Superresolution effect and resolvability criterion for the waves in anisotropic media

E.H. Lock^†^a, S.V. Gerus^‡^a, A.V. Sadovnikov^§^b
^aKotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Fryazino Branch, pl. Vvedenskogo 1, Fryazino, Moscow Region, 141190, Russian Federation
^bChernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410071, Russian Federation

The possibility of solving the problem of overcoming the diffraction limit in anisotropic media is discussed. Experimentally and theoretically demonstrated the occurrence of the superresolution effect, in which a distinct shadow from a point object is observed at distances much larger than the values obtained from the Rayleigh resolvability criterion. In particular, on the example of diffraction of spin waves with wavelength λ, the possibility of a distinct shadow from a through-hole in a ferrite film with diameter d < λ at a distance L ⪢ λ has been proved. It is established that super-directional wave propagation and super-resolving shadow from the object arise in the direction of the normal to the isofrequency dependence of the wave at the inflection point. The criterion of resolvability is formulated, which makes it possible to carry out evaluation calculations for waves in anisotropic media and confirms the possibility of super-directional and superresolution effects in them.

Correspondence should be addressed to
Keywords: diffraction, spin wave, superresolution effect, super-directional wave propagation, criterion of resolvability
PACS: 41.20.Gz, 41.20.Jb, 42.25.Fx, 75.70.−i (all)
DOI: 10.3367/UFNe.2026.03.040105
URL: https://ufn.ru/en/articles/2026/4/e/
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2026PhyU...69..375L
Citation: Lock E H, Gerus S V, Sadovnikov A V "Superresolution effect and resolvability criterion for the waves in anisotropic media" Phys. Usp. 69 375–391 (2026)

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Received: 16th, April 2025, revised: 28th, January 2026, accepted: 5th, March 2026

Оригинал: Локк Э Г, Герус С В, Садовников А В «Эффект сверхразрешения и критерий разрешимости для волн в анизотропных средах» УФН 196 403–421 (2026); DOI: 10.3367/UFNr.2026.03.040105

References (62) ↓ Similar articles (20)

Heintzmann R, Gustafsson M G L Nature Photon. 3 362 (2009)
Zhuang X Nature Photon. 3 365 (2009)
Hell S W, Schmidt R, Egner A Nature Photon. 3 381 (2009)
Pendry J B, Smith D R Phys. Today 57 (6) 37 (2004)
Eleftheriades G V, Balmain K G (Eds) Negative-Refraction Metamaterials. Fundamental Principles And Applications (New York: Wiley, IEEE Press, 2005)
’E’?с’?’?’?’?’? ’E ’I Usp. Fiz. Nauk 92 517 (1967); Veselago V G Sov. Phys. Usp. 10 509 (1968)
’’’?’?’? ’e ’I Usp. Fiz. Nauk 178 397 (2008); Lock E H Phys. Usp. 51 375 (2008)
’’’?’?’? ’e ’I Usp. Fiz. Nauk 182 1327 (2012); Lock E H Phys. Usp. 55 1239 (2012)
’’’?’?’? ’e ’I ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 60 102 (2015); Lokk E G J. Commun. Technol. Electron. 60 97 (2015)
’’’?’?’? ’e ’I ’R’?’?. ’i’B’v. ’l’?р. ф’?’?’?ch’?с’?’?ya 81 1104 (2017); Lock E H Bull. Russ. Acad. Sci. Phys. 81 996 (2017)
Annenkov A Yu, Gerus S V, Lock E H Europhys. Lett. 123 44003 (2018)
Annenkov A Yu, Gerus S V, Lock E H EPJ Web Conf. 185 02006 (2018)
Martyshkin A A et al Phys. Rev. Applied 22 014037 (2024)
’E’?sh’?’?’?с’?’?’? ’B ’E ’? ’?р ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 32 2295 (1987)
’E’?sh’?’?’?с’?’?’? ’B ’E ’? ’?р ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 33 876 (1988)
B’?sh’?’?’?с’?’?’? ’B ’E, ’lт’?’?ь’?’?kh’?’? ’B ’E, Sh’?kh’?’?’?’?рya’? ’K ’I Izv. Vyssh. Uchebn. Zaved. Fiz. (11) 67 (1988); Vashkovskii A V, Stal’makhov A V, Shakhnazaryan D G Sov. Phys. J. 31 908 (1988)
’E’?sh’?’?’?с’?’?’? ’B ’E, ’lт’?’?ь’?’?kh’?’? ’E ’l, Sh’?р’?’?’?с’?’?’? Yu ’z ’a’?’?’?’?т’?ст’?т’?ch’?с’?’?’? ’?’?’?’?ы ’? э’?’?’?тр’?’?’?’?’? с’?’?рkh’?ыс’?’?’?kh ch’?ст’?т (’l’?р’?т’?’?: ’R’?’?-’?’? ’l’?р’?т’?’?. у’?-т’?, 1993)
Veerakumar V, Camley R E Phys. Rev. B 74 214401 (2006)
Gieniusz R et al Appl. Phys. Lett. 102 102409 (2013)
Pirro P et al Nature Rev. Mater. 6 1114 (2021)
Zhang Z et al Appl. Phys. Lett. 115 232402 (2019)
Chumak A V et al IEEE Trans. Magn. 58 0800172 (2022)
Sebastian T et al Front. Phys. 3 35 (2015)
’v’?’?’?т’?’? ’l ’B ’? ’?р Usp. Fiz. Nauk 190 1009 (2020); Nikitov S A et al Phys. Usp. 63 945 (2020)
Demidov V E et al Appl. Phys. Lett. 105 172410 (2014)
’v’?’?’?т’?’? ’l ’B, ’s’?’?’?’?’?’?’?’? Yu ’B ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 70 292 (2025)
Davies C S et al Appl. Phys. Lett. 107 162401 (2015)
Shiota Y et al Appl. Phys. Lett. 116 192411 (2020)
’Kу’?’?’? ’I ’a ’? ’?р Zh. Tekh. Fiz. 92 1151 (2022); Dudko G M et al Tech. Phys. 67 970 (2022)
Makartsou U et al Appl. Phys. Lett. 124 192406 (2024)
Khут’?’?’?’? ’B ’G ’? ’?р ’R’?’?. ’i’B’v. ’l’?р. ф’?’?’?ch’?с’?’?ya 85 1542 (2021); Khutieva A B et al Bull. Russ. Acad. Sci. Phys. 85 1205 (2021)
Swyt M S et al Appl. Phys. Lett. 124 112410 (2024)
Bloch F Z. Phys. 61 206 (1930)
’Bkh’?’?’?’?р ’B ’R, ’G’?рьyakhт’?р ’E ’I, ’z’?’?’?т’?’?’?с’?’?’? ’l ’E ’l’?’?’?’?’?ы’? ’?’?’?’?ы (’a.: ’v’?у’?’?, 1967); ’z’?р. ’?’? ’?’?’?’?. ya’?., Akhiezer A I, Bar’yakhtar V G, Peletminskii S V Spin Waves (Amsterdam: North-Holland Publ. Co., 1968)
Damon R W, Eshbach J R J. Phys. Chem. Solids 19 308 (1961)
’Iур’?’?’?ch ’B ’I, ’a’?’?’?’?’? ’I ’B ’a’?’?’?’?т’?ы’? ’?’?’?’?’?’?’?’?ya ’? ’?’?’?’?ы (’a.: ’v’?у’?’?, 1994); ’z’?р. ’?’? ’?’?’?’?. ya’?., Gurevich A G, Melkov G A Magnetization Oscillations And Waves (Boca Raton, FL: CRC Press, 1996)
’’’?’?’? ’e ’I, ’I’?рус ’l ’E Usp. Fiz. Nauk 194 1330 (2024); Lock E H, Gerus S V Phys. Usp. 67 1257 (2024)
’E’?sh’?’?’?с’?’?’? ’B ’E ’? ’?р ’z’?сь’?’? Zh’n’s 12 487 (1986)
Vlannes N P J. Appl. Phys. 61 416 (1987)
’B’?’?’?’?’?’?’? ’B Yu, ’I’?рус ’l ’E ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 57 572 (2012); Annenkov A Yu, Gerus S V J. Commun. Technol. Electron. 57 519 (2012)
Borovik-Romanov A S, Kreines N M Phys. Rep. 81 351 (1982)
Demidov V E et al Appl. Phys. Lett. 90 172508 (2007)
Demokritov S O, Demidov V E IEEE Trans. Magn. 44 6 (2008)
Kruglyak V V, Demokritov S O, Grundler D J. Phys. D 43 264001 (2010)
Sadovnikov A V et al Phys. Rev. B 96 144428 (2017)
Gubanov V A et al Phys. Rev. B 107 024427 (2023)
Bessonov V D et al Phys. Rev. B 109 024415 (2024)
’I’?рус ’l ’E ’? ’?р ’R’?’?. ’i’B’v. ’l’?р. ф’?’?’?ch’?с’?’?ya 86 1642 (2022); Gerus S V et al Bull. Russ. Acad. Sci. Phys. 86 1361 (2022)
Gerus S V, Annenkov A Yu, Lock E H J. Magn. Magn. Mater. 563 169747 (2022)
’Oу’?’?’?’? ’E ’R, ’’’?’?’? ’e ’I, Shch’?’?’?’?’? ’E ’R ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 35 1617 (1990); Zubkov V I, Lokk E G, Shcheglov V I Sov. J. Commun. Technol. Electron. 35 (13) 66 (1990)
’Oу’?’?’?’? ’E ’R ’? ’?р Zh. Tekh. Fiz. 59 (12) 115 (1989)
’E’?р’?’?’?’?’?’? ’B ’E, ’I’?рус ’l ’E, ’Fр’?с’?’?zh’?’? ’’ ’B ’a’?’?р’?э’?’?’?тр’?’?’?’?’? 18 61 (1989)
’E’?sh’?’?’?с’?’?’? ’B ’E, ’’’?’?’? ’e ’I, Shch’?’?’?’?’? ’E ’R ’s’?’?’?’?’? т’?’?р’?’?’?’? т’?’?’? 41 2034 (1999); Vashkovskii A V, Lokk E G, Shcheglov V I Phys. Solid State 41 1868 (1999)
’I’?рус ’l ’E, ’’’?’?’? ’e ’I, ’B’?’?’?’?’?’?’? ’B Yu ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 66 1216 (2021); Gerus S V, Lock E H, Annenkov A Yu J. Commun. Technol. Electron. 66 1378 (2021)
Khут’?’?’?’? ’B ’G, ’l’?’?’?’?’?’?’?’?’? ’B ’E ’l’?’?’?. ’? ’?’?с. р’?’?’?стр’?ts’?’? ’?р’?’?р’?’?’?ы ’?’?ya ’e’E’a, 2020666510 ’?т 10.12.2020
Demidov V E et al Phys. Rev. B 77 064406 (2008)
’zр’?kh’?р’?’? ’B ’a (’I’?. р’?’?.) ’s’?’?’?ch’?с’?’?ya э’?ts’?’?’?’?’?’?’?’?ya Т. 3 (’a.: ’G’?’?ьsh’?ya ’i’?сс’?’?с’?’?ya э’?ts’?’?’?’?’?’?’?’?ya, 1992)
’zр’?kh’?р’?’? ’B ’a (’I’?. р’?’?.) ’s’?’?’?ch’?с’?’?ya э’?ts’?’?’?’?’?’?’?’?ya Т. 2 (’a.: ’G’?’?ьsh’?ya ’i’?сс’?’?с’?’?ya э’?ts’?’?’?’?’?’?’?’?ya, 1992)
Crawford F S (Jr.) Berkeley Physics Course Vol. 3 Waves (New York: McGraw-Hill, 1968)
’G’?р’? ’a, ’E’?’?ьф ’e ’dс’?’?’?ы ’?’?т’?’?’? (’a.: ’v’?у’?’?, 1970); ’z’?р. с ’?’?’?’?. ya’?., Born M, Wolf E Principles Of Optics (Oxford: Pergamon Press, 1969)
’’’?’?’? ’e ’I, ’I’?рус ’l ’E ’i’?’?’?’?т’?kh’?’?’?’? э’?’?’?тр’?’?’?’?’? 68 884 (2023); Lock E H, Gerus S V J. Commun. Technol. Electron. 68 971 (2023)
’a’?р’?’?’? ’I ’n, ’z’?тр’?’? ’G ’a, ’Iру’?’?’?с’?’?ya ’I ’z ’e’?’?’?тр’?’?’?’?’?’?’?’?’? ’? р’?с’?р’?стр’?’?’?’?’?’? р’?’?’?’?’?’?’?’? (’a.: ’l’?’?’?тс’?’?’? р’?’?’?’?, 1979)