28 January 2019 Waves stranded at sea: bound states in the continuum in a strong coupling regime
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An explanation of bound states in the continuum (BICs) is offered. With particular attention to Friedrich–Wintgen BICs, the commentary presents a study by Bogdanov et al., which appears in the same issue of Advanced Photonics.

What, exactly, is a bound state in the continuum (BIC)? A BIC is an unconventional state that remains localized even upon its coexistence with the continuum of radiating modes. In theory, a BIC is characterized by the infinite radiative quality factor and zero linewidth.1 Amongst the various types of BICs, the so-called Friedrich–Wintgen BIC arises due to the destructive interference of two resonances coupled to the same radiation channel. Once the eigenvalue of one of the resonances becomes purely real, the state turns into a BIC. Generally, Friedrich–Wintgen BICs lie in the vicinity of the frequency crossings of the uncoupled resonances.

Recently, the exploration of BICs in the strong coupling regime has gained increasing attention to diverse systems such as coupled photonic-plasmonic devices,2 2D materials,3 and low-contrast dielectric gratings.4 In some of these systems, strong coupling between resonances of different origin has been studied such as the interaction of plasmonic modes and the optical waveguide modes of a hybrid system2 or the coupling of excitons and polaritons in a photonic crystal coupled to WSe2 monolayers.3 Such heterogeneous systems offer great opportunities for realizing new hybrid quasiparticles with rich physics. The Friedrich–Wintgen BICs arising in the vicinity of the avoided crossing of the resonance lead to very high-quality resonances.

BIC in a nanoparticle in the strong coupling regime.


In this issue of Advanced Photonics, Bogdanov et al.5 reveal the formation of the Friedrich–Wintgen BICs in a tiny resonant system as small as a nanoparticle (see Figure). First, the authors explore quasi-BIC states that arise due to the strong coupling between two classical phenomena (Mie-like and Fabry–Perot-like modes) supported by such a resonator. They then demonstrate that surprisingly high quality factors and strong light localization can be supported by a subwavelength cylinder due to the excitation of the quasi-BIC state. They also analytically examine the curious, tight relationship between the existence of the quasi-BIC states and the peculiarities of the Fano asymmetry parameter in the strong coupling regime, showing that the Fano asymmetry parameter becomes singular at the quasi-BIC point. The team confirmed this unusual strong coupling experimentally. By measuring the scattering cross-section of a cylindrical resonator filled with water, the authors are able to capture the “avoided crossing” (a direct confirmation of the case of strong coupling6) as a function of the cylinder aspect ratio.

The innovative ideas proposed and experimentally demonstrated by Bogdanov et al. could serve as a new paradigm for rapidly projecting the nascent BIC methodology onto numerous optical phenomena and applications that rely on high field localization and high quality factors, which now can be achieved with a single-particle resonator at the subwavelength scale, something that was difficult to achieve previously. On-a-chip applications such as low-threshold lasing and high-harmonic generation are examples of the many possibilities that would make use of such an exciting ultracompact novel nanophotonic platform.



Hsu C. W. et al., “Bound states in the continuum,” Nat. Rev. Mater., 1 16048 (2016). https://doi.org/10.1038/natrevmats.2016.48 Google Scholar


Azzam S. I. et al., “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett., 121 (25), 253901 (2018). https://doi.org/10.1103/PhysRevLett.121.253901 PRLTAO 0031-9007 Google Scholar


Koshelev K. L. et al., “Strong coupling between excitons in transition metal dichalcogenides and optical bound states in the continuum,” Phys. Rev. B, 98 (16), 161113 (2018). https://doi.org/10.1103/PhysRevB.98.161113 Google Scholar


Bulgakov E. N., Maksimov D. N., “Avoided crossings and bound states in the continuum in low-contrast dielectric gratings,” Phys. Rev. A, 98 (5), 053840 (2018). https://doi.org/10.1103/PhysRevA.98.053840 Google Scholar


Bogdanov A. et al., “Bound states in the continuum and Fano resonances in the strong mode coupling regime,” Adv. Photonics, 1 (1), 016001 (2019). https://doi.org/10.1117/1.AP.1.1.016001 Google Scholar


Novotny L., “Strong coupling, energy splitting, and level crossings: a classical perspective,” Am. J. Phys., 78 1199 –1202 (2010). https://doi.org/10.1119/1.3471177 AJPIAS 0002-9505 Google Scholar


Shaimaa I. Azzam is working towards her PhD in electrical and computer engineering at Purdue University. She received her MS and BS degrees in electrical engineering in 2014 and 2011, respectively. Her research interests include metasurfaces, lasers and nanolasers, multiphysics time and frequency domain photonics simulations, passive and active plasmonics, and topological states of light.

Alexander V. Kildishev works in the field of the theory and numerical models for nanophotonics. He has had a number of breakthrough results on negative refractive index metamaterials, optical artificial magnetic structures, loss compensation in metamaterials, plasmonic nanolasers, and optical metasurfaces, as well as optical cloaks and hyperlenses. His current h-factors are WEB of Science-50, Google Scholar-60. He is a coinventor of 14 issued and pending patents (7 U.S. patents).

© 2019 SPIE and CLP
Shaimaa I. Azzam and Alexander V. Kildishev "Waves stranded at sea: bound states in the continuum in a strong coupling regime," Advanced Photonics 1(1), 010503 (28 January 2019). https://doi.org/10.1117/1.AP.1.1.010503

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