S. L. Prosvirnin, V. V. Khardikov, V. V. Yachin, V. A. Plakhtii, N. V. Sydorchuk


Subject and Purpose. Theoretical demonstration of controllable features of a non-conventional resonant back refl ection of light, realizable with the aid of a structured silicon-on-metal covering.

Methods and Methodology. The investigation has been performed through a full-wave numerical simulation in a finite-element technique.

Results. The nonlinear optical properties of a planar structure, involving a set of silicon disks disposed periodically on a silver substrate, have been studied in the Littrow scenario of wave refl ection. The structure manifests a bistable resonant reflectivity property. The magnitudes of both specular and back reflection ratios can be controlled by means of varying the incident light intensity.

Conclusions. An array of identical silicon disks, placed in a periodic order on a silver substrate, can be employed as an efficiently excitable and tunable nonlinear resonant reflective structure implementing Littrow’s non-specular diffraction scenario. As has been found, the effect of nonlinear response from the silicon disks can be used for implementing a regimen of bistable back refl ection, controllable by means of varying the incident wave’s intensity. The nonlinear tunability of the silicon-on-silver structure does promise extensions of the operation area of classical metamaterials of sub-wavelength scale sizes as it offers new applications for the effects of light-matter interaction.

Keywords: metasurface, non-specular reflection, Littrow’s scenario, nonlinear tunability, bistability, numerical simulation

Manuscript submitted 09.05.2022

Radio phys. radio astron. 2022, 27(3):181-187


1. Enoch, J.M., 2006. History of Mirrors Dating Back 8000 Years. Optom. Vis. Sci., 83(10), pp. 775—781. DOI: 10.1097/01.opx.0000237925.65901.c0

2. Glybovski, S.B., Tretyakov, S.A., Belov, P.A., Kivshar, Y.S. and Simovski, C.R., 2016. Metasurfaces: From microwaves to visible. Phys. Rep., 634, pp. 1—72. DOI:

3. Wang, B.-X., Zhai, X., Wang, G.-Z., Huang, W.-Q. and Wang, L.-L., 2015. A novel dual-band terahertz metamaterial absorber for a sensor application. J. Appl. Phys., 117(1), p. 014504. DOI:

4. Yahiaoui, R., Tan, S., Cong, L., Singh, R., Yan, F. and Zhang, W., 2015. Multispectral terahertz sensing with highly flexible ultrathin metamaterial absorber. J. Appl. Phys., 118(8), p. 083103. DOI:

5. Sydorchuk, N. and Prosvirnin, S., 2017. Analysis of terahertz wave reflection by an array of double dielectric elements placed on a reflective substrate. In: XXIInd Int. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Th eory (DIPED): proc. Dnipro, Ukraine, 25—28 Sept. 2017, pp. 58—63. DOI:

6. Lee, Y., Kim, S.-J., Park, H. and Lee, B., 2017. Metamaterials and Metasurfaces for Sensor Applications. Sensors, 17(8), pp. 1708—1726. DOI:

7. Collin, S., 2014. Nanostructure arrays in free-space: optical properties and applications. Rep. Prog. Phys., 77(12), p. 126402. DOI:

8. Zhu, L., Kapraun, J., Ferrara, J. and Chang-Hasnain, C.J., 2015. Flexible photonic metastructures for tunable coloration. Optica, 2(3), pp. 255—258. DOI:

9. Esfandyarpour, M., Garnett, E.C., Cui, Y., Mcgehee, M.D. and Brongersma, M.L., 2014. Metamaterial mirrors in optoelectronic devices. Nat. Nanotechnol., 9(7), pp. 542—547. DOI:

10. Badloe, T., Mun, J. and Rho, J., 2017. Metasurfaces-Based Absorption and Reflection Control: Perfect Absorbers and Reflectors. J. Nanomater., 2017(2), pp. 1—18. DOI:

11. Eggleston, M.S., Messer, K., Zhang, L., Yablonovitch, E. and Wu, M.C., 2015. Optical antenna enhanced spontaneous emission. Proc. Natl. Acad. Sci. USA, 112(6), pp. 1704—1709. DOI:

12. Li, D.C., Boone, F., Bozzi, M., Perregrini, L. and Wu, K., 2008. Concept of Virtual Electric/Magnetic Walls and its Realization with Artificial Magnetic Conductor Technique. IEEE Microwave Wireless Compon. Lett., 18(11), pp. 743—745. DOI:

13. Jahani, S. and Jacob, Z., 2016. All-dielectric metamaterials. Nat. Nanotechnol., 11(1), pp. 23—36. DOI:

14. Shestopalov, V.P., Litvinenko, L.N., Masalov, S.A. and Sologub, V.G., 1973. Diffraction of waves by gratings. Kharkiv, Ukraine: Kharkov State Univ. Publ. (in Russian).

15. Jull, E. and Ebbeson, G., 1977. The reduction of interference from large reflecting surfaces. IEEE Trans. Antennas Propag., 25(4), pp. 565—570. DOI:

16. Masalov, S.A. and Sirenko, Yu.K., 1980. Excitation of reflecting lattices by a plane wave in the autocollimation mode. Radiophys. Quantum Electron., 23(4), pp. 332—338. DOI:

17. Hard, T.M., 1970. Laser Wavelength Selection and Output Coupling by a Grating. Appl. Opt., 9(8), p. 1825—1830. DOI:

18. Lotem, H., 1994. Littrow-mounted diffraction grating cavity. Appl. Opt., 33(6), pp. 930—934. DOI:

19. Gribovsky, A.V. and Yeliseyev, O.A., 2014. Nonspecular reflection of Gaussian wave beams on a two-dimensional periodic array with shorted waveguides of rectangular cross-section. J. Opt., 16(3), p. 035701. DOI:

20. Litchinitser, N.M. and Sun, J., 2015. Optical meta-atoms: Going nonlinear. Science, 350(6264), pp. 1033—1034. DOI:

21. Boyd, R.W., 2019. Nonlinear optics. Amsterdam: Academic Press.

22. Prosvirnin, S.L., Khardikov, V.V., Domina, K.L., Maslovskiy, O.A., Kochetova, L.A. and Yachin, V.V., 2011. Non-specular reflection by a planar resonant metasurface. Preprint.

23. Van de Groep, J. and Polman, A., 2013. Designing dielectric resonators on substrates: Combining magnetic and electric resonances. Opt. Express, 21(22), pp. 26285—26302. DOI:

24. Ene-Dobre, M., Banciu, M.G., Nedelcu, L., Stoica, G., Busuioc, C. and Alexandru, H.V., 2011. Microwave antennas based on Ba1–xPbxNd2Ti5O14. J. Optoelectron. Adv. Mater., 13(10), pp. 1298—1304.

25. Dinu, M., Quochi, F. and Garcia, H., 2003. Third-order nonlinearities in silicon at telecom wavelengths. Appl. Phys. Lett., 82(18), pp. 2954—2956. DOI:

26. Gholami, F., Zlatanovic, S., Simic, A., Liu, L., Borlaug, D., Alic, N., Nezhad, M.P., Fainman, Y. and Radic, S., 2011. Third-order nonlinearity in silicon beyond 2350 nm. Appl. Phys. Lett., 99(8), p. 081102. DOI:

27. Wang, T., Venkatram, N., Gosciniak, J., Cui, Y., Qian, G., Ji, W. and Tan, D.T.H., 2013. Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths. Opt. Express, 21(26), pp. 32192—32198. DOI:

28. Krasnok, A., Tymchenko, M. and Al`u, A., 2018. Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Mater. Today, 21(1), pp. 8—21. DOI:

29. Werner, W.S.M., Glantschnig, K. and Ambrosch-Draxl, C., 2009. Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals. J. Phys. Chem. Ref. Data, 38(4), pp. 1013—1092. DOI:

30. Prosvirnin, S., Domina, K., Khardikov, V. and Yachin, V., 2021. Non-specular reflection of light controlled by light. In: 2021 IEEE 26th Int. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED): proc. Tbilisi, Georgia, 08—10 Sept. 2021. DOI:

Full Text:


Creative Commons License
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)