메뉴 건너뛰기




Volumn 219, Issue 1, 2006, Pages 120-143

Finite element computation of grating scattering matrices and application to photonic crystal band calculations

Author keywords

Bloch modes; Finite element method; Photonic crystals; Scattering matrix; Transfer matrix method

Indexed keywords

CRYSTAL STRUCTURE; DIFFRACTION GRATINGS; FINITE ELEMENT METHOD; NUMERICAL METHODS; TRANSFER MATRIX METHOD;

EID: 33750347962     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.03.029     Document Type: Article
Times cited : (54)

References (43)
  • 2
    • 0006078242 scopus 로고    scopus 로고
    • An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I. Scalar case
    • Axmann W., and Kuchment P. An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I. Scalar case. J. Comput. Phys. 150 2 (1999) 468-481
    • (1999) J. Comput. Phys. , vol.150 , Issue.2 , pp. 468-481
    • Axmann, W.1    Kuchment, P.2
  • 3
    • 3142690613 scopus 로고    scopus 로고
    • Variational methods for diffractive optics modeling
    • Mathematical Modeling in Optical Science, SIAM, Philadelphia, PA
    • Bao G., and Dobson D.C. Variational methods for diffractive optics modeling. Mathematical Modeling in Optical Science. Frontiers in Applied Mathematics vol. 22 (2001), SIAM, Philadelphia, PA 37-69
    • (2001) Frontiers in Applied Mathematics , vol.22 , pp. 37-69
    • Bao, G.1    Dobson, D.C.2
  • 4
    • 0037097833 scopus 로고    scopus 로고
    • Y junctions in photonic crystal channel waveguides: high transmission and impedance matching
    • Boscolo S., Midrio M., and Krauss T.F. Y junctions in photonic crystal channel waveguides: high transmission and impedance matching. Opt. Lett. 27 12 (2002) 1001-1003
    • (2002) Opt. Lett. , vol.27 , Issue.12 , pp. 1001-1003
    • Boscolo, S.1    Midrio, M.2    Krauss, T.F.3
  • 5
    • 0036179716 scopus 로고    scopus 로고
    • Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides
    • Boscolo S., Midrio M., and Someda C.G. Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides. IEEE J. Quantum Electron. 38 1 (2002) 47-53
    • (2002) IEEE J. Quantum Electron. , vol.38 , Issue.1 , pp. 47-53
    • Boscolo, S.1    Midrio, M.2    Someda, C.G.3
  • 8
    • 0000957136 scopus 로고    scopus 로고
    • Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method
    • Botten L.C., Nicorovici N.-A.P., Asatryan A.A., McPhedran R.C., de Sterke C.M., and Robinson P.A. Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method. J. Opt. Soc. Am. A 17 12 (2000) 2165-2176
    • (2000) J. Opt. Soc. Am. A , vol.17 , Issue.12 , pp. 2165-2176
    • Botten, L.C.1    Nicorovici, N.-A.P.2    Asatryan, A.A.3    McPhedran, R.C.4    de Sterke, C.M.5    Robinson, P.A.6
  • 9
    • 0000957137 scopus 로고    scopus 로고
    • Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation
    • Botten L.C., Nicorovici N.-A.P., Asatryan A.A., McPhedran R.C., de Sterke C.M., and Robinson P.A. Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation. J. Opt. Soc. Am. A 17 12 (2000) 2177-2190
    • (2000) J. Opt. Soc. Am. A , vol.17 , Issue.12 , pp. 2177-2190
    • Botten, L.C.1    Nicorovici, N.-A.P.2    Asatryan, A.A.3    McPhedran, R.C.4    de Sterke, C.M.5    Robinson, P.A.6
  • 11
    • 0009910336 scopus 로고    scopus 로고
    • Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides
    • Cao Q., Lalanne P., and Hugonin J.-P. Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides. J. Opt. Soc. Am. A 19 2 (2002) 335-338
    • (2002) J. Opt. Soc. Am. A , vol.19 , Issue.2 , pp. 335-338
    • Cao, Q.1    Lalanne, P.2    Hugonin, J.-P.3
  • 12
    • 44749084639 scopus 로고    scopus 로고
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA Reprint of the 1978 original (North-Holland, Amsterdam)
    • Ciarlet P.G. The Finite Element Method for Elliptic Problems (2002), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA Reprint of the 1978 original (North-Holland, Amsterdam)
    • (2002) The Finite Element Method for Elliptic Problems
    • Ciarlet, P.G.1
  • 13
    • 1542315300 scopus 로고    scopus 로고
    • Polarisation dependent loss calculation in echelle gratings using finite element method and Rayleigh expansion
    • Delâge A., and Dossou K. Polarisation dependent loss calculation in echelle gratings using finite element method and Rayleigh expansion. Opt. Quantum Electron. 36 1-3 (2004) 223-238
    • (2004) Opt. Quantum Electron. , vol.36 , Issue.1-3 , pp. 223-238
    • Delâge, A.1    Dossou, K.2
  • 14
    • 0027733293 scopus 로고
    • Finite-element method for gratings
    • Delort T., and Maystre D. Finite-element method for gratings. J. Opt. Soc. Am. A 10 12 (1993) 2592-2601
    • (1993) J. Opt. Soc. Am. A , vol.10 , Issue.12 , pp. 2592-2601
    • Delort, T.1    Maystre, D.2
  • 15
    • 0000060612 scopus 로고    scopus 로고
    • An efficient method for band structure calculations in 2D photonic crystals
    • Dobson D.C. An efficient method for band structure calculations in 2D photonic crystals. J. Comput. Phys. 149 2 (1999) 363-376
    • (1999) J. Comput. Phys. , vol.149 , Issue.2 , pp. 363-376
    • Dobson, D.C.1
  • 16
    • 85189853080 scopus 로고    scopus 로고
    • K. Dossou, L.C. Botten, S. Chen, J. Brnovic, C.M. de Sterke, R.C. McPhedran, A.A. Asatryan, Efficient couplers for photonic crystal waveguides, J. Opt. Commun. (2006) (to appear).
  • 17
    • 13644284060 scopus 로고    scopus 로고
    • Analysis of diffraction gratings by using an edge element method
    • Dossou K., Packirisamy M., and Fontaine M. Analysis of diffraction gratings by using an edge element method. J. Opt. Soc. Am. A 22 2 (2005) 278-288
    • (2005) J. Opt. Soc. Am. A , vol.22 , Issue.2 , pp. 278-288
    • Dossou, K.1    Packirisamy, M.2    Fontaine, M.3
  • 19
    • 0032164329 scopus 로고    scopus 로고
    • Diffraction in periodic structures and optimal design of binary gratings. I. Direct problems and gradient formulas
    • Elschner J., and Schmidt G. Diffraction in periodic structures and optimal design of binary gratings. I. Direct problems and gradient formulas. Math. Methods Appl. Sci. 21 14 (1998) 1297-1342
    • (1998) Math. Methods Appl. Sci. , vol.21 , Issue.14 , pp. 1297-1342
    • Elschner, J.1    Schmidt, G.2
  • 22
    • 85189846704 scopus 로고    scopus 로고
    • Gmsh. Available from: .
  • 23
    • 0012263267 scopus 로고    scopus 로고
    • From scattering or impedance matrices to Bloch modes of photonic crystals
    • Gralak B., Enoch S., and Tayeb G. From scattering or impedance matrices to Bloch modes of photonic crystals. J. Opt. Soc. Am. A 19 8 (2002) 1547-1554
    • (2002) J. Opt. Soc. Am. A , vol.19 , Issue.8 , pp. 1547-1554
    • Gralak, B.1    Enoch, S.2    Tayeb, G.3
  • 24
    • 0036575423 scopus 로고    scopus 로고
    • Out-of-plane losses of line-defect photonic crystal waveguides
    • Hadley G.R. Out-of-plane losses of line-defect photonic crystal waveguides. IEEE Photon. Technol. Lett. 14 5 (2002) 642-644
    • (2002) IEEE Photon. Technol. Lett. , vol.14 , Issue.5 , pp. 642-644
    • Hadley, G.R.1
  • 25
    • 21344463379 scopus 로고    scopus 로고
    • Determination of floquet modes in asymmetric periodic structures, optical and quantum electronics
    • Helfert S.F. Determination of floquet modes in asymmetric periodic structures, optical and quantum electronics. Opt. Quantum Electron. 37 1-3 (2005) 185-197
    • (2005) Opt. Quantum Electron. , vol.37 , Issue.1-3 , pp. 185-197
    • Helfert, S.F.1
  • 27
    • 0000278298 scopus 로고    scopus 로고
    • Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis
    • Johnson S.G., and Joannopoulos J.D. Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Opt. Exp. 8 (2001) 173-190
    • (2001) Opt. Exp. , vol.8 , pp. 173-190
    • Johnson, S.G.1    Joannopoulos, J.D.2
  • 28
    • 0033535260 scopus 로고    scopus 로고
    • Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering
    • Kosaka H., Kawashima T., Tomita A., Notomi M., Tamamura T., Sato T., and Kawakami S. Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering. Appl. Phys. Lett. 74 10 (1999) 1370-1372
    • (1999) Appl. Phys. Lett. , vol.74 , Issue.10 , pp. 1370-1372
    • Kosaka, H.1    Kawashima, T.2    Tomita, A.3    Notomi, M.4    Tamamura, T.5    Sato, T.6    Kawakami, S.7
  • 29
    • 0036647688 scopus 로고    scopus 로고
    • Electromagnetic analysis of photonic crystal waveguides operating above the light cone
    • Lalanne P. Electromagnetic analysis of photonic crystal waveguides operating above the light cone. IEEE J. Quantum Electron. 38 7 (2002) 800-804
    • (2002) IEEE J. Quantum Electron. , vol.38 , Issue.7 , pp. 800-804
    • Lalanne, P.1
  • 30
    • 85189852279 scopus 로고    scopus 로고
    • LAPACK. Available from: .
  • 31
    • 0037527766 scopus 로고    scopus 로고
    • Photonic band structures solved by a plane-wave-based transfer-matrix method
    • Li Z.-Y., and Lin L.-L. Photonic band structures solved by a plane-wave-based transfer-matrix method. Phys. Rev. E 67 (2003) 046607
    • (2003) Phys. Rev. E , vol.67 , pp. 046607
    • Li, Z.-Y.1    Lin, L.-L.2
  • 32
    • 0038613500 scopus 로고    scopus 로고
    • Mach Zehnder interferometer employing coupled-resonator optical waveguides
    • Martinez A., Griol A., Sanchis P., and Marti J. Mach Zehnder interferometer employing coupled-resonator optical waveguides. Opt. Lett. 28 6 (2003) 405-407
    • (2003) Opt. Lett. , vol.28 , Issue.6 , pp. 405-407
    • Martinez, A.1    Griol, A.2    Sanchis, P.3    Marti, J.4
  • 33
    • 33744560785 scopus 로고
    • Photonic band gaps for arrays of perfectly conducting cylinders
    • Nicorovici N.A., McPhedran R.C., and Botten L.C. Photonic band gaps for arrays of perfectly conducting cylinders. Phys. Rev. E 52 (1995) 1135-1145
    • (1995) Phys. Rev. E , vol.52 , pp. 1135-1145
    • Nicorovici, N.A.1    McPhedran, R.C.2    Botten, L.C.3
  • 34
    • 4944261021 scopus 로고
    • Calculation of photon dispersion relations
    • Pendry J.B., and MacKinnon A. Calculation of photon dispersion relations. Phys. Rev. Lett. 69 (1992) 2772-2775
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2772-2775
    • Pendry, J.B.1    MacKinnon, A.2
  • 35
    • 0003654832 scopus 로고
    • Petit R. (Ed), Springer, New York
    • In: Petit R. (Ed). Electromagnetic Theory of Gratings. Topics in Current Physics vol. 22 (1980), Springer, New York
    • (1980) Topics in Current Physics , vol.22
  • 36
    • 0042631392 scopus 로고    scopus 로고
    • Photonic crystal continuous taper for low-loss direct coupling into 2D photonic crystal channel waveguides and further device functionality
    • Pottier P., Ntakis I., and De La Rue R.M. Photonic crystal continuous taper for low-loss direct coupling into 2D photonic crystal channel waveguides and further device functionality. Opt. Commun. 223 4-6 (2003) 339-347
    • (2003) Opt. Commun. , vol.223 , Issue.4-6 , pp. 339-347
    • Pottier, P.1    Ntakis, I.2    De La Rue, R.M.3
  • 37
    • 0004135568 scopus 로고
    • Academic Press, New York
    • Reed M., and Simon B. Methods of Modern Mathematical Physics. Analysis of Operators vol. IV (1978), Academic Press, New York
    • (1978) Analysis of Operators , vol.IV
    • Reed, M.1    Simon, B.2
  • 39
    • 36149033427 scopus 로고
    • Scattering of electromagnetic waves by periodic structures
    • Stefanou N., Karathanos V., and Modinos A. Scattering of electromagnetic waves by periodic structures. J. Phys.: Condens. Matter. 4 36 (1992) 7389-7400
    • (1992) J. Phys.: Condens. Matter. , vol.4 , Issue.36 , pp. 7389-7400
    • Stefanou, N.1    Karathanos, V.2    Modinos, A.3
  • 40
    • 3943053405 scopus 로고    scopus 로고
    • High-bandwidth transmission of an efficient photonic-crystal mode converter
    • Talneau A., Agio M., Soukoulis C.M., Mulot M., Anand S., and Lalanne Ph. High-bandwidth transmission of an efficient photonic-crystal mode converter. Opt. Lett. 29 15 (2004) 1745-1747
    • (2004) Opt. Lett. , vol.29 , Issue.15 , pp. 1745-1747
    • Talneau, A.1    Agio, M.2    Soukoulis, C.M.3    Mulot, M.4    Anand, S.5    Lalanne, Ph.6
  • 41
    • 79956019447 scopus 로고    scopus 로고
    • Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm
    • Talneau A., Le Gouezigou L., Bouadma N., Kafesaki M., Soukoulis C.M., and Agio M. Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm. Appl. Phys. Lett. 80 4 (2002) 547-549
    • (2002) Appl. Phys. Lett. , vol.80 , Issue.4 , pp. 547-549
    • Talneau, A.1    Le Gouezigou, L.2    Bouadma, N.3    Kafesaki, M.4    Soukoulis, C.M.5    Agio, M.6
  • 42
    • 0345761541 scopus 로고    scopus 로고
    • Ultracompact resonant filters in photonic crystals
    • White T.P., Botten L.C., McPhedran R.C., and de Sterke C.M. Ultracompact resonant filters in photonic crystals. Opt. Lett. 28 24 (2003) 2452-2454
    • (2003) Opt. Lett. , vol.28 , Issue.24 , pp. 2452-2454
    • White, T.P.1    Botten, L.C.2    McPhedran, R.C.3    de Sterke, C.M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.