Photonics RussiaPhotonics RussiaФотоника1993-72962686-844XTechnosphera JSC68689110.22184/1993-7296.FRos.2025.19.4.296.303MetatronicsМетатроникаResearch ArticleInfluence of dielectric particle porosity on the position of Mie resonancesВлияние пористости диэлектрической частицы на положение Ми резонансовhttps://orcid.org/0009-0000-8711-8711GainutdinovAzat R.ГайнутдиновАзат Радикович
Russian Federation

postgraduate student; Institute of Physics

аспирант; Институт физики

azat794@mail.ruKazan (Volga Region) Federal UniversityКазанский (Приволжский) федеральный университет240720251942963030707202507072025Copyright ©; 2025, Gainutdinov A.R.Copyright ©; 2025, Гайнутдинов А.Р.2025Gainutdinov A.R.Гайнутдинов А.Р.https://journals.eco-vector.com/1993-7296/article/view/686891

The dielectric particles with a high refractive index demonstrate Mie resonances in the infrared region of spectrum, where the typical absorption bands of many hydrocarbons are observed. The article provides a numerical determination of the dependence of the refractive index of a dielectric particle located in a target substance matrix on the particle porosity value. It is shown that an increased particle porosity leads to a linear decrease in the particle refractive index and to a linear shift of the Mie resonance to the region of short wavelengths. An estimate is given for the shift in the spectral range of the Mie resonance manifestation when the particle porosity value is changed by a few percent.

Диэлектрические частицы с высоким показателем преломления демонстрируют резонансы Ми в инфракрасной области спектра, где наблюдаются характеристические полосы поглощения многих углеводородов. В статье представлено численное определение зависимости показателя преломления диэлектрической частицы, находящейся в матрице целевого вещества, от значения пористости частицы. Показано, что увеличение пористости частицы приводит к линейному уменьшению показателя преломления частицы и к линейному смещению Ми резонанса в область коротких длин волн. Дана оценка смещения спектрального диапазона проявления резонанса Ми при изменении значения пористости частицы на единицы процентов.

Mie resonancesexpress detection of low hydrocarbon concentrationsdielectric particlesrefractive indexparticle porositysilicon particlesрезонансы Миэкспресс-детектирование низких концентраций углеводородовдиэлектрические частицыпоказатель преломленияпористость частицыкремниевые частицыMinin I. V., Minin O. V. Tomsk Polytechnic University, Tomsk, RussiaOptical Super-Resonance in the Dielectric Mesoscale Spheres. Photonics Russia. 2022; 16(4): 306–317. doi: 10.22184/1993-7296.FRos.2022.16.4.306.317. Минин И. В, Минин О. В. Оптический суперрезонанс в мезоразмерных диэлектрических сферах. Фотоника. 2022; 16(4): 306–317. doi: 10.22184/1993-7296.FRos.2022.16.4.306.317.Tzarouchis D., Sihvola A. Light Scattering by a Dielectric Sphere: Perspectives on the Mie Resonances. Appl. Sci. 2018; 8 (2): 184(1–22). doi:10.3390/app8020184.Fu Y. H., Kuznetsov A. I., Miroshnichenko A. E., Yu Y. F., Luk’yanchuk B. Directional visible light scattering by silicon nanoparticles. Nature Communications. 2013; 4(1). 1527–1532. doi:10.1038/ncomms2538.Tonkaev P., Kivshar Y. High-Q dielectric Mie-resonant nanostructures (brief review). JETP Letters. 2020; 112 (10): 615–622. doi.10.1134/S0021364020220038.Kivshar Y. The rise of Mie-tronics. Nano Letters. 2022; 22 (9). 3513–3515. doi: 10.1021/acs.nanolett.2c00548.Garifullin A. I., Gainutdinov R. K., Khamadeev M. A. Acceleration of Chemical Reactions in Hybrid One-Dimensional Photonic Crystals Based on High-Index Metamaterials. Bulletin of the Russian Academy of Sciences: Physics. 2022; 86(1). 66–70. doi:10.3103/S106287382270040X.Gainutdinov R. K., Nabieva L. J., Garifullin A. I., Mutygullina A. A. Dressing of superconducting qubits by their interaction with a low frequency photon reservoir. Journal of Physics: Conference Series. 2019; 1283(1): 012004(1–6). doi:10.1088/1742-6596/1283/1/012004.Garifullin A. I., Arslanov N. M. Optimization of SI3N4 nanophotonic resonator taking into account the substrate influence. Optical Technologies for Telecommunications. 2023; 13168: 430–435. doi: 10.1117/12.3026578.Barreda A. I., Saiz J. M., González F., Moreno F., Albella P. Recent advances in high refractive index dielectric nanoantennas. Basics and applications. AIP Advances.2019; 9(4): e202100248(1–10). doi:10.1002/cptc.202100248.Shilkin D. A., Lyubin E. V., Shcherbakov M. R., Lapine M., Fedyanin A. A. Directional Optical Sorting of Silicon Nanoparticles. ACS Photonics.2017; 4(9): 2312–2319. doi:10.1021/acsphotonics.7b00574.Babicheva V. E., Evlyukhin A. B. Mie-resonant metaphotonics. Adv. Opt. Photon. 2024; 16: 539–658. doi:10.1364/AOP.510826.Luk’yanchuk B. S., Voshchinnikov N. V., Paniagua-Domínguez R., Kuznetsov A. I. Optimum Forward Light Scattering by Spherical and Spheroidal Dielectric Nanoparticles with High Refractive Index. ACS Photonics. 2015; 2(7): 993–999. doi:10.1021/acsphotonics.5b00261.Kuznetsov A. I., Miroshnichenko A. E., Brongersma M. L., Kivshar, Y. S., Luk’yanchuk B. Optically resonant dielectric nanostructures. Science. 2016; 354(6314): 846–855. doi:10.1126/science.aag2472.Galante А., Contestabile А., Capocefalo А., Galdi V, Rizza C., Alecci M. Observation of radio-frequency Mie resonances in high-permittivity dielectric spheres J. Phys. D: Appl. Phys. 2025; 58: 135122 (1–6). doi: 10.1088/1361-6463/adaf35.Yao X., Hong X., Liu Y. Visible Mie resonances in dielectric hollow spheres: Principle, regulation, and applications. Responsive Materials. 2023; 1(2): e20230019(1–14). doi. 10.1002/rpm.20230019.LаMer V.K., Dinegar R. H. Theory, production and mechanism of formation of monodispersed hydrosols. J. Am. Chem. Soc. 1950; 72 (11): 4847–4854. doi: 10.1021/ja01167a001.Bogush, G.H., Zukoski C. F. Uniform silicа particle precipitation: an aggregative growth model. J. Colloid Interface Sci. 1991; 142 (1): 19–34. doi: 10.1016/0021-9797(91)90030-C.Philipse A. P. Quantitative aspects of the growth of (charged) silica spheres. Colloid & Polymer Science. 1988; 266(12): 1174–1180. doi: 10.1007/bf01414407.Keefer K. D., Schaefer D. W. Growth of Fractally Rough Colloids. Physical Review Letters. 1986; 56(22): 2376–2379. doi: 10.1103/physrevlett.56.2.Van Blaaderen A., Vrij A. Synthesis and Characterization of Monodisperse Colloidal Organo-silica Spheres. Journal of Colloid and Interface Science. 1993; 156(1): 1–18. doi:10.1006/jcis.1993.1073.Stöber W., Fink A., Bohn E. Controlled growth of monodisperse silica spheres in the micron size range. Journal of Colloid and Interface Science. 1968; 26(1): 62–69. doi: 10.1016/0021-9797(68)90272-5.Karpov I. A., Samarov E. N., Masalov V. M., Bozhko S. I., Emelchenko G. A. The intrinsic structure of spherical particles of opal. Phys. Solid State. 2005; 47: 347–351. doi: 10.1134/1.1866417.Jones J. B.. Segnit E. R. Water in sphere-type opal. Mineral. Magazine. 1969; 37(287): 357–361. doi:10.1180/minmag.1969.037.287.07.Giesche H. Synthesis of monodispersed silica powders.I. Particles properties and reaction kinetics. J. Eur.Ceram. Soc. 1994; 14(3): 189–204. doi: 10.1016/0955-2219(94)90087-6.Bogush G. H., Tracy M. A., Zukoski C. F. Preparation of monodisperse silica particles: Control of size and mass fraction. Journal of Non-Crystalline Solids. 1988; 104(1): 95–106. doi:10.1016/0022-3093(88)90187-1.Van Helden A. K., Jansen J. W., Vrij A. Preparation and characterization of spherical monodisperse silica dispersions in nonaqueous solvents. Journal of Colloid and Interface Science. 1981; 81(2): 354–368. doi: 10.1016/0021-9797(81)90417-3.Si T., Wang Y., Wei W., Lv P., Ma G., Su Z. Effect of acrylic acid weight percentage on the pore size in poly (N-Isopropyl acrylamide-co-acrylic acid) microspheres. Reactive and Functional Polymers. 2011; 71(7): 728–735. doi: 10.1016/j.reactfunctpolym.2011.04.003.Maltsev V. P., Chernyshev A. V., Sem’yanov K. A., Soini E. Absolute real-time determination of size and refractive index of individual microspheres. Measurement Science and Technology. 1997; 8(9): 1023–1027. doi: 10.1088/0957-0233/8/9/011.Ratnikov V. V. Determining the porosity of synthetic opals and porous silicon by x-ray methods. Phys. Solid State. 1997; 39: 856–858. doi: 10.1134/1.1129984.Akhmadeev A. A., Gainutdinov A. R., Khamadeev M. A., Salakhov M. K. Determination of the Porosity of Silicon Dioxide Microparticles by the Method of Refractive Index Matching. Optics and Spectroscopy. 2020; 128(9): 1388–1392. doi: 10.1134/s0030400x20090027.Wiederseiner S., Andreini N., Epely-Chauvin G., Ancey C. Refractive-index and density matching in concentrated particle suspensions: a review. Experiments in Fluids. 2010; 50(5): 1183–1206. doi: 10.1007/s00348-010-0996-8.Apresyan L. A., Vlasov D. V., Zadorin D. A., Krasovsky V. I. On the effective medium model for particles with a complex structure. Tech. Phys. 2017; 62: 6–13. doi: 10.1134/S1063784217010029.Bohren C. F., Huffman D. R. Absorption and scattering of light by small particles. – John Wiley & Sons.1983.530 p.Tarasevich B. N. IK spektry osnovnykh klassov organicheskikh soedineniy [IR Spectra of the Main Classes of Organic Compounds]. – M.: MGU, 2012. 54 p. Тарасевич Б. Н. ИК спектры основных классов органических соединений. – М.: МГУ. 2012. 55 с.