Mathematical model of an optical linear acceleration transducer based on controlled coupled optical waveguides

Various linear acceleration transducers are reviewed, and their advantages and disadvantages are noted. Classical microelectromechanical accelerometers are miniature but susceptible to electromagnetic interference, and their metrological characteristics are insufficiently stable. Traditional fiber-optic sensors based on fiber Bragg gratings or Fabry-Perot interferometers provide high sensitivity but are characterized by complex optical schemes, large dimensions, and high sensitivity to temperature drifts, which hinders their integration into navigation, avionics, and space technology systems. An optical linear acceleration transducer based on controlled coupled optical waveguides has been developed. The functional scheme of the transducer includes a sensing element, an optical radiation source, photodetectors, current-to-voltage converters, and a differential signal processing circuit. A mathematical model is proposed describing the dependence of the coupling coefficient of optical waveguides on mechanical stresses induced by acceleration. The model takes into account the influence of the photoelastic effect. Mathematical modeling of the transducer operation was performed for various geometric parameters of the sensing element design. Experimental studies of the optical linear acceleration transducer were conducted, which confirmed the validity of the proposed model: a sensitivity of 10.5 mV·s²·m^–1 was achieved with nonlinearity not exceeding 0.68 % in an acceleration range of ±200 m/s². The operability of the transducer based on an optical splitter with fused waveguides has been demonstrated. Such a transducer can also be implemented using planar coupled waveguides.

1. Akbaba C. E., Tanrıkulu M. Y. MEMS capacitive accelerometer: A review. Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi, 6(2), 41–58 (2023). https://doi.org/10.55198/artibilimfen.1386846

2. Veena S., Newton Rai, H. L. Suresh, Nagaraja V. S. Design, modelling, and simulation analysis of a Single Axis MEMS-based Capacitive Accelerometer. International Journal of Engineering Trends and Technology, 69(10), 82–88 (2021). https://doi.org/10.14445/22315381/IJETT-V69I10P211

3. Alekseeva V. V., Papko A. A., Kalinin M. A., Kiryanina I. V., Sheptalina S. V. Increasing the resolution and the stability of metrological characteristics of micromechanical accelerometers. Izmeritel’naya Tekhnika, (3), 19–21 (2011). (In Russ.) https://elibrary.ru/nduxwd

4. Gomathi K., Balaji A., Mrunalini T. Design and optimization of differential capacitive micro accelerometer for vibration measurement. Journal of the Mechanical Behavior of Materials, 30(1), 19–27 (2021). https://doi.org/10.1515/jmbm-2021-0003

5. Lu Q. B., Wang Y. N., Wang X. X., Yao Y., Wang X. W. et al. Review of micromachined optical accelerometers: from mg to sub-μg. OptoElectron, 4(3), 200045 (2021). https://doi.org/10.29026/oea.2021.200045

6. Kim T. H. Analysis of optical communications, fiber optics, sensors and laser applications. Journal of Machine and Computing, 3(2), 115–125 (2023). https://doi.org/10.53759/7669/jmc202303012

7. Xin C., Xu Y., Zhang Z., Li M. Micro-opto-electro-mechanical systems for high-precision displacement sensing: A Review. Micromachines, 15(8), 1011 (2024). https://doi.org/10.3390/mi15081011

8. Xu N., Tang J. D., Lv X. M., Li T., Guo M. L., Zhou Q. Recent advances in nano-opto-electro-mechanical systems. Nanophotonics, 10(9), 2265–2281 (2021). https://doi.org/10.1515/nanoph-2021-0082

9. Yurin A. I., Dmitriev A. V., Krasivskaya M. I., Zloodeev G. Yu. Adaptive contactless fiber-optic transducer of vibration displacement. Izmeritel’naya Tekhnika, (11), 11–13 (2016). (In Russ.) https://elibrary.ru/xbshpf

10. Flynn C., Cao H., Applegate B. E., Tkaczyk T. S. Fabrication of waveguide directional couplers using 2-photon lithography. Optics Express, 31(16), 26323–26334 (2023). https://doi.org/10.1364/OE.495363

11. Zhang R., Deng C., Zhao J., Zhang F., Huang Y., Zhang X., Wang A. Compact and efficient three-mode (de)multiplexer based on horizontal polymer waveguide couplers. Optics Express, 30(3), 3632–3644 (2022). https://doi.org/10.1364/OE.449688

12. Tong W., Wei Y., Zhou H., Dong J., Zhang X. The design of a low-loss, fast-response, metal thermo-optic phase shifter based on coupled-mode theory. Photonics, 9(7), 447 (2022). https://doi.org/10.3390/photonics9070447

13. Busurin V. I., Kazaryan A. V., Zheglov M. A., Tyunin A. N. Patent RU 2839318 C1, Inventions. Utility models, no. 13 (2025).

14. Black R. J. Optical waveguide modes Polarization, Coupling and Summetry. McGraw-Hill Publ., New York (2010).

15. Li C. Optical stress sensor based on electro-optic compensation for photoelastic birefringence in a single crystal. Applied Optics, 50(27), 5315–5320 (2011). https://doi.org/10.1364/AO.50.005315

16. Tarabini M., Saggin B., Scaccabarozzi D., Moschioni G. The potential of micro-electro-mechanical accelerometers in human vibration measurements. Journal of Sound and Vibration, 331(2), 487–499 (2012). https://doi.org/10.1016/j.jsv.2011.08.030

17. Miani T., Gurung L., Young D., Parajuli M., Sobreviela-Falces G., Baker C., Seshia A. A. Correlation of scale factor non-linearity and vibration rectification error in vibrating beam accelerometers. IEEE Access, 13, 120895–120904 (2024). https://doi.org/10.1109/ACCESS.2025.3586063