Extending the scope of the self-imaging phenomenon, traditionally associated with linear optics, to the domain of magnonics, this study presents the experimental demonstration and numerical analysis of spin-wave (SW) self-imaging in an in-plane magnetized yttrium iron garnet film. We explore this phenomenon using a setup in which a plane SW passes through a diffraction grating, and the resulting interference pattern is detected using Brillouin light scattering. We have varied the frequencies of the source dynamic magnetic field to discern the influence of the anisotropic dispersion relation and the caustic effect on the analyzed phenomenon. We found that at low frequencies and diffraction fields, the caustics determine the interference pattern. However, at large distances from the grating, when the waves of high diffraction order and number of slits contribute to the interference pattern, the self-imaging phenomenon and Talbot-like patterns are formed. This methodological approach not only sheds light on the behavior of SW interference under different conditions but also enhances our understanding of the SW self-imaging process in both isotropic and anisotropic media.

1.
D. D.
Stancil
and
A.
Prabhakar
,
Spin Waves: Theory and Applications
(
Springer US
,
2009
), pp.
1
355
.
2.
A. G.
Gurevich
and
G. A.
Melkov
,
Magnetization Oscillations and Waves
(
CRC Press
,
Boca Raton
,
1996
).
3.
F.
Garcia-Sanchez
,
P.
Borys
,
R.
Soucaille
,
J. P.
Adam
,
R. L.
Stamps
, and
J. V.
Kim
, “
Narrow magnonic waveguides based on domain walls
,”
Phys. Rev. Lett.
114
,
247206
(
2015
).
4.
K.
Wagner
,
A.
Kákay
,
K.
Schultheiss
,
A.
Henschke
,
T.
Sebastian
, and
H.
Schultheiss
, “
Magnetic domain walls as reconfigurable spin-wave nanochannels
,”
Nat. Nanotech.
11
,
432
436
(
2016
).
5.
G.
Duerr
,
K.
Thurner
,
J.
Topp
,
R.
Huber
, and
D.
Grundler
, “
Enhanced transmission through squeezed modes in a self-cladding magnonic waveguide
,”
Phys. Rev. Lett.
108
,
227202
(
2012
).
6.
J.
Lan
,
W.
Yu
,
R.
Wu
, and
J.
Xiao
, “
Spin-wave diode
,”
Phys. Rev. X
5
,
041049
(
2015
).
7.
A. Y.
Annenkov
,
S. V.
Gerus
, and
E. H.
Lock
, “
Superdirectional beam of surface spin wave
,”
Europhys. Lett.
123
,
44003
(
2018
).
8.
P.
Pirro
,
V. I.
Vasyuchka
,
A. A.
Serga
, and
B.
Hillebrands
, “
Advances in coherent magnonics
,”
Nat. Rev. Mater.
6
,
1114
1135
(
2021
).
9.
N. J.
Whitehead
,
S. A. R.
Horsley
,
T. G.
Philbin
, and
V. V.
Kruglyak
, “
Graded index lenses for spin wave steering
,”
Phys. Rev. B
100
,
094404
(
2019
).
10.
M.
Kiechle
,
A.
Papp
,
S.
Mendisch
,
V.
Ahrens
,
M.
Golibrzuch
,
G. H.
Bernstein
,
W.
Porod
,
G.
Csaba
, and
M.
Becherer
, “
Spin-wave optics in YIG realized by ion-beam irradiation
,”
Small
19
,
2207293
(
2023
).
11.
N. J.
Whitehead
,
S. A. R.
Horsley
,
T. G.
Philbin
, and
V. V.
Kruglyak
, “
A luneburg lens for spin waves
,”
Appl. Phys. Lett.
113
,
212404
(
2018
).
12.
M.
Vogel
,
B.
Hillebrands
, and
G.
von Freymann
, “
Optical elements for anisotropic spin-wave propagation
,”
Appl. Phys. Lett.
116
,
262404
(
2020
).
13.
V. E.
Demidov
,
S. O.
Demokritov
,
K.
Rott
,
P.
Krzysteczko
, and
G.
Reiss
, “
Mode interference and periodic self-focusing of spin waves in permalloy microstripes
,”
Phys. Rev. B
77
,
064406
(
2008
).
14.
S.
Mansfeld
,
J.
Topp
,
K.
Martens
,
J. N.
Toedt
,
W.
Hansen
,
D.
Heitmann
, and
S.
Mendach
, “
Spin wave diffraction and perfect imaging of a grating
,”
Phys. Rev. Lett.
108
,
047204
(
2012
).
15.
R.
Khomeriki
, “
Self-focusing magnetostatic beams in thin magnetic films
,”
Eur. Phys. J. B
41
,
219
222
(
2004
).
16.
R.
Gieniusz
,
P.
Gruszecki
,
M.
Krawczyk
,
U.
Guzowska
,
A.
Stognij
, and
A.
Maziewski
, “
The switching of strong spin wave beams in patterned garnet films
,”
Sci. Rep.
7
,
8771
(
2017
).
17.
H.
Körner
,
J.
Stigloher
, and
C.
Back
, “
Excitation and tailoring of diffractive spin-wave beams in nife using nonuniform microwave antennas
,”
Phys. Rev. B
96
,
100401
(
2017
).
18.
R.
Gieniusz
,
V. D.
Bessonov
,
U.
Guzowska
,
A. I.
Stognii
, and
A.
Maziewski
, “
An antidot array as an edge for total non-reflection of spin waves in yttrium iron garnet films
,”
Appl. Phys. Lett.
104
,
082412
(
2014
).
19.
H.
Talbot
, “
Lxxvi. Facts relating to optical science. No. iv
,”
London, Edinburgh Dublin Philos. Mag. J. Sci.
9
,
401
407
(
1836
).
20.
L.
Rayleigh
, “
On copying diffraction gratings and on some phenomenon connected therewith
,”
Philos. Mag.
11
,
196
(
1881
).
21.
J.
Wen
,
Y.
Zhang
, and
M.
Xiao
, “
The Talbot effect: Recent advances in classical optics, nonlinear optics, and quantum optics
,”
Adv. Opt. Photonics
5
,
83
130
(
2013
).
22.
A.
Bravin
,
P.
Coan
, and
P.
Suortti
, “
X-ray phase-contrast imaging: From pre-clinical applications towards clinics
,”
Phys. Med. Biol.
58
,
R1
R35
(
2012
).
23.
T.
Sato
, “
Focus position and depth of two-dimensional patterning by Talbot effect lithography
,”
Microelectron. Eng.
123
,
80
83
(
2014
).
24.
S.
Zhou
,
J.
Liu
,
Q.
Deng
,
C.
Xie
, and
M.
Chan
, “
Depth-of-focus determination for Talbot lithography of large-scale free-standing periodic features
,”
IEEE Photonics Technol. Lett.
28
,
2491
2494
(
2016
).
25.
A.
Vetter
,
R.
Kirner
,
D.
Opalevs
,
M.
Scholz
,
P.
Leisching
,
T.
Scharf
,
W.
Noell
,
C.
Rockstuhl
, and
R.
Voelkel
, “
Printing sub-micron structures using Talbot mask-aligner lithography with a 193 nm CW laser light source
,”
Opt. Express
26
,
22218
22233
(
2018
).
26.
D.
Bigourd
,
B.
Chatel
,
W. P.
Schleich
, and
B.
Girard
, “
Factorization of numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses
,”
Phys. Rev. Lett.
100
,
030202
(
2008
).
27.
O. J.
Farías
,
F.
de Melo
,
P.
Milman
, and
S. P.
Walborn
, “
Quantum information processing by weaving quantum Talbot carpets
,”
Phys. Rev. A
91
,
062328
(
2015
).
28.
K.
Sawada
and
S. P.
Walborn
, “
Experimental quantum information processing with the Talbot effect
,”
J. Opt.
20
,
075201
(
2018
).
29.
M. R.
Dennis
,
N. I.
Zheludev
, and
F. J. G.
de Abajo
, “
The plasmon Talbot effect
,”
Opt. Express
15
,
9692
9700
(
2007
).
30.
N.
Sungar
,
J.
Sharpe
,
J.
Pilgram
,
J.
Bernard
, and
L.
Tambasco
, “
Faraday–Talbot effect: Alternating phase and circular arrays
,”
Chaos
28
,
096101
(
2018
).
31.
A.
Bakman
,
S.
Fishman
,
M.
Fink
,
E.
Fort
, and
S.
Wildeman
, “
Observation of the Talbot effect with water waves
,”
Am. J. Phys.
87
,
38
43
(
2019
).
32.
T.
Gao
,
E.
Estrecho
,
G.
Li
,
O. A.
Egorov
,
X.
Ma
,
K.
Winkler
,
M.
Kamp
,
C.
Schneider
,
S.
Höfling
,
A. G.
Truscott
, and
E. A.
Ostrovskaya
, “
Talbot effect for exciton polaritons
,”
Phys. Rev. Lett.
117
,
097403
(
2016
).
33.
M.
Gołębiewski
,
P.
Gruszecki
,
M.
Krawczyk
, and
A. E.
Serebryannikov
, “
Spin-wave Talbot effect in a thin ferromagnetic film
,”
Phys. Rev. B
102
,
134402
(
2020
).
34.
M.
Gołębiewski
,
P.
Gruszecki
, and
M.
Krawczyk
, “
Self-imaging of spin waves in thin, multimode ferromagnetic waveguides
,”
IEEE Trans. Magn.
58
,
1
5
(
2022
).
35.
M.
Gołębiewski
,
P.
Gruszecki
, and
M.
Krawczyk
, “
Self-imaging based programmable spin-wave lookup tables
,”
Adv. Electrode Mater.
8
,
2200373
(
2022
).
36.
A.
Vansteenkiste
,
J.
Leliaert
,
M.
Dvornik
,
M.
Helsen
,
F.
Garcia-Sanchez
, and
B.
Van Waeyenberge
, “
The design and verification of mumax3
,”
AIP Adv.
4
,
107133
(
2014
).
37.
B. A.
Kalinikos
and
A. N.
Slavin
, “
Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions
,”
J. Phys. C: Solid State Phys.
19
,
7013
(
1986
).
38.
T.
Ogasawara
, “
Time-resolved vector-field imaging of spin-wave propagation in permalloy stripes using wide-field magneto-optical Kerr microscopy
,”
Phys. Rev. Appl.
20
,
024010
(
2023
).
39.
V.
Veerakumar
and
R. E.
Camley
, “
Magnon focusing in thin ferromagnetic films
,”
Phys. Rev. B
74
,
214401
(
2006
).
40.
T.
Schneider
,
A. A.
Serga
,
A. V.
Chumak
,
C. W.
Sandweg
,
S.
Trudel
,
S.
Wolff
,
M. P.
Kostylev
,
V. S.
Tiberkevich
,
A. N.
Slavin
, and
B.
Hillebrands
, “
Nondiffractive subwavelength wave beams in a medium with externally controlled anisotropy
,”
Phys. Rev. Lett.
104
,
197203
(
2010
).
41.
R.
Gieniusz
,
H.
Ulrichs
,
V. D.
Bessonov
,
U.
Guzowska
,
A. I.
Stognii
, and
A.
Maziewski
, “
Single antidot as a passive way to create caustic spin-wave beams in yttrium iron garnet films
,”
Appl. Phys. Lett.
102
,
102409
(
2013
).
42.
S.
Muralidhar
,
R.
Khymyn
,
A. A.
Awad
,
A.
Alemán
,
D.
Hanstorp
, and
J.
Åkerman
, “
Femtosecond laser pulse driven caustic spin wave beams
,”
Phys. Rev. Lett.
126
,
037204
(
2021
).
43.
O.
Büttner
,
M.
Bauer
,
S. O.
Demokritov
,
B.
Hillebrands
,
Y. S.
Kivshar
,
V.
Grimalsky
,
Y.
Rapoport
, and
A. N.
Slavin
, “
Linear and nonlinear diffraction of dipolar spin waves in yttrium iron garnet films observed by space- and time-resolved Brillouin light scattering
,”
Phys. Rev. B
61
,
11576
11587
(
2000
).
44.
A.
Wartelle
,
F.
Vilsmeier
,
T.
Taniguchi
, and
C. H.
Back
, “
Caustic spin wave beams in soft thin films: Properties and classification
,”
Phys. Rev. B
107
,
144431
(
2023
).
45.
J.
Gräfe
,
P.
Gruszecki
,
M.
Zelent
,
M.
Decker
,
K.
Keskinbora
,
M.
Noske
,
P.
Gawronski
,
H.
Stoll
,
M.
Weigand
,
M.
Krawczyk
,
C. H.
Back
,
E. J.
Goering
, and
G.
Schütz
, “
Direct observation of spin-wave focusing by a Fresnel lens
,”
Phys. Rev. B
102
,
024420
(
2020
).
46.
U.
Makartsou
et al (2024). “
Spin-wave self-imaging: Experimental and numerical demonstration of caustic and talbot-like diffraction patterns
,”
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