Siberian Federal University

The efficiency of optoelectronic devices that generate, transmit and use light, whether they are lasers, waveguides, sensors, or light filters, is determined by a parameter called Q-factor. Oscillations of standing or travelling light waves occur in all these systems. The Q-factor determines how many times the energy reserves in the system are greater than the energy loss during a single period of oscillation. The concept of bound states in the continuum enables to implement devices with a configurable Q-factor, the value of which can be arbitrarily large and is limited only by unavoidable losses in the system materials themselves.

Bound state in the continuum (BIC) is a state of the wave in which it has enough energy to leave the system, but it cannot do this due to destructive interference (the addition of waves, in which they extinguish each other). The Q-factor of such a system is infinite, so the wave does not come out of it, i.e. there are no losses. BIC was first described for an electron in an atom in 1929 by Wigner and von Neumann, during the heyday of quantum mechanics. The scientists came up with a special kind of atomic potential that was not found in reality. The fact is that an electron manifests itself as a wave, which is a key concept of quantum mechanics, and the potential of an atom is a barrier of a special shape, on which such a wave falls when the electron leaves the atom. In this case, the electron wave is repeatedly reflected from the barrier and forms a set of waves that eventually destructively interfere with each other. This means that they prevent each other from leaving, and therefore the electron is bound to the atom, although its energy is sufficient to break away from it, i. e. to ionize the atom.

Long time BIC was simply a paradox until in 1985 Friedrich and Wintgen showed that it was not necessary to create a complex potential (a barrier to electronic waves) for their implementation. They considered a simpler system and showed that for the implementation of BIC it is enough to provide destructive interference of only two waves propagating in the system. After this work, BIC was found experimentally in many physical systems. However, there is a theorem that prohibits the implementation of BIC in one-dimensional structures in which parameters change only in one direction.

In the first part of the work, the Krasnoyarsk scientists managed to circumvent this theorem and show the possibility of the existence of BIC in a one-dimensional layered structure. To do this, they introduced a new degree of freedom in the form of a magnetic field applied to the system instead of the second spatial dimension. Only three layers were considered, in the central one of which the direction of the magnetic field is rotated relative to the outer ones. An electron wave incident on the central layer splits into two waves, which can destructively interfere when leaving this layer with certain parameters of the system, and thus lock themselves inside it.

However, the experimental implementation of even such a simple system, as in the case of electronic waves, is fraught with significant difficulties. Therefore, the scientists decided to carry out an experimental implementation for another type of waves — light.

“As you know, interference is a fundamental property of all types of waves, whether they are electronic, sound, light or radio waves. We have considered a similar optical structure — it also consists of three parts: two photonic crystals (a multi-layer pie of dielectric layers of alternating materials), between which a liquid crystal layer is enclosed. The liquid crystal in different directions has anisotropic (different) properties due to its structure. We can distinguish the so-called optical axis -the direction in which the elongated liquid crystal molecules line up. The light wave incident on the liquid crystal layer splits into two waves, which can destructively interfere when exiting this layer with a certain orientation of the optical axis, and thus lock themselves inside it. The problem is similar to that described for electronic waves, and the rotated optical axis plays the role of a rotated magnetic field,” explained Pavel Pankin, senior lecturer at the Department of Electric Technology and Electrical Engineering, SibFU.

The scientist noted that the Krasnoyarsk team of researchers managed to develop a theoretical model and perform all the calculations, and their colleagues from National Chiao Tung University (Taiwan) made a sample and carried out the necessary optical measurements: “As a result, we succeeded in confirming the existence of bound states in the continuum described by Friedrich and Wintgen. We were the first in the world to do this in one-dimensional layered structures. In addition, we succeeded to show that it is possible to adjust the Q-factor of the system, approaching or moving away from BIC by a simple mechanical rotation of the optical axis of the liquid crystal.”

This work was supported by the Russian Foundation for Basic Research within the framework of grants 19-52-52006 and 19-02-00055.