Skip to main content
SpringerLink
Log in

“Dark” States As a Particular Case of the Emission Spectrum of an Exceptional Surface Wave

  • ATOMS, MOLECULES, OPTICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Under conditions of total internal reflection (TIR) of a plane bulk electromagnetic wave incident from outside on the surface of an optically transparent layered structure, the case where the numerator and denominator of the input surface wave impedance turn simultaneously to zero may correspond to the formation of a “dark” state. This is related to the occurrence of a point of degeneracy of the spectra of leaking exceptional surface waves (ESWs) of the first and second kind against the background of the continuous spectrum of radiative modes. For these waves, the instantaneous energy flux through the interface with a semibounded optical denser medium in an open radiative channel is zero at any instant. When approaching the point of dark state occurrence, the local maxima of the effects of first-order nonspecular reflection, accompanying resonant excitation of leaky ESWs, unlimitedly increase.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

REFERENCES

  1. J. von Neuman and E. Wigner, Z. Phys. 30, 467 (1929).

    Google Scholar 

  2. S. I. Azzam and A. V. Kildishev, Adv. Opt. Mater. 9, 2001469 (2021).

  3. C. W. Hsu, B. Zhen, A. D. Stone, et al., Nat. Rev. Mater. 1, 16048 (2016).

    Article  ADS  Google Scholar 

  4. M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, Phys. Rev. Lett. 108, 070401 (2012).

  5. J. Gomis-Bresco, D. Artigas, and L. Torner, Nat. Photon. 11, 232 (2017).

    Article  ADS  Google Scholar 

  6. S. Mukherjee, J. Gomis-Bresco, P. Pujol-Closa, et al., Phys. Rev. A 98, 063826 (2018).

  7. S. Mukherjee, J. Gomis-Bresco, P. Pujol-Closa, et al., Opt. Lett. 44, 5362 (2019).

    Article  ADS  Google Scholar 

  8. S. Mukherjee, J. Gomis-Bresco, D. Artigas, et al., Opt. Lett. 46, 2545 (2021).

    Article  ADS  Google Scholar 

  9. S. Mukherjee, D. Artigas, and L. Torner, Phys. Rev. B 105, L201406 (2022).

  10. T. Tamir and A. A. Oliner, Proc. IEEE 110, 310 (1963).

    Google Scholar 

  11. A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering Reactions and Decays in Nonrelativistic Quantum Mechanics (Nauka, Moscow, 1966; Israel Program for Sci. Transl., Jerusalem, 1969).

  12. F. I. Fedorov, Optics of Anisotropic Media, 2nd ed. (URSS, Moscow, 2004) [in Russian].

    Google Scholar 

  13. M. Rybin and Y. Kivshar, Nature (London, U.K.) 541, 164 (2017).

    Article  ADS  Google Scholar 

  14. T. Tamir and H. L. Bertoni, J. Opt. Soc. Am. 61, 1397 (1971).

    Article  ADS  Google Scholar 

  15. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1980; Akad. Nauk SSSR, Moscow, 1957).

  16. Ch. S. Kim, A. M. Satanin, Yu. S. Dzhoe, et al., J. Exp. Theor. Phys. 89, 144 (1999).

    Article  ADS  Google Scholar 

  17. H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).

    Article  ADS  Google Scholar 

  18. D. V. Kulagin, A. S. Savchenko, A. S. Tarasenko, S. V. Tarasenko, and V. G. Shavrov, JETP Lett. 95, 229 (2012).

    Article  ADS  Google Scholar 

  19. Yu. V. Gulyaev, S. V. Tarasenko, and V. G. Shavrov, Phys. Usp. 63, 872 (2020).

    Article  ADS  Google Scholar 

  20. V. I. Al’shits, V. N. Lyubimov, and A. Radowicz, J. Exp. Theor. Phys. 104, 9 (2007).

    Article  ADS  Google Scholar 

  21. M. A. Miller and V. I. Talanov, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 4, 795 (1961).

    Google Scholar 

  22. S. V. Biryukov, Yu. V. Gulyaev, V. V. Krylov, and V. P. Plesskii, Surface Acoustic Waves in Inhomogeneous Media (Nauka, Moscow, 1991; Springer Science, New York, 2012).

  23. I. A. Viktorov, Sound Surface Waves in Solids (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  24. D. Chauvat, O. Emile, F. Bretenaker, et al., Phys. Rev. Lett. 84, 71 (2000).

    Article  ADS  Google Scholar 

  25. V. N. Lyubimov, D. G. Sannikov, Sov. Phys. Solid State 14, 575 (1972).

    Google Scholar 

  26. L. G. Naryshkina and M. E. Gertsenshtein, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 10, 91 (1967).

    Google Scholar 

  27. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, Upper Saddle River, 1984).

    Google Scholar 

Download references

Funding

This study was supported by the Russian Science Foundation, grant no. 20-19-00745-P.

Author information

Authors and Affiliations

  1. Faculty of Physics and Technology, Donetsk State University, 283001, Donetsk, Russia

    O. S. Sukhorukova

  2. Galkin Institute for Physics and Engineering, 283114, Donetsk, Russia

    O. S. Sukhorukova, A. S. Tarasenko & S. V. Tarasenko

  3. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 125009, Moscow, Russia

    V. G. Shavrov

Authors
  1. O. S. Sukhorukova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Tarasenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. V. Tarasenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. G. Shavrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Tarasenko.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Translated by Yu. Sin’kov

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

APPENDIX A

$${\mathbf{E}}_{{\text{o}}}^{{{\text{t}},{\text{r}}}} = k_{{||{\text{o}}}}^{{{\text{t}},{\text{r}}}}( \pm \sin \vartheta {\mathbf{b}} \mp \cos \vartheta {\mathbf{a}}),$$
$${\mathbf{H}}_{{\text{o}}}^{{{\text{t}},{\text{r}}}} = \frac{h}{{{{k}_{0}}}}{{(k_{{||{\text{o}}}}^{{{\text{t}},{\text{r}}}}{\text{)}}}^{2}}\cos \vartheta {\mathbf{b}} + \left( {\frac{{{{k}_{0}}}}{h}{{\varepsilon }_{{{\text{o}} \mp }}}\sin \vartheta } \right){\mathbf{a}},$$
$${\mathbf{E}}_{{\text{e}}}^{{{\text{t}},{\text{r}}}} = {{(k_{{||{\text{o}}}}^{{{\text{t}},{\text{r}}}}{\text{)}}}^{2}}\cos \vartheta {\mathbf{b}} + \left( {\frac{{k_{{\text{o}}}^{2}}}{{{{h}^{2}}}}{{\varepsilon }_{{{\text{o}} \mp }}}\sin \vartheta } \right){\mathbf{a}},$$
$${\mathbf{H}}_{{\text{e}}}^{{{\text{t}},{\text{r}}}} = \frac{{{{k}_{0}}}}{h}{{\varepsilon }_{{{\text{o}} \mp }}}k_{{||{\text{e}}}}^{{{\text{t}},{\text{r}}}}( \mp \sin \vartheta {\mathbf{b}} \mp \cos \vartheta ).$$

APPENDIX B

$$\bar {\bar {Q}} \equiv \left( {\begin{array}{*{20}{c}} {{{Q}_{{11}}}}&{{{Q}_{{12}}}} \\ {{{Q}_{{21}}}}&{{{Q}_{{22}}}} \end{array}} \right).$$
$${{Q}_{{11}}} = ({{{\mathbf{H}}}_{{\text{e}}}}{\mathbf{a}}){{s}_{{{\text{ey}}}}} - \frac{{({{{\mathbf{E}}}_{{\text{e}}}}{\mathbf{a}}){{c}_{{{\text{ed}}}}}}}{{({{{\mathbf{E}}}_{{\text{o}}}}{\mathbf{a}}){{c}_{{{\text{od}}}}}}}({{{\mathbf{H}}}_{{\text{o}}}}{\mathbf{a}}){{s}_{{{\text{oy}}}}},$$
$${{Q}_{{12}}} = ({{{\mathbf{H}}}_{{\text{e}}}}{\mathbf{a}}){{c}_{{{\text{ey}}}}} - \frac{{({{{\mathbf{E}}}_{{\text{e}}}}{\mathbf{a}}){{s}_{{{\text{ed}}}}}}}{{({{{\mathbf{E}}}_{{\text{o}}}}{\mathbf{a}}){{s}_{{{\text{od}}}}}}}({{{\mathbf{H}}}_{{\text{o}}}}{\mathbf{a}}){{c}_{{{\text{oy}}}}},$$
$${{Q}_{{21}}} = ({{{\mathbf{E}}}_{{\text{e}}}}{\mathbf{b}}){{c}_{{{\text{ey}}}}} - \frac{{({{{\mathbf{E}}}_{{\text{e}}}}{\mathbf{a}}){{c}_{{{\text{ed}}}}}}}{{({{{\mathbf{E}}}_{{\text{o}}}}{\mathbf{a}}){{c}_{{{\text{od}}}}}}}({{{\mathbf{E}}}_{{\text{o}}}}{\mathbf{b}}){{c}_{{{\text{oy}}}}},$$
$${{Q}_{{22}}} = ({{{\mathbf{E}}}_{{\text{e}}}}{\mathbf{b}}){{s}_{{{\text{ey}}}}} - \frac{{({{{\mathbf{E}}}_{{\text{e}}}}{\mathbf{a}}){{s}_{{{\text{ed}}}}}}}{{({{{\mathbf{E}}}_{{\text{o}}}}{\mathbf{a}}){{s}_{{{\text{od}}}}}}}({{{\mathbf{E}}}_{{\text{o}}}}{\mathbf{b}}){{s}_{{{\text{oy}}}}}.$$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sukhorukova, O.S., Tarasenko, A.S., Tarasenko, S.V. et al. “Dark” States As a Particular Case of the Emission Spectrum of an Exceptional Surface Wave. J. Exp. Theor. Phys. 137, 753–762 (2023). https://doi.org/10.1134/S1063776123120142

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776123120142

Search

Navigation