Vol. 35, issue 07, article # 8

Geints Yu. E., Minin I. V., Minin O. V. Coupled optical resonances in a dielectric microsphere: physical concept of miniature optical pressure sensor. // Optika Atmosfery i Okeana. 2022. V. 35. No. 07. P. 581–588. DOI: 10.15372/AOO20220708 [in Russian].
Copy the reference to clipboard


Optical resonance of the internal field of a dielectric microparticle occurs when the frequency of the incident light is tuned to the frequency of one of the particle spatial eigenmodes which leads to a sharp increase in optical intensity and higher field localization near the particle rim providing the formation of annularly-periodic structures in the form of standing waves, the so-called “whispering gallery” modes (WGM). We theoretically consider the case where a dielectric microsphere is placed near a flexible light reflecting membrane, which acts as an external pressure sensor. In this case, due to reflection from the reflecting membrane, the WGMs of the sphere are excited twice by direct and reflected backward radiation, which then couples within the microparticle volume. The optical intensity of the resulting WGM carries enough information about the position of the flexible loaded membrane. This allows one to propose a physical concept of a new miniature all-optical pressure sensor. We show that the pressure sensitivity of such a sensor depends on the quality factor of the excited resonant mode, as well as the geometrical and mechanical parameters of the flexible membrane. Important advantages of the sensor proposed are the miniature design (the size of the sensor is determined by the diameter of the flexible membrane) and the non-contact type of the pressure sensor placement.


optical resonance, optical pressure sensor, whispering gallery modes, wave reflection, optical wave interference, mesowavelength particle


1. Boyd R.W., Heebner J.E. Sensitive disk resonator photonic biosensor // Appl. Opt. 2001. V. 40. P. 5742–5747.
2. Ward J., Benson O. WGM microresonators: sensing, lasing and fundamental optics with microspheres // Laser Photon. Rev. 2011. V. 5. P. 553–570. DOI: 10. 1002/lpor.201000025.
3. Foreman M.R., Swaim J.D., Vollmer F. Whispering gallery mode sensors // Adv. Opt. Photon. 2015. V. 7. P. 168–240. DOI: 10.1364/AOP.7.000168.
4. Zheng Y., Wu Z.F., Shum P.P., Xu Z.L., Keiser G., Humbert G., Zhang H., Zeng Sh., Dinh X.Q. Sensing and lasing applications of whispering gallery mode microresonators // Opt. Electron. Adv. 2018. V. 1. P. 180015.
5. Ali A.R. Micro-optical vibrometer/accelerometer using dielectric microspheres // Appl. Opt. 2019. V. 58. P. 4211–4219. DOI: 10.1364/AO.58.004211.
6. Conwell P.R., Barber P.W., Rushforth C.K. Resonant spectra of dielectric spheres // J. Opt. Soc. Am. 1984. V. A 1. P. 62–67.
7. Benner R.E., Barber P.W., Owen J.F., Chang R.K. Observation of structure resonances in the fluorescence spectra from microspheres // Phys. Rev. Lett. 1980. V. 44. P. 475–478.
8. Chýlek P. Resonance structure of Mie scattering: Distance between resonances // J. Opt. Soc. Am. 1990. V. A 7. P. 1609–1613.
9. Cai L., Pan J., Hu S. Overview of the coupling methods used in whispering gallery mode resonator systems for sensing // Opt. Lasers Engin. 2020. V. 127. P. 105968. DOI: 10.1016/j.optlaseng.2019.105968.
10. Zemlyanov A.A., Gejnts Yu.E. Effektivnost' vozbuzhdeniya rezonansnyh prostranstvennyh konfiguratsij vnutrennego opticheskogo polya sfericheskih mikrochastits fokusirovannymi lazernymi puchkami // Optika atmosf. i okeana. 2000. V. 13, N 5. P. 447–456.
11. Bobbert P.A., Vlieger J. Light scattering by a sphere on a substrate // Physica. 1986. V. 137A. P. 209–242.
12. Liu C., Wiegel T., Schweiger G. Structural resonances in a dielectric sphere on a dielectric surface illuminated by an evanescent wave // Opt. Commun. 2000. V. 185. P. 249–261.
13. Luk’yanchuk B.S., Zheng Y.W., Lu Y.F. Laser cleaning of solid surface: Optical resonance and near-field effects // Proc. SPIE. 2000. V. 4065. P. 576–587.
14. Xifre-Perez E., Shi L., Tuzer U., Fenollosa R., Ramiro-Manzano F., Quidant R., Meseguer F. Mirror-image-induced magnetic modes // ACS Nano. 2012. V. 7, N 1. P. 664–668. DOI: 10.1021/nn304855t.
15. Vasista A.B., Tiwari S., Sharma D.K., Chaubey Sh.K., Pavan Kumar G.V. Vectorial fluorescence emission from microsphere coupled to gold mirror // Adv. Opt. Mater. 2018. V. 6. P. 1801025.
16. Yao J., Yin Y., Ye L., Cai G., Liu Q.H. Enhancing third-harmonic generation by mirror-induced electric quadrupole resonance in a metal–dielectric nanostructure // Opt. Lett. 2020. V. 45, N 20. P. 5864–5867. DOI: 10.1364/OL.400593.
17. Yue L., Yan B., Monks J., Dhama R., Wan Z., Minin O.V., Minin I.V. Photonic jet by a near-unity-refractive-index sphere on a dielectric substrate with high index contrast // Ann. Phys. 2018. V. 530, N 6. P. 1800032.
18. Aspnes D.E., Studna A.A. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 Ev // Phys. Rev. 1983. V. B 27. P. 985–1009.
19. Roll G., Schweiger G. Geometrical optics model of Mie resonances // J. Opt. Soc. Am. 2000. V. A17. P. 1301–1311.
20. Boren K., Hafmen D. Pogloshchenie i rasseyanie sveta malymi chastitsami. M.: Mir, 1986. 660 p.
21. Huber T., Davanco M., Müller M., Shuai Y., Gazzano O., Solomon G.S. Filter-free single-photon quantum dot resonance fluorescence in an integrated cavity-waveguide device // Optica. 2020. V. 7. P. 380–385. DOI: 10.1364/OPTICA.382273.
22. Noginov M.A., Zhu G., Belgrave A., Bakker R., Shalaev V.M., Narimanov E.E., Stout S., Herz E., Suteewong T., Wiesner U. Demonstration of a spaser-based nanolaser // Nature. 2009. V. 460. P. 1110–1112. DOI: 10.1038/nature08318.
23. Lu D., Pedroni M., Labrador-Páez L., Marqués M.I., Jaque D., Haro-González P. Nanojet trapping of a single sub-10 nm upconverting nanoparticle in the full liquid water temperature range // Small. 2021. V. 17. P. 2006764. DOI: 10.1002/smll.202006764.
24. Sarkar A., Venkataraj R., Nampoori V.P.N., Kaila­snath M. Silver nanoparticle assisted enhanced WGM lasing by silica microresonator // Opt. Commun. 2021. V. 494. P. 127045. DOI: 10.1016/j.optcom.2021.127045.
25. Grudinkin S.A., Dontsov A.A., Feoktistov N.A., Baranov M.A., Bogdanov K.V., Averkiev N.S., Golubev V.G. Whispering gallery modes in a spherical microcavity with a photoluminescent shell // Semicon­ductors. 2015. V. 49. P. 1369–1374. DOI: 10.1134/ S1063782615100085.
26. Wienhold T., Kraemmer S., Bacher A., Kalt H., Koos C., Koeber S., Mappes T. Efficient free-space read-out of WGM lasers using circular micromirrors // Opt. Express. 2015. V. 23. P. 1025–1034. DOI: 10.1364/ OE.23.001025.
27. Slezinger I.N. On the theory of flexible elastic plates // Sov. Appl. Mechan. 1972. V. 8. P. 732–737. DOI: 10.1007/BF00886279.
28. Reddy J.N. Theory and Analysis of Elastic Plates and Shells. Florida: CRC Press, 2006. 568 p. DOI: 10.1201/ 9780849384165.
29. Li M., Wang Y., Tian M., Cheng J., Jiang X., Tan Y. A compact and highly sensitive voice-eavesdropping microresonator // J. Lightwave Technol. 2021. V. 39. P. 6327–6333.
30. Zemlyanov A.A., Geints Yu.E. Intensity of optical field inside a weakly absorbing spherical particle irradiated by a femtosecond laser pulse // Opt. Spectrosc. 2004. V. 96. P. 298–304.
31. Kozlova E.S., Kotlyar V.V. Modelirovanie rezonansnoj fokusirovki pikosekundnogo i femtosekundngo impul'sov dielektricheskim mikrotsilindrom // Komp'yuternaya optika. 2015. V. 39, N 3. P. 319–323.