Vol. 27

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2012-11-09

The Unfolding of Bandgap Diagrams of Hexagonal Photonic Crystals Computed with FDTD

By Bartlomiej Salski
Progress In Electromagnetics Research M, Vol. 27, 27-39, 2012
doi:10.2528/PIERM12081313

Abstract

The application of the finite-difference time-domain method with rectangular periodic boundary conditions to the analysis of a hexagonal photonic crystal results in a folded bandgap diagram. The aim of this paper is to introduce a new unfolding method, which allows unambiguously determining the position of the modes in a wave-vector space by taking the advantage of the fast Fourier transform of modal field distributions. Unlike alternative solutions, it does not require any modifications of the FDTD method and is based solely on the postprocessing of the simulation results. The proposed method can be applied to any non-rectangular lattice types, such as hexagonal, face-centered cubic or body-centered cubic.

Citation


Bartlomiej Salski, "The Unfolding of Bandgap Diagrams of Hexagonal Photonic Crystals Computed with FDTD," Progress In Electromagnetics Research M, Vol. 27, 27-39, 2012.
doi:10.2528/PIERM12081313
http://www.jpier.org/PIERM/pier.php?paper=12081313

References


    1. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd Ed., Princeton University Press, 2008.

    2. Mekis, A., J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Physical Review Letters, Vol. 77, No. 18, 3787-3790, 1996.
    doi:10.1103/PhysRevLett.77.3787

    3. Yamamoto, N., Y.Watanabe, and K. Komori, "Design of photonic crystal directional coupler with high extinction ratio and small coupling length," Jpn. J. Appl. Phys., Vol. 44, No. 4B, 2575-2578, 2005.
    doi:10.1143/JJAP.44.2575

    4. Shen, L.-P., W.-P. Huang, and S.-S. Jian, "Design of photonic crystal fibers for dispersion-related applications," IEEE/OSA J. Lightwave Technol., Vol. 21, No. 7, 1644-1651, 2003.
    doi:10.1109/JLT.2003.814397

    5. Fan, S., P. R. Villeneuve, and J. D. Joannopoulos, "Channel drop filters in photonic crystals," Optics Letters, Vol. 3, No. 1, 4-11, 1998.

    6. Lu, L., A. Mock, T. Yang, M. H. Shih, E. H. Hwang, M. Bagheri, A. Stapleton, S. Farrell, J. O'Brien, and P. D. Dapkus, "120 μW peak output power from edge-emitting photonic crystal double-heterostructure nanocavity lasers," Appl. Phys. Lett., Vol. 94, 111101, 2009.
    doi:10.1063/1.3097278

    7. Salski, B., "Application of semi-analytical algorithms in the finite-di®erence time-domain modeling of electromagnetic radiation and scattering problems,", Ph.D. Thesis, Warsaw University of Technology, 2010.

    8. Collin, R. E., Field Theory of Guided Waves, McGraw-Hill Inc., New York, 1960.

    9. Liu, L. and J. T. Liu, "Photonic band structure in the nearly plane wave approximation," Eur. Phys. J. B, Vol. 9, 381-388, 1999.
    doi:10.1007/s100510050781

    10. Johnson, S. G. and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Optics Express, Vol. 8, No. 3, 173-190, 2001.
    doi:10.1364/OE.8.000173

    11. Axmann, W. and P. Kuchment, "An efficient finite element method for computing spectra of photonic and acoustic band-gap materials --- I. Scalar case," J. Comput. Phys., Vol. 150, 468-481, 1999.
    doi:10.1006/jcph.1999.6188

    12. Guo, S., F.Wu, S. Albin, and R. S. Rogowski, "Photonic band gap analysis using finite-difference frequency-domain method," Optics Express, Vol. 12, No. 8, 1741-1746, 2004.
    doi:10.1364/OPEX.12.001741

    13. Taflove, A. and S. C. Hagness, "Computational Electrodynamics --- The Finite-difference Time-domain Method," Artech House,, 2005.

    14. Gwarek, W. K., "Analysis of an arbitrarily-shaped planar circuit --- A time-domain approach," IEEE Trans. Microw. Theory Tech., Vol. 33, No. 10, 1067-1072, 1985.
    doi:10.1109/TMTT.1985.1133170

    15. Krietenstein, B., R. Schuhmann, P. Thoma, and T.Weiland, "The perfect boundary approximation technique facing the big challenge of high precision field computation," 19th International Linear Accelerator Conference, 860-862, 1998.

    16. Salski, B., K. Lesniewska-Matys, and P. Szczepanski, "On the applicability of photonic crystal membranes to multi-channel propagation," Photonic Crystals --- Innovative Systems, Lasers and Waveguides, Chapter 7, InTech, 2012.

    17. Loncar, M., B. G. Lee, L. Diehl, M. Belkin, and F. Capasso, "Design and fabrication of photonic crystal quantum cascade lasers for optofluidics," Optics Express, Vol. 15, No. 8, 4499-4514, 2007.
    doi:10.1364/OE.15.004499

    18. Celuch-Marcysiak, M. and W. K. Gwarek, "Spatially looped algorithms for time-domain analysis of periodic structures," IEEE Trans. Microw. Theory Tech., Vol. 43, No. 4, 860-865, 1995.
    doi:10.1109/22.375235

    19. Ko, W. L. and R. Mittra, "Implementation of Floquet boundary condition in FDTD for FSS analysis," IEEE APS Int. Symp. Dig., Vol. 1, 14-17, 1993.

    20. Holland, R., "Finite-difference solution of Maxwell's equations in generalized nonorthogonal coordinate," IEEE Trans. Nucl. Sci., Vol. 30, No. 6, 4589-4591, 1983.
    doi:10.1109/TNS.1983.4333176

    21. Qiu, M. and S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," Appl. Phys., Vol. 87, 8268-8275, 1992.

    22. Yu, C. and H. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Optics Express, Vol. 12, No. 7, 1397-1408, 2004.
    doi:10.1364/OPEX.12.001397

    23. Ma, Z. and K. Ogusu, "FDTD analysis of 2D triangular-lattice photonic crystals with arbitrary-shape inclusions based on unit cell transformation," Optics Communications, Vol. 282, 1322-1325, 2009.
    doi:10.1016/j.optcom.2008.12.055

    24. Kuang, W., W. J. Kim, and J. D. O'Brien, "Finite-difference time domain method for nonorthogonal unit-cell two-dimensional photonic crystals," J. Lightw. Technol., Vol. 25, No. 9, 2612-2617, 2007.
    doi:10.1109/JLT.2007.903827

    25. Gwarek, W., M. Celuch, A. Wieckowski, and M. Sypniewski, QuickWave User Manual, Warsaw, 1997-2012, www.qwed.eu..

    26. Salski, B., M. Celuch, and W. K. Gwarek, "Review of Complex Looped FDTD and its new applications," 24th Annual Review of Progress in Applied Computational Electromagnetics, Niagara,Falls, 2008.

    27. Johnson, S. G. and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Optics Express, Vol. 8, No. 3, 173-190, 2001.
    doi:10.1364/OE.8.000173