Bound state in the continuum

Schematic picture of energy levels and examples of different states. Discrete spectrum states^{[nb 1]} (green), resonant states (blue dotted line) ^[1] and bound states in the continuum (red). Partially reproduced from ^[2] and ^[3]

A bound state in the continuum (BIC) is an eigenstate of some particular quantum system with the following properties:

Energy lies in the continuous spectrum of propagating modes of the surrounding space;
The state does not interact with any of the states of the continuum (it cannot emit and cannot be excited by any wave that came from the infinity);
Energy is real and Q factor is infinite, if there is no absorption in the system.

BICs are observed in electronic, photonic, acoustic systems. Bound states in the forbidden zone, where there are no finite solutions at infinity, are widely known (atoms, quantum dots, defects in semiconductors). For solutions in a continuum that are associated with this continuum, resonant states^[1] are known, which decay (lose energy) over time. They can be excited, for example, by an incident wave with the same energy. The bound states in the continuum have real energy eigenvalues and therefore do not interact with the states of the continuous spectrum and cannot decay.^[2]

Cite error: There are <ref group=nb> tags on this page, but the references will not show without a {{reflist|group=nb}} template (see the help page).

^ ^a ^b Maheswari, A. Uma; Prema, P.; Shastry, C. S. (2010). "Resonant states and transmission coefficient oscillations for potential wells and barriers". American Journal of Physics. 78 (4): 412–417. Bibcode:2010AmJPh..78..412M. doi:10.1119/1.3276053.
^ ^a ^b Hsu, Chia Wei; Zhen, Bo; Stone, A. Douglas; Joannopoulos, John D.; Soljačić, Marin (2016). "Bound states in the continuum". Nature Reviews Materials. 1 (9): 16048. Bibcode:2016NatRM...116048H. doi:10.1038/natrevmats.2016.48. hdl:1721.1/108400. S2CID 123778221.
^ Koshelev, K .; Bogdanov, A .; Kivshar, Y. Engineering with bound states in the continuum. Opt. Photonics News 2020, 31, 38−45

[resonant-2] Maheswari, A. Uma; Prema, P.; Shastry, C. S. (2010). "Resonant states and transmission coefficient oscillations for potential wells and barriers". American Journal of Physics. 78 (4): 412–417. Bibcode:2010AmJPh..78..412M. doi:10.1119/1.3276053.

[hsu-3] Hsu, Chia Wei; Zhen, Bo; Stone, A. Douglas; Joannopoulos, John D.; Soljačić, Marin (2016). "Bound states in the continuum". Nature Reviews Materials. 1 (9): 16048. Bibcode:2016NatRM...116048H. doi:10.1038/natrevmats.2016.48. hdl:1721.1/108400. S2CID 123778221.

[4] Koshelev, K .; Bogdanov, A .; Kivshar, Y. Engineering with bound states in the continuum. Opt. Photonics News 2020, 31, 38−45

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