Abstract
In this research, we have investigated electromagnetic light propagation through both planar and annular photonic crystals numerically. Three types of structures including, (A) constant length multilayers, (B) Thue-Morse sequence-based structures, and (C) Fibonacci-ordered multilayer systems are compared. For this purpose, we have used the transfer matrix formalism in the Cartesian and cylindrical coordinates. Using this numerical schema, we study the effect of the number of layers, the refractive index of layers, and the radius of the innermost medium on the transmission properties of the assumed systems.
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References
Abadla, M.M., Elsayed, H.A., Mehaney, A.: Sensitivity enhancement of annular one dimensional photonic crystals temperature sensors with nematic liquid crystals. Phys. Scr. 95, 085508 (2020)
Abadla, M.M., Elsayed, H.A., Mehaney, A.: Novel design for the temperature sensing using annular photonic crystals. SILICON 13(12), 4737–4735 (2021). https://doi.org/10.1007/s12633-020-00788-5
Amini, M., Soleimani, M., Ehsani, M.H.: Electronic and optical properties of GaAs/AlGaAs Fibonacci ordered multiple quantum well systems. Superlatt. Microstruct. 112, 680–687 (2017)
Bindi, L., Steinhardt, P.J., Yao, N., Lu, P.J.: Natural Quasicrystals. Science 324, 1306 (2009)
Bombieri, E., Taylor, J.E.: Which distributions of matter diffract? An initial investigation. J. Phys. (paris) Colloq. 47, C3-19–28 (1986)
Chang, T.-W., Hsu, H.-T., Wu, C.-J.: Investigation of Photonic Band Gap in a Circular Photonic Crystal. J. Electromagn. Waves and Appl. 25, 2222 (2011)
Chattopadhyay, S., Chakrabarti, A.: Hidden dimers and their effect on the optical and electronic transmission in Thue-Morse aperiodic structures. J. Phys. Condens. Mater. 12, 5681 (2000)
Chen, M.-S., Wu, C.-J., Yang, T.-J.: Wave properties of an annular periodic multilayer structure containing the single-negative materials. Phys. Lett. A 373, 3594–3600 (2009a)
Chen, M.-S., Wu, C.-J., Yang, T.-J.: Optical properties of a superconducting annular periodic multilayer structure. Solid State Commun. 149, 1888–1893 (2009b)
Chen, M.-S., Wu, C.-J., Yang, T.-J.: Narrowband reflection-and-transmission filter in an annular defective photonic crystal containing an ultrathin metallic film. Opt. Commun. 285, 3143–3149 (2012)
Chourasia, R.K., Prasad, S., Singh, V.: A novel Bragg fiber waveguide based narrow band inline optical filter. Optik 169, 269–276 (2018)
Dal Negro, L., Boriskina, S.V.: Deterministic aperiodic nanostructures for photonics and plasmonics applications. Laser Photonics Rev. 6, 178–218 (2012)
Dal Negro, L., Oton, C.J., Gaburro, Z., Pavesi, L., Johnson, P., Lagendijk, A., Righini, R., Colocci, M., Wiersma, D.S.: Light transport through the band-edge states of Fibonacci quasicrystals. Phys. Rev. Let. 90, 055501 (2003)
David, A., Benisty, H., Weisbuch, C.: Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs. J. Display Technol. 3, 133–148 (2007)
El-Naggar, S.A.: Properties of defect modes in cylindrical photonic crystals. Optik 200, 163447 (2020)
Even-Dar Mandel, S., Lifshitz, R.: Electronic energy spectra of square and cubic Fibonacci quasicrystals. Phil. Mag. 88, 2261–2273 (2008)
Ferrando, V., Gimenez, F., Furlan, W.D., Monsoriu, J.A.: Bifractal focusing and imaging properties of Thue-Morse Zone Plates. Opt. Expr. 27, 19846–19853 (2015)
Foresi, J.S., Villeneuve, P.R., Ferrera, J., Thoen, E.R., Steinmeyer, G., Fan, S., Joannopoulos, J.D., Kimerling, L.C., Smith, H.I., Ippen, E.P.: Photonic bandgap microcavities in optical waveguides. Nature 390, 143–145 (1997)
Gu, J., Xi, X., Ma, J., Yu, Z., Sun, X.: Parity–time-symmetric circular Bragg lasers: a proposal and analysis. Sci. Rep. 6, 37688 (2016)
He, X.Y., Wang, Q.J., Yu, S.F.: Investigation of multilayer subwavelength metallic-dielectric stratified structures. IEEE J. Quantum Electron. 48, 1554–1559 (2012)
Hong, B.B., Huang, L.P., Xu, X.L., Xia, Y.X., Tang, C.J.: Hollow core photonic crystal for terahertz gyrotron oscillator. J. Phys. d: Appl. Phys. 48, 045104 (2015)
Hsueh, W.J., Wun, S.J., Lin, Z.J., Cheng, Y.H.: Features of the perfect transmission in Thue-Morse dielectric multilayers. J. Opt. Soc. Am. B 28, 2584–2591 (2011)
Hu, D.J.J., Alagappan, G., Yeo, Y.K., Shum, P.P., Wu, P.: Broadband transmission in hollow-core Bragg fibers with geometrically distributed multilayered cladding. Opt. Expr. 18, 18671–18684 (2010)
Hu, C.A., Yang, S.L., Yang, T.J.: Switchable tunneling mode for cylindrical photonic quantum well consisting of photonic crystals containing liquid crystal. Opt. Commun. 297, 141–146 (2013a)
Hu, C.A., Wu, C.J., Yang, T.J., Yang, S.L.: Analysis of optical properties in cylindrical dielectric photonic crystal. Opt. Commun. 291, 424–434 (2013b)
Kaliteevski, M.A., Abram, R.A., Nikolaev, V.V., Sokolovski, G.S.: Bragg reflectors for cylindrical waves. J. Mod. Opt. 46, 875–890 (1999)
Kitano, K., Suzuki, K., Ishizaki, K., Noda, S.: Three-dimensional photonic crystals fabricated by simultaneous multidirectional etching. Phys. Rev. B 91, 155308 (2015)
Kohmoto, M., Sutherland, B., Iguchi, K.: Localization of optics: Quasiperiodic media. Phys. Rev. Lett. 58, 2436 (1987)
Kumar Chourasia, R., Singh Yadav, C., Upadhyay, A., Kumar Chourasia, N., Singh, V.: Analysis of Bragg fiber waveguides having a defect layer for biosensing application. Optik 200, 163400 (2020)
Li, L., Matha, C.J., Gangopadhyay, S., Yang, X., Gao, J.: Spontaneous emission rate enhancement with aperiodic Thue- Morse multilayer. Sci. Rep. 9, 8473 (2019)
Lisiecki, F., Rychły, J., Kuświk, P., Głowiński, H., Kłos, J.W., Groß, F., Bykova, I., Weigand, M., Zelent, M., Goering, E.J., Schütz, G.: Reprogrammability and scalability of magnonic fibonacci quasicrystals. Phys. Rev. Appl. 11, 054003 (2019)
Little, C.E., Anufriev, R., Iorsh, I., Kaliteevski, M.A., Abram, R.A., Brand, S.: Tamm plasmon polaritons in multilayered cylindrical structures. Phys. Rev. B 86, 235425 (2012)
Maciá, E.: Thermal conductivity of one-dimensional Fibonacci quasicrystals. Phys. Rev. B 61, 6645 (2000)
Mukhopadhyay, S., Panchadhyayee, P., Biswas, R., Sinha, C.: Influence of Al-concentration on the current density in GaAs/AlcGa1-cAs generalized Thue-Morse superlattices. Eur. Phys. J. B 80, 477–483 (2011)
Prkna, L., Hubalek, M., Ctyroky, J.: "Field modeling of circular microresonators by film mode matching. IEEE J. Sel. Top. Quantum Electron. 11, 217–223 (2005)
Riklund, R., Severin, M., Liu, Y., Internat.: The Thue-Morse aperiodic crystal, a link between the Fibonacci quasicrystal and the periodic crystal. J. Mod. Phys. B 1, 121–132 (1987)
Roshan Entezar, S.: Optical properties of grapheme based annular photonic crystals. J. Modern Opt. 64, 1588–1596 (2017)
Ryu, C.S., Oh, G.Y., Lee, M.H.: Extended and critical wave functions in a Thue-Morse chain. Phys. Rev. B 46, 5162 (1992)
Salehani, H.K., Tehrani, D.H.T., Solaimani, M.: Persistent currents in the presence of the radial electric fields of charged rods and off-centre positively and negatively charged impurities. Philos. Mag. 26, 1–20 (2021)
Shechtman, D., Blech, I., Gratias, D., Cahn, J.W.: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951 (1984)
Singh, B.K., Thapa, K.B., Pandey, P.C.: Optical reflectance and omnidirectional bandgaps in Fibonacci quasicrystals type 1-D multilayer structures containing exponentially graded material. Opt. Commun. 297, 65–73 (2013)
Solaimani, M.: Optical rectification coefficient of GaAs/AlxGa1-xAs Thue-Morse multiple quantum wells. Eur. Phys. J. plus 135, 455 (2020)
Solaimani, M.: Frequency filtering and vibrational spectrum of multiple-valley one-dimensional phononic crystals. Eur. Phys. J. plus 136, 406 (2021)
Solaimani, M., Aleomraninejad, S.M.A.: A hyper-block self-consistent approach to nonlinear Schrodinger equations: Breeding, metamorphosis, and killing of Hofstadter Butterflies. Commun. Nonlinear Sci. Numer. Simulat. 97, 105724 (2021)
Solaimani, M., Izadifard, M., Arabshahi, H., Sarkardei, M.R.: Effect of the magnetic field on optical properties of GaN/AlN multiple quantum wells. J. Lumin. 134, 88–95 (2013)
Solaimani, M., Ghalandari, M., Lavaei, L.: Donor impurity effects on optical properties of GaN/AlN constant total effective radius multishell quantum dots. J. Opt. Soc. Am. B 33, 420–425 (2016)
Solaimani, M., Ghalandari, M., Aghajamali, A.: Band gap engineering in constant total length nonmagnetized plasma-dielectric multilayers. Optik 207, 164476 (2020)
Sordelet, D.J., Dubois, J.M.: Quasicrystals perspectives and potential applications. MRS Bull. 22, 34–39 (1997)
Srivastava, S.K., Aghajamali, A.: Investigation of reflectance properties in 1D ternary annular photonic crystal containing semiconductor and high-T c superconductor. J. Supercond. Nov. Magn. 29, 1423–1431 (2016)
Srivastava, S.K., Aghajamali, A.: Study of optical reflectance properties in 1D annular photonic crystal containing double negative (DNG) metamaterials. Phys. B 489, 67–72 (2016)
Wang, L., Yang, X., Chen, T.: Second harmonic generation in generalized Thue-Morse ferroelectric superlattices. Phys. B 404, 3425–3430 (2009)
Wang, Q.-Y., Liu, S., Gui, D., Zhang, H.-F.: Nonreciprocal absorption characteristics of one-dimensional cylindrical magnetized plasma photonic crystals. Phys. Scr. 96, 065501 (2021)
Wu, C.-J., Gwo, S.: Calculations of optical properties of an annular dielectric mirror. J. Electromagn. Waves Appl. 21, 821–827 (2007)
Yablonovitch, E., Gmitter, T.J., Meade, R.D., Rappe, M., Brommer, K.D., Joannopoulos, J.D.: Donor and acceptor’modes in photonic band structure. Phys. Rev. Lett. 67, 3380–3383 (1991)
Zamudio-Lara, A., Escobedo-Alatorre, J., Sanchez-Mondragon, J., Tecpoyotl-Torres, M.: A comparison between unidimensional, circular and spherical photonic crystal stacks. Opt. Mater. 27, 1255 (2005)
Zhang, H.-F., Liu, S.-B., Kong, X.-K., Bian, B.-R.: The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice. Optics Commun. 288, 82–90 (2013a)
Zhang, H.-F., Liu, S.-B., Kong, X.-K.: Enlarged omnidirectional band gap in one-dimensional plasma photonic crystals with ternary Thue-Morse aperiodic structure. Phys. B 410, 244–250 (2013b)
Zhang, H.-F., Liu, S.-B., Li, B.-X.: Investigation on the properties of omnidirectional photonic band gaps in two-dimensional plasma photonic crystals. Phys. Plasmas 23, 12105 (2016)
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The paper properly credits the meaningful contributions of co-authors and co-researchers. Mostafa Aghahasani and Mehdi Soleimani wrote the main manuscript text and prepared figures. Mohammad Hossein Ehsani and Mehdi soleimani are supervisors and reviewed the manuscript.
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Agha-Hassani, M., Ehsani, M.H. & Soleimani, M. Transmission properties of thue-morse, fibonacci and fixed length photonic crystals: comparing the planar and annular geometries. Opt Quant Electron 55, 499 (2023). https://doi.org/10.1007/s11082-023-04768-y
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DOI: https://doi.org/10.1007/s11082-023-04768-y