Self-generation of microwave nonlinear waveforms in the magnonic-optoelectronic oscillator (MOEO) was investigated. Nonlinear dynamics of the MOEO was due to both optical and magnonic paths of the oscillator circuit. Four-magnon parametric interactions in the magnonic path and cosine transfer function of the electro-optical modulator caused double nonlinearity of the MOEO. Gain coefficient was used as a control parameter. We found that during a route from regular to chaotic dynamics, the oscillator generates two unusual waveforms: symmetry-breaking soliton-like modes of Möbius type and periodic pulses with chaotic amplitude modulation. Nonlinear waveforms were characterized using a time series analysis. Peculiarities of the signals and their spectra in regular and chaotic regimes of self-generation are discussed. We expect that the multiple nonlinearity of the MOEO may be useful for investigation of various fundamental effects in complex time-delayed systems and for development of novel circuits for neuromorphic computing.

1.
2.
S. H.
Strogatz
,
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
(
CRC Press
,
2019
).
3.
J.-P.
Goedgebuer
,
P.
Levy
,
L.
Larger
,
C.-C.
Chen
, and
W. T.
Rhodes
,
IEEE J. Quantum Electron.
38
,
1178
(
2002
).
4.
N.
Gastaud
,
S.
Poinsot
,
L.
Larger
,
J. M.
Merolla
,
M.
Hanna
,
J. P.
Goedgebuer
, and
F.
Malassenet
,
Electron. Lett.
40
,
898
(
2004
).
5.
A. B.
Ustinov
,
A. V.
Kondrashov
, and
B. A.
Kalinikos
,
Tech. Phys. Lett.
42
,
403
(
2016
).
6.
A. V.
Kondrashov
,
A. B.
Ustinov
, and
B. A.
Kalinikos
,
Tech. Phys.
62
,
287
(
2017
).
7.
A. B.
Cohen
,
B.
Ravoori
,
T. E.
Murphy
, and
R.
Roy
,
Phys. Rev. Lett.
101
,
154102
(
2008
).
8.
T.
Erneux
,
L.
Larger
,
M. W.
Lee
, and
J. P.
Goedgebuer
,
Physica D
194
,
49
(
2004
).
9.
L.
Weicker
,
T.
Erneux
,
O.
d’Huys
,
J.
Danckaert
,
M.
Jacquot
,
Y.
Chembo
, and
L.
Larger
,
Phys. Rev. E
86
,
055201
(
2012
).
10.
Y. C.
Kouomou
,
P.
Colet
,
L.
Larger
, and
N.
Gastaud
,
Phys. Rev. Lett.
95
,
203903
(
2005
).
11.
K. E.
Callan
,
L.
Illing
,
Z.
Gao
,
D. J.
Gauthier
, and
E.
Schöll
,
Phys. Rev. Lett.
104
,
113901
(
2010
).
12.
G. R. G.
Chengui
,
J. H. T.
Mbé
,
A. F.
Talla
,
P.
Woafo
, and
Y. K.
Chembo
,
IEEE J. Quantum Electron.
54
,
5000207
(
2018
).
13.
J. H. T.
Mbé
,
J. S. D.
Kamaha
,
Y. K.
Chembo
, and
P.
Woafo
,
IEEE J. Quantum Electron.
55
,
1
(
2019
).
14.
M.
Wu
,
Solid State Phys.
62
,
163
(
2010
).
15.
V. E.
Demidov
and
N. G.
Kovshikov
,
J. Exp. Theor. Phys. Lett.
66
,
261
(
1997
).
16.
V. E.
Demidov
and
N. G.
Kovshikov
,
Tech. Phys. Lett.
24
,
274
276
(
1998
).
17.
V. E.
Demidov
and
N. G.
Kovshikov
,
Tech. Phys. Lett.
24
,
647
(
1998
).
18.
V. E.
Demidov
and
N. G.
Kovshikov
,
Tech. Phys.
44
,
960
(
1999
).
19.
A. M.
Hagerstrom
,
W.
Tong
,
M.
Wu
,
B. A.
Kalinikos
, and
R.
Eykholt
,
Phys. Rev. Lett.
102
,
207202
(
2009
).
20.
A. M.
Hagerstrom
and
M.
Wu
,
Magnonics, Top. Appl. Phys.
125
,
29
(
2013
).
21.
A.
Hagerstrom
,
M.
Wu
,
R.
Eykholt
, and
B. A.
Kalinikos
,
Phys. Rev. B
83
,
104402
(
2011
).
22.
E. N.
Beginin
,
S. V.
Grishin
, and
Y. P.
Sharaevskii
,
Tech. Phys. Lett.
36
,
325
328
(
2010
).
23.
S. V.
Grishin
,
V. S.
Grishin
,
A. E.
Hramov
, and
Y. P.
Sharaevskii
,
Tech. Phys.
53
,
620
628
(
2008
).
24.
M.
Wu
,
B. A.
Kalinikos
, and
C. E.
Patton
,
Phys. Rev. Lett.
95
,
237202
(
2005
).
25.
E. N.
Beginin
,
S. V.
Grishin
, and
Y. P.
Sharaevsky
,
JETP Lett.
88
,
647
(
2008
).
26.
S. V.
Grishin
,
T. M.
Golova
,
M. A.
Morozova
,
D. V.
Romanenko
,
E. P.
Seleznev
,
I. V.
Sysoev
, and
Y. P.
Sharaevskii
,
J. Exp. Theor. Phys.
121
,
623
(
2015
).
27.
S. V.
Grishin
,
B. S.
Dmitriev
,
O. I.
Moskalenko
,
V. N.
Skorokhodov
, and
Y. P.
Sharaevskii
,
Phys. Rev. E
98
,
022209
(
2018
).
28.
A. V.
Kondrashov
,
A. B.
Ustinov
,
B. A.
Kalinikos
, and
H.
Benner
,
Tech. Phys. Lett.
34
,
492
(
2008
).
29.
A. V.
Kondrashov
,
A. B.
Ustinov
, and
B. A.
Kalinikos
,
Tech. Phys. Lett.
36
,
224
(
2010
).
30.
A. V.
Kondrashov
,
A. B.
Ustinov
, and
B. A.
Kalinikos
,
Tech. Phys. Lett.
42
,
208
(
2016
).
31.
M.
Wu
,
A. M.
Hagerstrom
,
A.
Kondrashov
, and
B. A.
Kalinikos
,
Phys. Rev. Lett.
102
,
237203
(
2009
).
32.
Z.
Wang
,
A.
Hagerstrom
,
J. Q.
Anderson
,
W.
Tong
,
M.
Wu
,
L. D.
Carr
,
R.
Eykholt
, and
B. A.
Kalinikos
,
Phys. Rev. Lett.
107
,
114102
(
2011
).
33.
A. B.
Ustinov
,
A. V.
Kondrashov
,
I.
Tatsenko
,
A. A.
Nikitin
, and
M. P.
Kostylev
,
Phys. Rev. B
104
,
L140410
(
2021
).
34.
A. B.
Ustinov
,
A. A.
Nikitin
, and
B. A.
Kalinikos
,
Tech. Phys.
60
,
1392
(
2015
).
35.
A. B.
Ustinov
,
A. A.
Nikitin
, and
B. A.
Kalinikos
,
IEEE Magn. Lett.
6
,
1
(
2015
).
36.
A. B.
Ustinov
,
A. V.
Kondrashov
,
A. A.
Nikitin
,
V. V.
Lebedev
,
A. N.
Petrov
,
A. V.
Shamrai
, and
B. A.
Kalinikos
,
J. Phys.: Conf. Ser.
1326
,
012015
(
2019
).
37.
Y.
Xiong
,
Z.
Zhang
,
Y.
Li
,
M.
Hammami
,
J.
Sklenar
,
L.
Alahmed
,
P.
Li
,
T.
Sebastian
,
H.
Qu
,
A.
Hoffmann
,
V.
Novosad
, and
W.
Zhang
,
Rev. Sci. Instrum.
91
,
125105
(
2020
).
38.
Y. K.
Chembo
,
D.
Brunner
,
M.
Jacquot
, and
L.
Larger
,
Rev. Mod. Phys.
91
,
035006
(
2019
).
39.
A. B.
Ustinov
,
A. V.
Kondrashov
,
A. A.
Nikitin
,
A. V.
Drozdovskii
, and
B. A.
Kalinikos
,
Phys. Solid State
60
,
2127
(
2018
).
40.
A. V.
Kondrashov
,
A. B.
Ustinov
, and
B. A.
Kalinikos
,
J. Phys.: Conf. Ser.
1697
,
012166
(
2020
).
41.
X. S.
Yao
and
L.
Maleki
,
Electron. Lett.
30
,
1525
(
1994
).
42.
M. E.
Belkin
,
A. V.
Loparev
,
Y.
Semenova
,
G.
Farrell
, and
A. S.
Sigov
,
Microw. Opt. Technol. Lett.
53
,
2474
(
2011
).
43.
A. B.
Ustinov
,
I.
Yu. Tatsenko
,
A. A.
Nikitin
,
A. V.
Kondrashov
,
A. V.
Shamray
, and
A. V.
Ivanov
,
Photonics Russia
15
,
228
(
2021
).
44.
V. S.
Udaltsov
,
J.-P.
Goedgebuer
,
L.
Larger
,
J.-B.
Cuenot
,
P.
Levy
, and
W. T.
Rhodes
,
Phys. Lett. A
308
,
54
(
2003
).
45.
A.
Prabhakar
and
D. D.
Stancil
,
Spin Waves: Theory and Applications
(
Springer
,
2009
), Vol. 5.
46.
B. A.
Kalinikos
,
M. M.
Scott
, and
C. E.
Patton
,
Phys. Rev. Lett.
84
,
4697
(
2000
).
47.
L. D.
Carr
,
C. W.
Clark
, and
W. P.
Reinhardt
,
Phys. Rev. A
62
,
063610
(
2000
).
48.
L. D.
Carr
,
C. W.
Clark
, and
W. P.
Reinhardt
,
Phys. Rev. A
62
,
063611
(
2000
).
49.
S. O.
Demokritov
,
A. A.
Serga
,
V. E.
Demidov
,
B.
Hillebrands
,
M. P.
Kostylev
, and
B. A.
Kalinikos
,
Nature
426
,
159
(
2003
).
50.
P.
Grassberger
and
I.
Procacia
,
Phys. Rev. Lett.
50
,
346
(
1983
).
51.
J.
Torrejon
,
M.
Riou
,
F. A.
Araujo
,
S.
Tsunegi
,
G.
Khalsa
,
D.
Querlioz
,
P.
Bortolotti
,
V.
Cros
,
K.
Yakushiji
,
A.
Fukushima
,
H.
Kubota
, and
S.
Yuasa
,
Nature
547
,
428
(
2017
).
52.
S.
Watt
and
M.
Kostylev
,
Phys. Rev. Appl.
13
,
034057
(
2020
).
53.
S.
Watt
,
M.
Kostylev
, and
A. B.
Ustinov
,
J. Appl. Phys.
129
,
044902
(
2021
).
54.
S.
Watt
,
M.
Kostylev
,
A. B.
Ustinov
, and
B. A.
Kalinikos
,
Phys. Rev. Appl.
15
,
064060
(
2021
).
55.
A. A.
Nikitin
,
A. A.
Nikitin
,
A. B.
Ustinov
,
S.
Watt
, and
M. P.
Kostylev
,
J. Appl. Phys.
131
,
113903
(
2022
).
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