메뉴 건너뛰기




Volumn 5, Issue 1, 2015, Pages 14-44

Bloch modes and evanescent modes of photonic crystals: Weak form solutions based on accurate interface triangulation

Author keywords

Band gap material; Band structure; Evanescent modes; Mesh representations; Photonic crystals; Reflectance; Single gyroid; Weak form solutions

Indexed keywords


EID: 84961292213     PISSN: None     EISSN: 20734352     Source Type: Journal    
DOI: 10.3390/cryst5010014     Document Type: Article
Times cited : (21)

References (54)
  • 1
    • 26544437684 scopus 로고
    • Strong Localization of Photons in Certain Disordered Dielectric Superlattices
    • John, S. Strong Localization of Photons in Certain Disordered Dielectric Superlattices. Phys. Rev. Lett. 1987, 58, 2486–2489.
    • (1987) Phys. Rev. Lett , vol.58 , pp. 2486-2489
    • John, S.1
  • 3
    • 84961386092 scopus 로고    scopus 로고
    • Simulation of Finite Photonic Crystals Made of Biisotropic or Chiral Material
    • NATO Science Series; Zouhdi, S., Sihvola, A., Arsalane, M., Eds.; Springer: Berlin, Germany
    • Karkashadze, D.; Bogdanov, F.; Zaridze, R.; Bijamov, A.; Hafner, C.; Erni, D. Simulation of Finite Photonic Crystals Made of Biisotropic or Chiral Material. In Advances in Electromagnetics of Complex Media and Metamaterials; NATO Science Series; Zouhdi, S., Sihvola, A., Arsalane, M., Eds.; Springer: Berlin, Germany, 2002; Volume 89, pp. 175–193.
    • (2002) Advances in Electromagnetics of Complex Media and Metamaterials , vol.89 , pp. 175-193
    • Karkashadze, D.1    Bogdanov, F.2    Zaridze, R.3    Bijamov, A.4    Hafner, C.5    Erni, D.6
  • 4
    • 30144436034 scopus 로고    scopus 로고
    • Polarization gaps in spiral photonic crystals
    • Lee, J.; Chan, C.T. Polarization gaps in spiral photonic crystals. Opt. Express 2005, 13, 8083–8088.
    • (2005) Opt. Express , vol.13 , pp. 8083-8088
    • Lee, J.1    Chan, C.T.2
  • 7
    • 84855955365 scopus 로고    scopus 로고
    • A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals
    • Lawrence, F.J.; Botten, L.C.; Dossou, K.B.; McPhedran, R.C.; Martijn de Sterke, C. A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals. J. Appl. Phys. 2012, 111, doi:10.1063/1.3674281.
    • (2012) J. Appl. Phys , vol.111
    • Lawrence, F.J.1    Botten, L.C.2    Dossou, K.B.3    McPhedran, R.C.4    De Martijn Sterke, C.5
  • 8
    • 84864567418 scopus 로고    scopus 로고
    • A combined three-dimensional finite element and scattering matrix method for the analysis of plane wave diffraction by bi-periodic, multilayered structures
    • Dossou, K.B.; Botten, L.C. A combined three-dimensional finite element and scattering matrix method for the analysis of plane wave diffraction by bi-periodic, multilayered structures. J. Comput. Phys. 2012, 231, 6969–6989.
    • (2012) J. Comput. Phys , vol.231 , pp. 6969-6989
    • Dossou, K.B.1    Botten, L.C.2
  • 9
    • 0019586874 scopus 로고
    • Rigorous coupled-wave analysis of planar-grating diffraction
    • Moharam, M.G.; Gaylord, T.K. Rigorous coupled-wave analysis of planar-grating diffraction. J. Opt. Soc. Am. 1981, 71, 811–818.
    • (1981) J. Opt. Soc. Am , vol.71 , pp. 811-818
    • Moharam, M.G.1    Gaylord, T.K.2
  • 11
    • 0000649189 scopus 로고    scopus 로고
    • Scattering-matrix treatment of patterned multilayer photonic structures
    • Whittaker, D.M.; Culshaw, I.S. Scattering-matrix treatment of patterned multilayer photonic structures. Phys. Rev. B 1999, 60, 2610–2618.
    • (1999) Phys. Rev. B , vol.60 , pp. 2610-2618
    • Whittaker, D.M.1    Culshaw, I.S.2
  • 12
    • 84867379032 scopus 로고    scopus 로고
    • Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention
    • Rumpf, R.C. Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention. Prog. Electromagn. Res. B 2011, 35, 241–261.
    • (2011) Prog. Electromagn. Res. B , vol.35 , pp. 241-261
    • Rumpf, R.C.1
  • 13
    • 33749450891 scopus 로고    scopus 로고
    • A plane-wave-based approach for complex photonic band structure and its applications to semi-infinite and finite system
    • Feng, C.S.; Mei, L.M.; Cai, L.Z.; Yang, X.L.; Wei, S.S.; Li, P. A plane-wave-based approach for complex photonic band structure and its applications to semi-infinite and finite system. J. Phys. D 2006, 39, doi:10.1088/0022-3727/39/20/005.
    • (2006) J. Phys. D , vol.39
    • Feng, C.S.1    Mei, L.M.2    Cai, L.Z.3    Yang, X.L.4    Wei, S.S.5    Li, P.6
  • 14
    • 84922989925 scopus 로고    scopus 로고
    • Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure. Mater
    • Saba, M.; Wilts, B.; Hielscher, J.; Schröder-Turk, G.E. Absence of circular polarisation in reflections of butterfly wing scales with chiral Gyroid structure. Mater. Today Proc. 2014, doi:10.1016/j.matpr.2014.09.023.
    • (2014) Today Proc
    • Saba, M.1    Wilts, B.2    Hielscher, J.3    Schröder-Turk, G.E.4
  • 17
    • 0000278298 scopus 로고    scopus 로고
    • Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis
    • Johnson, S.G.; Joannopoulos, J.D. Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 2001, 8, 173–190.
    • (2001) Opt. Express , vol.8 , pp. 173-190
    • Johnson, S.G.1    Joannopoulos, J.D.2
  • 18
    • 84896538292 scopus 로고    scopus 로고
    • Group theory of circular-polarization effects in chiral photonic crystals with four-fold rotation axes applied to the eight-fold intergrowth of gyroid nets
    • Saba, M.; Turner, M.D.; Mecke, K.; Gu, M.; Schröder-Turk, G.E. Group theory of circular-polarization effects in chiral photonic crystals with four-fold rotation axes applied to the eight-fold intergrowth of gyroid nets. Phys. Rev. B 2013, 88, doi:10.1103/PhysRevB.88.245116.
    • (2013) Phys. Rev. B , vol.88
    • Saba, M.1    Turner, M.D.2    Mecke, K.3    Gu, M.4    Schröder-Turk, G.E.5
  • 19
    • 0026237483 scopus 로고
    • Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena
    • Cangellaris, A.; Wright, D. Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena. IEEE Trans. Antennas Propag. 1991, 39, 1518–1525.
    • (1991) IEEE Trans. Antennas Propag , vol.39 , pp. 1518-1525
    • Cangellaris, A.1    Wright, D.2
  • 22
    • 0031537321 scopus 로고    scopus 로고
    • Gyroids of constant mean curvature
    • Große-Brauckmann, K. Gyroids of constant mean curvature. Exp. Math. 1997, 6, 33–50.
    • (1997) Exp. Math , vol.6 , pp. 33-50
    • Große-Brauckmann, K.1
  • 23
    • 36348983797 scopus 로고    scopus 로고
    • Gyroid cuticular structures in butterfly wing scales: Biological photonic crystals
    • Michielsen, K.; Stavenga, D.G. Gyroid cuticular structures in butterfly wing scales: Biological photonic crystals. J. R. Soc. Interface 2008, 5, 85–94.
    • (2008) J. R. Soc. Interface , vol.5 , pp. 85-94
    • Michielsen, K.1    Stavenga, D.G.2
  • 24
    • 83455198291 scopus 로고    scopus 로고
    • Three-Dimensionally Isotropic Negative Refractive Index Materials from Block Copolymer Self-Assembled Chiral Gyroid Networks
    • Hur, K.; Francescato, Y.; Giannini, V.; Maier, S.A.; Hennig, R.G.; Wiesner, U. Three-Dimensionally Isotropic Negative Refractive Index Materials from Block Copolymer Self-Assembled Chiral Gyroid Networks. Angew. Chem. Int. Ed. 2011, 50, 11985–11989.
    • (2011) Angew. Chem. Int. Ed , vol.50 , pp. 11985-11989
    • Hur, K.1    Francescato, Y.2    Giannini, V.3    Maier, S.A.4    Hennig, R.G.5    Wiesner, U.6
  • 25
    • 84875778618 scopus 로고    scopus 로고
    • Weyl points and line nodes in gyroid photonic crystals
    • Lu, L.; Fu, L.; Joannopoulos, J.D.; Soljacic, M. Weyl points and line nodes in gyroid photonic crystals. Nat. Photon. 2013, 7, 294–299.
    • (2013) Nat. Photon , vol.7 , pp. 294-299
    • Lu, L.1    Fu, L.2    Joannopoulos, J.D.3    Soljacic, M.4
  • 27
    • 84872720483 scopus 로고    scopus 로고
    • On the Origin of Chirality in Nanoplasmonic Gyroid Metamaterials. Adv
    • Oh, S.S.; Demetriadou, A.; Wuestner, S.; Hess, O. On the Origin of Chirality in Nanoplasmonic Gyroid Metamaterials. Adv. Mater. 2012, 25, 612–617.
    • (2012) Mater , vol.25 , pp. 612-617
    • Oh, S.S.1    Demetriadou, A.2    Wuestner, S.3    Hess, O.4
  • 29
    • 1542776405 scopus 로고
    • Theories of Optical Rotatory Power
    • Condon, E.U. Theories of Optical Rotatory Power. Rev. Mod. Phys. 1937, 9, 432–457.
    • (1937) Rev. Mod. Phys , vol.9 , pp. 432-457
    • Condon, E.U.1
  • 30
    • 2542460960 scopus 로고
    • Electromagnetic Modeling of Bi-Isotropic Media
    • Sihvola, A.H. Electromagnetic Modeling of Bi-Isotropic Media. PIER 1994, 9, 45–86.
    • (1994) PIER , vol.9 , pp. 45-86
    • Sihvola, A.H.1
  • 34
    • 10644261473 scopus 로고    scopus 로고
    • High order isoparametric finite element method for the computation of waveguide modes
    • Dossou, K.; Fontaine, M. A high order isoparametric finite element method for the computation of waveguide modes. Comput. Methods Appl. Mech. Eng. 2005, 194, 837–858.
    • (2005) Comput. Methods Appl. Mech. Eng , vol.194 , pp. 837-858
    • Dossou, K.1    Fontaine, M.A.2
  • 35
    • 0005486236 scopus 로고
    • Fast Fourier Transforms of Piecewise Constant Functions
    • Sorets, E. Fast Fourier Transforms of Piecewise Constant Functions. J. Comput. Phys. 1995, 116, 369–379.
    • (1995) J. Comput. Phys , vol.116 , pp. 369-379
    • Sorets, E.1
  • 37
    • 0004223416 scopus 로고    scopus 로고
    • Cambridge University Press: Cambridge, UK
    • Cromwell, P.R. Polyhedra; Cambridge University Press: Cambridge, UK, 1997.
    • (1997) Polyhedra
    • Cromwell, P.R.1
  • 40
    • 0000152139 scopus 로고
    • On the Dynamical Theory of Gratings
    • Rayleigh, L. On the Dynamical Theory of Gratings. Proc. R. Soc. A 1907, 79, 399–416.
    • (1907) Proc. R. Soc. A , vol.79 , pp. 399-416
    • Rayleigh, L.1
  • 42
    • 84897864467 scopus 로고    scopus 로고
    • Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality
    • Cao, Y.; Li, J. Complete band gaps in one-dimensional photonic crystals with negative refraction arising from strong chirality. Phys. Rev. B 2014, 89, doi:10.1103/PhysRevB.89.115420.
    • (2014) Phys. Rev. B , vol.89
    • Cao, Y.1    Li, J.2
  • 43
    • 11744273384 scopus 로고
    • The surface evolver
    • Brakke, K.A. The surface evolver. Exp. Math. 1992, 1, 141–165.
    • (1992) Exp. Math , vol.1 , pp. 141-165
    • Brakke, K.A.1
  • 44
    • 0000685099 scopus 로고
    • On the division of space with minimum partitional area
    • Thomson, W. On the division of space with minimum partitional area. Philos. Mag. 1887, 24, 503–514.
    • (1887) Philos. Mag , vol.24 , pp. 503-514
    • Thomson, W.1
  • 45
    • 0242427736 scopus 로고    scopus 로고
    • Photonic band gaps in materials with triply periodic surfaces and related tubular structures
    • Michielsen, K.; Kole, J.S. Photonic band gaps in materials with triply periodic surfaces and related tubular structures. Phys. Rev. B 2003, 68, doi:10.1103/PhysRevB.68.115107.
    • (2003) Phys. Rev. B , vol.68
    • Michielsen, K.1    Kole, J.S.2
  • 47
    • 84967820816 scopus 로고
    • Local field effects and effective medium theory: A microscopic perspective
    • Aspnes, D.E. Local field effects and effective medium theory: A microscopic perspective. Am. J. Phys. 1982, 50, 704–709.
    • (1982) Am. J. Phys , vol.50 , pp. 704-709
    • Aspnes, D.E.1
  • 48
    • 54049140953 scopus 로고    scopus 로고
    • A short history of an elusive yet ubiquitous structure in chemistry, materials and mathematics
    • Hyde, S.T.; O’Keeffe, M.; Proserpio, D.M. A short history of an elusive yet ubiquitous structure in chemistry, materials and mathematics. Angew. Chem. Int. Ed. 2008, 47, 7996–8000.
    • (2008) Angew. Chem. Int. Ed , vol.47 , pp. 7996-8000
    • Hyde, S.T.1    O’Keeffe, M.2    Proserpio, D.M.3
  • 54
    • 34250103285 scopus 로고
    • A new family of mixed finite elements in R3
    • Nédélec, J. A new family of mixed finite elements in R3. Numer. Math. 1986, 50, 57–81.
    • (1986) Numer. Math , vol.50 , pp. 57-81
    • Nédélec, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.