Vol. 27
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2012-11-09
The Unfolding of Bandgap Diagrams of Hexagonal Photonic Crystals Computed with FDTD
By
Progress In Electromagnetics Research M, Vol. 27, 27-39, 2012
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
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