OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 3 — Mar. 1, 2010
  • pp: 532–543

Modeling and analysis of transients in periodic gratings. I. Fully absorbing boundaries for 2-D open problems

Kostyantyn Y. Sirenko, Yuriy K. Sirenko, and Nataliya P. Yashina  »View Author Affiliations


JOSA A, Vol. 27, Issue 3, pp. 532-543 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000532


View Full Text Article

Enhanced HTML    Acrobat PDF (365 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Frequency domain methods allow us to simulate and study efficiently only some of the periodic structures that are widespread in optics and spectroscopy. Time domain approaches could be more effective, but their deployment is held back by a number of unsolved problems associated mainly with a proper truncation of the computation space in the so-called open problems. This paper is devoted to analysis of these problems in the 2-D case (infinite one-dimensionally periodic semitransparent and reflecting gratings in the field of pulsed E- and H-polarized waves).

© 2010 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.3870) General : Mathematics
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(050.5745) Diffraction and gratings : Resonance domain

ToC Category:
Diffraction and Gratings

History
Original Manuscript: November 6, 2009
Manuscript Accepted: January 3, 2010
Published: February 25, 2010

Citation
Kostyantyn Y. Sirenko, Yuriy K. Sirenko, and Nataliya P. Yashina, "Modeling and analysis of transients in periodic gratings. I. Fully absorbing boundaries for 2-D open problems," J. Opt. Soc. Am. A 27, 532-543 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-3-532


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L.B.Felsen, ed., Transient Electromagnetic Fields (Springer-Verlag, 1976).
  2. V. V. Borisov, Transient Fields in Waveguides (Leningrad State Univ. Press, 1991) (in Russian).
  3. E. K. Miller, “Time-domain modeling in electromagnetics,” J. Electromagn. Waves Appl. 8, 1125-1172 (1994). [CrossRef]
  4. V. V. Borisov, Electromagnetic Fields of Transient Currents (St. Petersburg Univ. Press, 1996) (in Russian).
  5. S. He, S. Strom, and V. Weston, Time Domain Wave-Splittings and Inverse Problems (Oxford Univ. Press, 1998).
  6. S. M. Rao, Time Domain Electromagnetics (Academic, 1999).
  7. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).
  8. Y. K. Sirenko, S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques (Springer, 2007). [PubMed]
  9. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629-651 (1977). [CrossRef]
  10. G. Mur, “Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981). [CrossRef]
  11. P. A. Tirkas, C. A. Balanis, and R. A. Renaut, “Higher order absorbing boundary conditions for FDTD-method,” IEEE Trans. Antennas Propag. 40, 1215-1222 (1992). [CrossRef]
  12. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
  13. J.-P. Berenger, “Three-dimensional perfectly matched layer for absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996). [CrossRef]
  14. Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995). [CrossRef]
  15. A. R. Maikov, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme for the Maxwell transient equations in waveguide systems,” J. Comput. Math. Math. Phys. 26, 851-863 (1986) (in Russian).
  16. A. R. Maikov, A. D. Poezd, A. G. Sveshnikov, and S. A. Yakunin, “Difference scheme of initial boundary-value problems for Maxwell equations in unlimited domain,” J. Comput. Math. Math. Phys. 29, 239-250 (1989) (in Russian).
  17. A. O. Perov, Y. K. Sirenko, and N. P. Yashina, “Explicit conditions for virtual boundaries in initial boundary value problems in the theory of wave scattering,” J. Electromagn. Waves Appl. 13, 1343-1371 (1999). [CrossRef]
  18. Y. K. Sirenko, V. L. Pazynin, A. I. Vyazmitinova, and K. Y. Sirenko, “Compact obstacles in free space: virtual boundaries for scalar and vector “open” initial boundary-value problems in electromagnetic wave scattering theory,” Electromag. Waves Electron. Syst. 8, 33-54 (2003) (in Russian).
  19. K. Y. Sirenko and Y. K. Sirenko, “Exact “absorbing” conditions in the initial boundary-value problems of the theory of open waveguide resonators,” Comput. Math. Math. Phys. 45, 490-506 (2005).
  20. K. Y. Sirenko, “Transport operators in the axially-symmetrical problems of the electrodynamics of pulsed waves,” Electromag. Waves Electron. Syst. 11, 15-26 (2006) (in Russian).
  21. K. Y. Sirenko and V. L. Pazynin, “Axially-symmetrical radiators of pulsed and monochromatic TM0n- and TM0n-waves,” Success Modern Radioelectron. No.4, 52-69 (2006) (in Russian).
  22. V. L. Pazynin and K. Y. Sirenko, “The strong approach to analysis of transients in the axially symmetrical waveguide units,” Telecomm. Radio Eng. 65, 1-18 (2006). [CrossRef]
  23. K. Y. Sirenko, “Slot resonances in axially symmetric radiators of pulse-modulated and monochromatic TM0n-modes,” Telecomm. Radio Eng. 66, 9-21 (2007). [CrossRef]
  24. K. Y. Sirenko, “Splitting of super-broadband pulses by simple inhomogeneities of circular and coaxial waveguide,” Telecomm. Radio Eng. 67, 1425-1428 (2008).
  25. O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics (Springer-Verlag, 1985).
  26. V. S. Vladimirov, Equations of Mathematical Physics (Dekker, 1971).
  27. Y. K. Sirenko and N. P. Yashina, “Nonstationary model problems for waveguide open resonator theory,” Electromagnetics 19, 419-442 (1999). [CrossRef]
  28. Y. K. Sirenko and N. P. Yashina, “Time domain theory of open waveguide resonators: canonical problems and a generalized matrix technique,” Radio Sci. 38, VIC 26-1-VIC 26-12 (2003). [CrossRef]
  29. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).
  30. H. Bateman and A. Erdelyi, Tables of Integral Transforms, Vol. 1 (McGraw-Hill, 1954).
  31. B. R. Waynberg, Asymptotic Methods in the Equations of Mathematical Physics (Moscow State Univ. Press, 1982) (in Russian).
  32. Y. K. Sirenko, Simulation and Analysis of Transient Processes in Open Periodic, Waveguide, and Compact Resonators (EDENA, 2003) (in Russian). [PubMed]
  33. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1961).
  34. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).
  35. V. P. Shestopalov and Y. K. Sirenko, Dynamic Theory of Gratings (Naukova Dumka, 1989) (in Russian).
  36. Y. K. Sirenko, L. G. Velychko, and F. Erden, “Time-domain and frequency-domain methods combined in the study of open resonance structures of complex geometry,” PIER 44, 57-79 (2004). [CrossRef]
  37. L. G. Velychko, Y. K. Sirenko, and O. S. Shafalyuk, “Time-domain analysis of open resonators. Analytical grounds,” PIER 61, 1-26 (2006). [CrossRef]
  38. I. K. Kuzmitchev, P. M. Melezhyk, V. L. Pazynin, K. Y. Sirenko, Y. K. Sirenko, O. S. Shafalyuk, and L. G. Velychko, “Model synthesis of energy compressors,” Radiophys. Electron. 13, 166-172 (2008).
  39. V. F. Kravchenko, V. L. Pazynin, K. Y. Sirenko, and Y. K. Sirenko, “The plane problems of the electrodynamics of pulsed waves for compact open resonators with the waveguide feeder line. Gratings as pattern forming structures,” Electromag. Waves Electron. Syst. 14, 34-20 (2009) (in Russian).
  40. L. G. Velychko and Y. K. Sirenko, “Controlled changes in spectra of open quasi-optical resonators,” PIER B 16, 85-105 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited