Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Bound states in the continuum

Ferroelectric lithium niobate (LiNbO3) is widely used in integrated and guided-wave optics because of its favorable optical, piezoelectric, electro-optic, elastic, photoelastic, and photorefractive properties. However, detailed summaries of its pertinent physical properties and crystal structure are not readily available. In this tutorial paper, the important tensor physical properties and their mathematical descriptions are compiled and presented. The essential features of the structure of lithium niobate, including its hexagonal and rhombohedral unit cells, are illustrated and the principal (Cartesian) axes used in the description of the anisotropic properties are specified relative to the crystal structure. Errors in property coefficient values and structure information that have been propagated in the literature are corrected.

Lithium niobate: Summary of physical properties and crystal structure

Integrated optics and new wave phenomena in optical waveguides

Ahrroct-A method of analysis which uses a combination of analytical and numerical techniques has been developed to obtain an accurate solution to the coupled electromagnetic and acoustic fields set up by an interdigital transducer on the surface of a piezoelectric substrate. Full account is taken of the coupling to bulk modes as well as surface modes, and the solution for the charge on the electrodes includes both electrostatic charge and piezoelectrically regenerated charge. Programs have been written for interdigital arrays with uniform aperture but varying electrode width and pitch and arbitrary electrical connections. The theory is also valid for arbitrary crystal orientations. Generation and detection may be analyzed separately with information being provided on the partition of power into the various acoustic modes and the external load impedance, and the bulk wave radiation patterns are also computed. The program may also be used to find the insertion loss of a pair of transducers. Results are presented for the BleusteinGulyaev orientation of PZT-4 ceramic and the YZ and 41” rotated YX orientations of lithium niobate.

Analysis of Generation and Detection of Surface and Bulk Acoustic Waves by Interdigital Transducers

A SAW filter comprising a piezoelectric substrate and at least two filter tracks formed on the substrate, each having at least two IDT electrodes for input and output. The two filter tracks have substantially the same phase within a pass band, while it is substantially inverse-phased outside the pass band. For realizing the above-described conditions, input IDT electrode of one filter track is connected in parallel with input IDT electrode of the other filter track, while output IDT electrode of one filter track is connected in parallel with output IDT electrode of the other filter track. Furthermore, frequency values of said two filter tracks substantially coincide at a point 3dB lower from the peak transfer function value. Thus the above-configured SAW filter of the present invention is smaller in the overall size and offers a broad pass band and a steep attenuation characteristic.

Surface-acoustic-wave filter

Velocities and attenuations of piezoelectric leaky surface waves in LiNbO3 are analyzed. As a result, we have found that the effective electromechanical coupling coefficient of the leaky surface wave propagating along the X axis of a 64° rotated Y‐cut plane is very large, K2 = 0.113, and the attenuation of this wave, caused by radiation of the energy into the solid, is 0.036 dB/wavelength for a free surface and goes to zero for a metalized surface. Moreover, K2 of the elastic surface wave for a 130° rotated Y‐cut, X propagation, is found to be larger than that for a Y cut, Z propagation. The theory is verified experimentally. The theoretical analysis and experiments on amplification are performed for these types of waves. In an experiment utilizing the leaky surface wave, net terminal gain of 13 dB/cm is observed for the interaction between the carrier in 200‐Ω cm Si wafer (0.3×3×10 mm), separately mounted on a LiNbO3 surface, and the leaky surface wave. The air gap between the Si wafer and LiNbO3 single crystal is about 0.5 mμ.

Propagation and Amplification of Rayleigh Waves and Piezoelectric Leaky Surface Waves in LiNbO3

The third‐order elastic constants of lithium niobate have been measured by small‐amplitude ultrasonic waves as a function of applied stress, including the piezoelectric effects.

Third‐order elastic constants of lithium niobate

Low Insertion Loss Acoustic Surface Wave Filter Using Group-Type Unidirectional Interdigital Transducer

Low Insertion Loss Acoustic Surface Wave Filter using Group-Type Unidirectional Interdigital Transducer

TEm‐TMn mode conversion by electro‐optic and acousto‐optic effects in a metal‐diffused optical waveguide is described theoretically. Elastic surface waves and laser beams propagate along the X axis on Y‐cut LiNbO3 single crystals, i.e., interactions are collinear. We predict completely the TE1‐TM1 mode conversion at an elastic surface wave power of 33 mW along an interaction length of 5 mm with a width of 1 mm.

Kimio Shibayama

Papers

Propagation and Amplification of Rayleigh Waves and Piezoelectric Leaky Surface Waves in LiNbO3

Third‐order elastic constants of lithium niobate

Low Insertion Loss Acoustic Surface Wave Filter Using Group-Type Unidirectional Interdigital Transducer

Low Insertion Loss Acoustic Surface Wave Filter using Group-Type Unidirectional Interdigital Transducer

TE‐TM mode conversion by interaction between elastic surface waves and a laser beam on a metal‐diffused optical waveguide