It has been shown that a bound state in the continuum of a symmetric quantum-mechanical waveguide with a resonator can be formed at an arbitrarily short length of the resonator. This effect is due to multimodal interference; therefore, it cannot be explained in the simplest two-mode approximation in the Friedrich–Wintgen model and requires the inclusion of at least three modes. The results obtained within the analytical model have been confirmed by the numerical simulation of the stubbed waveguide the attractive potential of the impurity in the resonator.
Similar content being viewed by others
REFERENCES
C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, Nat. Rev. Mater. 1, 16048 (2016).
A. F. Sadreev, Rep. Prog. Phys. 84, 055901 (2021).
N. M. Shubin and A. A. Gorbatsevich, Phys. Rev. B 96, 205441 (2017).
C. S. Kim, A. M. Satanin, Y. S Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
Ch. S. Kim, O. N. Roznova, A. M. Satanin, and V. B. Shtenberg, J. Exp. Theor. Phys. 94, 992 (2002).
M. L. L. de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).
K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Yu. Kivshar, Phys. Rev. Lett. 121, 193903 (2018).
S. A. Dyakov, M. V. Stepikhova, A. A. Bogdanov, A. V. Novikov, D. V. Yurasov, M. V. Shaleev, Z. F. Krasilnik, S. G. Tikhodeev, and N. A. Gippius, Laser Photon. Rev. 15, 2000242 (2021).
E. N. Bulgakov and A. F. Sadreev, Phys. Rev. A 99, 033851 (2019).
K. Koshelev, A. Bogdanov, and Yu. Kivshar, Sci. Bull. 64, 836 (2019).
S. I. Azzam, A. V. Kildishev, R.-M. Ma, C.-Z. Ning, R. Oulton, V. M. Shalaev, M. I. Stockman, J.-L. Xu, and X. Zhang, Light Sci. Appl. 9, 1 (2020).
A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Yu. S. Kivshar, and B. Lukyanchuk, Science (Washington, DC, U. S.) 354, aag2472 (2016).
A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, Z. F. Sadrieva, K. B. Samusev, Yu. S. Kivshar, and M. F. Limonov, Adv. Photon. 1, 016001 (2019).
K. Koshelev, S. Kruk, E. Melik-Gaykazyan, J. H. Choi, A. Bogdanov, H. G. Park, and Yu. Kivshar, Science (Washington, DC, U. S.) 367, 288 (2020).
V. V. Klimov, Nanoplasmonics (Fizmatlit, Moscow, 2009; Pan Stanford, Singapore, 2011).
A. F. Sadreev, E. N. Bulgakov, and I. Rotter, JETP Lett. 82, 498 (2005).
A. F. Sadreev, E. N. Bulgakov, and I. Rotter, Phys. Rev. B 73, 235342 (2006).
A. F. Sadreev and A. S. Pilipchuk, JETP Lett. 100, 585 (2014).
K. Pichugin, H. Schanz, and P. Seba, Phys. Rev. E 64, 056227 (2001).
S. F. Sadreev and T. V. Babushkina, JETP Lett. 88, 312 (2008).
S. V. Aksenov and M. Yu. Kagan, JETP Lett. 111, 286 (2020).
D. V. Evans and R. Porter, Q. J. Mech. Appl. Math. 51, 263 (1998).
C. M. Linton, M. McIver, P. McIver, K. Ratcliffe, and J. Zhang, Wave Motion 36, 67 (2002).
G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, Proc. IEEE 79, 1643 (1991).
M. Asada, Y. Miyamoto, and Y. Suematsu, IEEE J. Quantum Electron. 22, 1915 (1986).
J. Sancheza-Dehesa, J. A. Porto, F. Agullo-Rueda, and F. Meseguer, J. Appl. Phys. 73, 5027 (1993).
A. A. Gorbatsevich and V. V. Kapaev, Russ. Microelectron. 36, 1 (2007).
N. M. Shubin, A. V. Friman, V. V. Kapaev, and A. A. Gorbatsevich, Phys. Rev. B 104, 125414 (2021).
A. S. Pilipchuk and A. F. Sadreev, Phys. Lett. A 381, 720 (2017).
E. Bulgakov and A. Sadreev, Phys. Rev. B 83, 235321 (2011).
A. S. Pilipchuk, A. A. Pilipchuk, and A. F. Sadreev, Phys. Scr. 94, 115004 (2019).
A. S. Pilipchuk, A. A. Pilipchuk, and A. F. Sadreev, Phys. Scr. 95, 085002 (2020).
F. Remacle, M. Munster, V. B. Pavlov-Verevkin, and M. Desouter-Lecomte, Phys. Lett. A 145, 265 (1990).
G. Cattapan and P. Lotti, Eur. Phys. J. B 60, 51 (2007).
J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals (Princeton Univ. Press, Princeton, NJ, 2011).
D. Dragoman and M. Dragoman, Prog. Quant. Electron. 23, 131 (1999).
Funding
This work was supported by the Russian Science Foundation (project no. 21-19-00808).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by R. Tyapaev
Rights and permissions
About this article
Cite this article
Shubin, N.M., Kapaev, V.V. & Gorbatsevich, A.A. Bound States in the Continuum in a Quantum-Mechanical Waveguide with a Subwavelength Resonator. Jetp Lett. 116, 205–211 (2022). https://doi.org/10.1134/S0021364022601373
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364022601373