Vol. 38, issue 07, article # 1

Abstract:

The helical symmetry of a permittivity tensor causes Bragg’s reflection at wavelengths close to the screw (helicoid) pitch for circular polarization of light. The study has discovered and explained the resistance of a band gap short-wave boundary to the optical axis tilt towards helical axis (normal to the plane of layers) in helical photonic structures. For a conical helical structure, the long-wavelength boundary of the reflection area changes more than for a structure with a normal cone opening with optical axis perpendicular to helical axis. Still, the wavelength for the edge mode at the short-wave boundary strictly remains under arbitrary distortions. The findings of a numerical simulation with the use of anisotropic transfer matrix and Berreman transfer matrix are coherent and confirmed by analytical derivation.

Keywords:

helical photonic structure, partial disordering, circular Bragg’s phenomenon

Figures:

References:

1. Francis F.Ch. Helicon discharges and sources: A review // Plasma Sour. Sci. Technol. 2015. V. 24. P. 1–25. DOI: 10.1088/0963-0252/24/1/014001.
2. Maksfild B. Gelikony v tverdykh telakh // Uspekhi fiz. nauk. 1971. V. 103, N 2. P. 233–273.
3. Sun J., Bhushan B. Structure and mechanical properties of beetle wings: A review // RSC Adv. 2012. V. 2. P. 12606–12623. DOI: 10.1039/C2RA21276E.
4. Lopez-Garcia M., Masters N., O’Brien H.E., Lennon J., Atkinson G., Cryan M.J., Oulton R., Whitney H.M. Light-induced dynamic structural color by intracellular 3D photonic crystals in brown algae // Sci. Adv. 2018. V. 4. eaan8917. P. 1–8. DOI: 10.1126/sciadv.aan8917.
5. Afonasenko A.V., Iglakova A.N., Matvienko G.G., Oshlakov V.K., Prokop'ev V.E. Laboratornye i lidarnye izmereniya spektral'nykh kharakteristik list'ev berezy v razlichnye periody vegetatsii // Optika atmosf. i okeana. 2012. V. 25, N 3. P. 237–243.
6. Tarasov L.V. Fizika v prirode. M.: Prosveshchenie, 1988. 351 p.
7. Byalko A.V., Smorodinskii Ya.A. Nasha planeta – Zemlya. M.: Nauka, 1983. 208 p.
8. Huang K., Liu Y.-H., Lu Q., Hu Z., Lynch K.A., Hesse M., Vaivads A., Yang H. Auroral spiral structure formation through magnetic reconnection in the auroral acceleration region // Geophys. Res. Let. 2022. V. 49, N 18. P. e2022GL100466. DOI: 10.1029/2022GL100466.
9. Krasovskij V.I. Polar auroras // Space Sci. Rev. 1964. V. 3, N 2. P. 232–274. DOI: 10.1007/BF00180266.
10. Enengl F., Kotova D., Jin Y., Clausen L.B.N., Milochet W.J. Ionospheric plasma structuring in relation to auroral particle precipitation // J. Space Weather Space Clim. 2023. V. 13. P. 1. DOI: 10.1051/swsc/2022038.
11. Garab G. Self-assembly and structural-functional flexibility of oxygenic photosynthetic machineries: Personal perspectives // Photosynth. Res. 2016. V. 127. P. 131–150. DOI: 10.1007/s11120-015-0192-z.
12. Goss R., Garab G., Wilhelm C. Organization of the pigment molecules in the chlorophyll a/b/c-containing alga Mantoniella squamata (Prasinophyceae) studies by means of absorption, circular and linear dichroism spectroscopy // Biochim. Biophys. Acta. 2000. V. 1457, N 3. P. 190–199. DOI: 10.1016/S0005-2728(00)00101-8.
13. Szabó M., Lepetit B., Goss R., Wilhelm C., Mustárdy L., Garab G. Structurally flexible macro-organization of the pigment-protein complexes of the diatom Phaeodactylum tricornutum // Photo-synth Res. 2008. V. 95. P. 237–245. DOI: 10.1007/s11120-007-9252-3.
14. Shabanov V.F., Vetrov S.Ya., Shabanov A.V. Optika real'nykh fotonnykh kristallov. Jidkokristallicheskie defekty, neodnorodnosti. Novosibirsk: Izd-vo SO RAN, 2005. 209 p.
15. Sakoda K. Optical properties of photonic crystals. Berlin: Springer, 2005. 253 p. DOI: 10.1007/b138376.
16. Joannopoulos J.D., Johnson S.G., Winn J.N., Meade R.D. Photonic Crystals: Molding the Flow of Light. 2nd ed. Princeton: Princeton University Press, Princeton, NJ, USA, 2008. 304 p. DOI: 10.1515/9781400828241.
17. Yablonovitch E., Gmitter T.J., Leung K.M. Photonic band structures: The base-centered cubic case employing non-spherical atoms // Phys. Rev. Lett. 1991. V. 67. P. 2295–2298. DOI: 10.1103/PhysRevLett.67.2295.
18. Yariv A., Yeh P. Optical Waves in Crystals. New York: Wiley, 1984. 304 p.
19. Shabanov A.V., Korshunov M.A., Bukhanov E.R. Issledovanie elektromagnitnogo polya v odnomernykh fotonnykh kristallakh s defektami // Komp'yuternaya optika. 2017. V. 41, N 5. P. 680–686. DOI: 10.18287/2412-6179-2017-41-5-680-686.
20. Belyakov V.A., Sonin A.S. Optika kholestericheskikh jidkikh kristallov. M.: Nauka, 1982. 360 p.
21. Belyakov V.A. Diffraction Optics of Complex-Structured Periodic Media: Localized Optical Modes of Spiral Media. Switzerland: Springer International Publishing, 2019. 253 p. DOI: 10.1007/978-3-319-43482-7_9.
22. Vepachedu V., Lakhtakia A. Chiral sculptured thin films for circular polarization of mid-wavelength infrared light // App. Opt. 2018. V. 57, N 22. P. 6410–6416. DOI: 10.1364/AO.57.006410.
23. Makhmudov K.O., Makhmudov O.I., Tarkhanov N. Equations of Maxwell type // JMAA. 2011. V. 378, N 1. P. 64–75. DOI: 10.1016/j.jmaa.2011.01.012.
24. Abelès F. La théorie générale des couches minces // Journal de Physique et le Radium. 1950. V. 11, N 7. P. 307–309.
25. Berreman D.W. Optics in stratified and anisotropic media: 4 ´ 4-matrix formulation // J. Opt. Soc. Am. 1972. V. 62, N 22. P. 502–510. DOI: 10.1364/JOSA.62.000502.
26. Yeh P. Electromagnetic propagation in birefringent layered media // J. Opt. Soc. Am. 1979. V. 69, N 5. P. 742–756. DOI: 10.1364/JOSA.69.000742.
27. Vetrov S.Ya., Timofeev I.V., Shabanov V.F. Lokalizovannye mody v khiral'nykh fotonnykh strukturakh // Uspekhi fiz. nauk. 2020. V. 190, N 1. P. 37–62. DOI: 10.3367/UFNr.2018.11.038490.
28. Lakhtakia A. Resilience of circular-polarization-state-sensitive reflection against morphological disorder in chiral structures // J. Nanophotonics. 2024. V. 18, N 22. P. 036005-1–036005-17. DOI: 10.1117/1.JNP.18.036005.v.
29. Arkhipkin V.G., Gunyakov V.A., Myslivets S.A., Zyryanov V.Y., Shabanov V.F., Lee W. Electro- and magneto-optical switching of defect modes in one-dimensional photonic crystals // JETP. 2011. V. 112, N 4. P. 577–587. DOI: 10.1134/S1063776111040017.
30. Fang X., MacDonald K.F., Plum E., Zheludev N.I. Coherent control of light-matter interactions in polarization standing waves // Sci. Rep. 2016. V. 6. P. 31141. DOI: 10.1038/srep31141.