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0Numerical analysis of anomalous optical transmittance dynamics
in Au-Bi:YIG metasurface
D.A. Safiullin1*, M.A. Kiryanov1, G.S. Ostanin1, T.V. Dolgova1, M. Inoue2, A.A. Fedyanin1
1-Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991 Russia 2- Department of Electrical and Electronic Information Engineering, Toyohashi University of Technology 1-1
Tempaku-cho, Toyohashi, Aichi, 441-8580 Japan
* safiullinda@my.msu.ru
One of the important directions of nanophotonics is the study of optical effects in nanoscale hybrid metasurfaces allowing to control light by external influences. Using the hybrid metal-dielectric metasurfaces allows one to excite various electromagnetic resonances. The dynamics of ultrafast processes near the studied resonances can be investigated by "pump-probe" technique. One such process is the ultrafast heating of metal by an ultrashort laser pulse of high peak power, as a result of which the metal dielectric permittivity changes.
In this work, the differential transmittance (AT/T) spectra of the hybrid metasurface were numerically studied. The sample is a 2D periodic array of gold nanospheres coated with a layer of bismuth-substitute iron-yttrium garnet. The AT/T spectra were obtained previously by "pump-probe" technique at different delay times for different pump beam energy densities and p- and s-polarizations of the probe [1]. It supports various electromagnetic resonances in the visible spectral range, e.g., the quasi-waveguide mode (QWG) and surface lattice resonances (SLR). However, the time dependencies in the vicinity of the QWG mode show anomalous dynamics [1]. This, unlike SLR, is not described by the classical two-temperature model (TTM) [2].
The consideration of AT/T time dependences for only one wavelength does not allow us to correctly describe and explain the nature of the obtained anomalous effects. So, it is necessary to analyse the spectral window in which the studied resonance is located by Lorentzian approximation:
AT A(0 _ , , — =-—-= A(t) x L(A, t).
1 + ( Afi
The approximation makes it possible to obtain time dependences of the amplitude A, characteristic width AQ and spectral position ©0 of the resonance. A modified TTM is used to describe the amplitude, which takes into account the linear contribution of metal temperature to the change in dielectric permittivity [3]. As a result of the fitting, we obtained that at the beginning under the action of the laser pulse electron-electron thermalization occurs with characteristic time Tee ~ 100 fs. Further electrons transfer energy to the lattice, due to which electron-phonon relaxation occurs with characteristic time Tep ~ 2.5 fs. With increasing pump beam energy density, Tee decreases and Tep increases.
It was found that the spectral position of the QWG mode shifts to the blue region. The scale of this mode shift is commensurate with the characteristic width. It is assumed that the shift of the resonance is related to the change of the sample geometry caused by the thermal expansion of gold nanospheres with the following excitation of breathing vibrational modes [4]. The period of these oscillations can be estimated as T ~ 40 ps, with the oscillation period increasing with increasing pump beam energy density.
By determining the time dependences of the lorentzian parameters, we were able to distinguish two processes with different timescales manifesting in amplitude A(t) and spectral shape L(^,t). Thus, the anomalous dynamics of the differential transmittance in the vicinity of the QWG mode consists of the linear dependence of the resonance amplitude on temperature and the spectral shift of the resonance. Taking these two processes into account allows us to analytically describe the time dependence of AT/T in the vicinity of the QWG mode.
[1] M.A. Kiryanov, et al, JETP Lett., vol. 117, 196-201, (2023).
[2] S.I. Anisimov, et al, Sov. Phys. JETP, vol. 66, 375-377, (1974).
[3] T. Stoll, et al, Eur. Phys. J. B, vol. 87, 1-19, (2014).
[4] G.V. Hartland, et al, Chem. Rev., vol. 111, 3858-3887, (2011).
