acoustic systems.
The concept of BICs was proposed for unusual states of electron waves by two pioneers of quantum mechanics, John von Neumann and Eugene Wigner2. They discovered that specific potentials (potential-energy profiles) could support spatially localized electron states that have energies larger than the maximum energy of the potential. In other words, the states could be confined even though their energies would normally allow them to escape. In photonics, a light wave that is trapped by an optical resonator can be converted to a BIC under certain conditions3 — a discovery that was made only in 2008.
The main characteristic of an optical resonator is the quality factor — the ratio of the time over which the device can trap light to the period of the wave’s oscillation. If the light waves destructively interfere to form BICs, the quality factor greatly increases. Moreover, in the BIC regime, the quality factor theoretically tends to infinity when one of the system parameters, such as the size of the resonator, is tuned. By contrast, the quality factor of a conventional resonance is not substantially affected by parameter variations.
In practical optical resonators, the quality factors of BICs are fundamentally limited by inevitable fabrication defects, which scatter light out of the plane of the device. Any light wave that is scattered off a structural imperfection changes its wavevector. To prevent scattering losses, waves must remain trapped in the resonator even after these changes have occurred. In other words, the quality factor needs to be high both before and after scattering.
Jin and colleagues have suggested and demonstrated an innovative physical mechanism for achieving optical resonances that are extremely robust to out-of-plane scattering. They considered a structure called a photonic crystal slab, consisting of a submicrometre-thick dielectric (electrically insulating) membrane patterned with a square lattice of circular holes.
The authors first ran numerical simulations to study the optical resonances in their membrane. By carefully selecting the membrane’s parameters, they achieved several simulated BICs that had different wavevectors. They then altered the periodicity of the lattice until the BICs had the same wavevector. This gave rise to a new type of optical resonance: a merging BIC (which one might refer to as a super-BIC; Fig. 1). The hallmark of a merging BIC is that it increases the quality factor of all waves that have nearly the same wavevector as the resonance, reducing scattering losses from the resonator.
Jin et al. then experimentally demonstrated their mechanism by fabricating a set of silicon membranes that had different lattice periodicities. Some of these membranes supported a merging BIC at telecommunication wavelengths (about 1,550 nanometres) and others were close to this merging-BIC regime. The authors used a tunable telecommunication-wavelength laser to measure the intensity of scattered light along different directions for each of the samples. They found that the membranes supporting a merging BIC had a quality factor that was about 10 times larger than that for the membranes not in the merging-BIC regime. Moreover, they showed that the observed increase in quality factor was robust by finding a similar level of enhancement in all of the fabricated samples that had a merging-BIC design.
The demonstration could have many consequences for engineering high-quality resonances in nanophotonics. The ability to convert light waves into BICs allows the realization of the supercavity regime, in which highly compact resonators can have extremely large quality factors5. Dielectric materials that have high refractive indices could be used to reduce the resonator dimensions and to combine individual BIC resonators that have high-quality resonances into structured arrays6.
We predict that an electromagnetic theory will be developed for describing high-quality resonances in individual dielectric nanoparticles of high refractive index and arrays of such nanoparticles, and that they all will be expressed in terms of the mathematics used to study interference in quantum mechanics. In the real world, the engineering of quality factors in the BIC regime could lead to substantial enhancement of nonlinear and quantum effects, the development of lasers that consume little power, and the realization of nanoscale resonators that facilitate strong confinement of light and large boosts to its amplitude.
Nature 574, 491-492 (2019)