Vol. 66
Latest Volume
All Volumes
PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2017-03-02
Doubly-Periodic Photonic Crystals: Spectral Problems Analysis
By
Progress In Electromagnetics Research Letters, Vol. 66, 71-77, 2017
Abstract
The present work is devoted to the clarification of the conditions necessary for step-by-step justification of the possibility of reduction of the homogeneous system of linear algebraic equations for the spectral problems of 2-D photonic crystals by the plane waves method. The issues related to the algorithms and the numerical solutions of these spectral problems are analyzed. The possibility of analytical regularization is investigated, and the ways to improve the convergence of the obtained results are identified.
Citation
Seil S. Sautbekov, Yuriy Sirenko, and Hanna Sliusarenko, "Doubly-Periodic Photonic Crystals: Spectral Problems Analysis," Progress In Electromagnetics Research Letters, Vol. 66, 71-77, 2017.
doi:10.2528/PIERL16122303
References

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

2. Lourtioz, J.-M., H. Bensty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, Springer, New York, 2005.

3. 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

4. Velychko, L. G., Y. K. Sirenko, and O. S. Velychko, "Time-domain analysis of open resonators. Analytical grounds," Progress In Electromagnetics Research, Vol. 61, 1-26, 2006.
doi:10.2528/PIER06020701

5. Sirenko, Y. K., S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques, Springer, New York, 2007.

6. Velychko, L. G. and Y. K. Sirenko, "Controlled changes in spectra of open quasi-optical resonators," Progress In Electromagnetics Research B, Vol. 16, 85-105, 2009.
doi:10.2528/PIERB09060202

7. Kravchenko, V. F., Y. K. Sirenko, and K. Y. Sirenko, Electromagnetic Wave Transformation and Radiation by the Open Resonant Structures. Modelling and Analysis of Transient and Steady-State Processes, Fizmathlit, Moscow, 2011.

8. Vaynikko, G. M. and O. O. Karma, "On rapidity of convergence of approximate methods in problem of eigenvalues with nonlinear occurrence of parameter," Zhurnal Vychislitelnoy Matematiki I Matematicheskoy Fiziki, Vol. 14, No. 6, 1393-1408, 1974.

9. Hokhberg, I. Z. and M. G. Krein, Introduction into the Theory of Linear not Self-Adjoint Operators, Nauka, Moscow, 1965.

10. Hutson, V. C. L. and J. S. Pym, Applications of Functional Analysis and Operator Theory, Academic Press, New York, 1980.

11. Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order Differential Equations, Clarendon Press, Oxford, 1958.

12. Shestopalov, V. P. and Y. K. Sirenko, Dynamic Theory of Gratings, Naukova Dumka, Kiev, 1989.

13. Keldysh, M. V., "On the completeness of eigenfunctions of some classes of non-selfadjoint linear operators," Russian Mathematical Surveys, Vol. 26, No. 4, 15-44, 1971.
doi:10.1070/RM1971v026n04ABEH003985

14. Hokhberg, I. Z. and Y. I. Seagul, "Operator generalization of the theorem about logarithmic residue and the Rouche theorem," Matematicheckiy Sbornik, Vol. 84, No. 4, 607-629, 1971.

15. Reed, M. and B. Simon, Methods of Mathematical Physics. IV: Analysis of Operators, Academic Press, New York, 1978.

16. Hardy, G. H., J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, 1934.

17. Shestopalov, V. P., A. A. Kirilenko, and S. A. Masalov, Matrix Convolution-Type Equations in the Diffraction Theory, Naukova Dumka, Kiev, 1984.