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NONLINEAR AND TERAHERTS PHOTONICS
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Microsphere Sensors Based on Thermo-Optical Effect in Different Glasses:
Modelling and Experiment
M.P. Marisova, A.V. Andrianov, E.A. Anashkina
Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanov St., Nizhny Novgorod, 603950, Russia
marisova.mariya@rambler. ru
Microresonators with whispering-gallery modes (WGMs) are now widely used in photonics [1].The thermo-optical effect in microspheres leading to WGM shifts can be used for sensing applications [2]. Here we study temperature microsphere sensors made of different glasses and transient nonlinear WGM shifts caused by partial thermalization of a laser pump.
The most common glass microresonator design is a fused silica (SiO2) microsphere. However, investigating other materials could lead to the development of new microsensors with improved characteristics. In total, five optical glasses were considered: common silica (SiO2), germanate (GeO2), tellurite (TeO2-WO3-La2O3, TWL), and two types of chal-cogenide glass (As2S3 and As2Se3).
Eigenfrequencies of an ideal dielectric microsphere can be obtained from the characteristic equations [3]. A variation in ambient temperature AT causes microresonator size and the refractive index of the glass to change due to the effect of thermal expansion and the thermo-optic effect, respectively. These two phenomena inevitably lead to thermally-induced WGM frequency shift. To describe this process numerically, we developed a computer code for solving the characteristic equation; temperature increase and glass dispersion were taken into account.
We found that in the considered parameter range (microsphere radius R=20...200 ^m; temperature increase AT=0...100 K) the resulting WGM wavelength shift AA is an almost linear function of AT for modes near A«1.55 ^m. The corresponding temperature sensitivity AA/AT is practically independent of R (Fig. 1a) (detailed explanation is given in [4]). The largest sensitivity is achieved for chalcogenide glass microspheres: 42.2 pm/K for As2S3 and 48.1 pm/K for As2Se3; it is several times larger than for common SiO2 microsensors (13.4 pm/K). We also confirmed that for non-fundamental WGMs the differences are negligible.
The characteristic temperature relaxation time tat is another important parameter for sensing. To calculate tat we solved the heat equation numerically for an experiment-like geometry (Fig. 1b). It was found that tat~R2, as shown in Fig 1c for As2S3. This result coincides well both with the experiment and with the analytical solution for a uniformly heated ideal sphere [4].
This work was supported by the Russian Science Foundation, Grant No. 20-72-10188 (study of silica and tellurite microspheres) and by the Ministry of Science and Higher Education of the Russian Federation, Grant No. 075-15-2021633 (study of germanate and chalcogenide microspheres).
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20 50 100 150 200 Microsphere radius (R), tun
50 100 150 200 Microsphere radius (R), um
Fig. 1. (a) Calculated temperature sensitivity near A«1.55 ^m as a function of microsphere radius for different glasses. (b) Scheme of the geometry used in simulations. Blue areas mark pump absorption regions. (c) Calculated temperature relaxation time t as a function of R for As2S3 microspheres. Dashed line shows t~R2 fit.
[1] T.J. Kippenberg, A.L. Gaeta, M. Lipson, M.L. Gorodetsky, Dissipative Kerr solitons in optical microresonators, Science, vol. 361, eaan8083, (2018).
[2] X. Jiang, A.J. Qavi, S.H. Huang, L. Yang, Whispering-Gallery Sensors, Matter, vol. 3, pp. 371-392, (2020).
[3] A.N. Oraevsky, Whispering-Gallery Waves, Quantum Electronics, vol. 32, pp. 377-400, (2002).
[4] A.V. Andrianov, M.P. Marisova, E.A. Anashkina, Thermo-Optical Sensitivity of Whispering Gallery Modes in As2S3 Chalcogenide Glass Microresonators, Sensors, vol. 22, 4636, (2022).
