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Optical physics

Trapping the light fantastic

Using a material called a photonic crystal, researchers have designed a mirror that is, in a certain sense, perfect — there is in principle no light transmitted through it nor absorbed by it. See Letter p.188

Storing or confining light without absorbing it is of great importance for both science and technology. A device or system for trapping light is known as an optical resonator, and its most basic component is some kind of reflecting surface or region — a mirror in the general sense of the word. The most common type of mirror, a glass surface covered with a thin metal layer, has been around for two millennia, and mirrors of this type are crucial components of many optical systems. However, metal-based mirrors do absorb light to some degree. So, in modern optics research, scientists have developed many types of reflecting surfaces and resonators based on other principles. Given the tremendous and long-standing emphasis that optics places on trapping light, it is surprising that a substantially new type of mirror could still be discovered, but that is precisely what Hsu et al. have done1 (page 188 of this issue).

The authors have designed a mirror based on a well-established system in modern optical physics known as a photonic crystal2. This is a dielectric (non-conducting) material that is patterned, often simply by drilling or cutting out a series of air holes, so as to leave a spatially varying but three-dimensional, periodic structure (Fig. 1). The system can trap, guide and control light using optical interference in a similar manner to the familiar one-dimensional grating, but with much greater design flexibility.

Figure 1: A perfect mirror.
figure1

Hsu and colleagues1 have designed a photonic-crystal system that acts as a perfect mirror. The system consists of a silicon nitride (Si3N4) layer patterned periodically with holes, submerged in a liquid and mounted on a silicon dioxide (SiO2) substrate. The liquid has the same index of refraction as the SiO2 substrate, so that it gives the system up–down symmetry for light propagation. At one specific angle of incidence, θ, light of a certain frequency is perfectly reflected, with no absorption or transmission through the Si3N4 layer owing to a subtle interference effect. This indicates that a perfectly trapped state of light exists within the medium.

For example, one can make photonic-crystal waveguides that can confine or steer light just below the surface of the crystal. But just as for conventional waveguides, the light is totally internally reflected and thus fully confined only if it hits the surface at a sufficiently shallow angle. If it hits the surface at a steeper angle, it partially refracts out into the air and travels off to infinity. Such a partially trapped light wave is called a resonance; it can be observed by the strong reflection of an incident light wave, at the corresponding (steeper) angle, that penetrates into the crystal before reflecting back out.

However, Hsu et al. have discovered theoretically, and demonstrated experimentally, a photonic crystal that can violate this conventional behaviour at its surface: at a specific angle and frequency, the expected strong reflection resonance disappears. This implies that light cannot escape from inside at all, even though at this angle it is not totally internally reflected. Hence, at this angle and frequency, the system acts as a new kind of perfect mirror for a light wave approaching the surface of the crystal from inside. As a result of this behaviour, light can be trapped in the crystal indefinitely at a specific frequency and angle. Its lifetime, or 'Q value' in the language of resonance theory, is infinite.

The authors show that this effect is due to a subtle kind of coincidence, similar to a phenomenon in quantum theory known as accidental degeneracy, in which the coupling between light waves inside and outside the photonic crystal vanishes simultaneously for both possible polarization states of light, even though there is no symmetry principle that demands that this happen (cases in which symmetry prevents coupling were previously known). In their system, the designers can vary three parameters (the frequency and the tilt angle of the incident light in both directions perpendicular to the crystal surface), which are enough to ensure that this 'coincidence' always occurs. Hence, their effect is robust against many types of small imperfections, such as those that actually exist in their, and any, experiment. Such imperfections slightly perturb the angle at which the light is perfectly trapped, but they do not eliminate the effect. The ultimate source of the perfect trapping, the authors show, can be traced back to destructive interference between different escape channels.

In fact, this work relates to a long-standing question in wave physics, which was famously addressed by two giants of quantum theory, John von Neumann and Eugene Wigner, in 1929. They asked if the Schrödinger equation of quantum mechanics allows 'bound states' (in their case, localized, trapped electron states) in the continuum — that is, if a perfect potential-energy trap could exist for an electron at the same energy at which a free electron could exist at infinity3. Although conventional wisdom held that this was impossible, von Neumann and Wigner showed that it can indeed be done in principle, and they constructed mathematically the special type of potential-energy function (analogous to the photonic-crystal structure in the current work) that would allow this to happen, at one specific energy. However, such a potential-energy trap was impractical to realize, because it extended out an infinite distance from its centre. Since that time, there have been several proposals for creating bound states in the continuum, and a few4,5,6 were quite similar to Hsu and colleagues' realization. But none have been demonstrated experimentally, nor do they have the robustness and ease of implementation of the current work.

Hsu and co-authors' mirror presents a promising optical element for applications. Although in theory the mirror is perfect, and the current experiment indicates that it is extremely good, there are some imperfections that allow light to escape. The goal will be to tailor the leakage to be just right for proposed applications. A unique property of resonances of this type is that, although very little light will leak out to infinity, the electric field of the trapped light does extend outwards some distance across the entire surface. Resonances with such large surface area and high Q are just what are needed to make more powerful, highly directional, 'single-mode' lasers, as well as efficient surface sensors for biological and chemical applications.

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Correspondence to A. Douglas Stone.

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Stone, A. Trapping the light fantastic. Nature 499, 159–160 (2013). https://doi.org/10.1038/499159a

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