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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 11 — Jun. 2, 2014
  • pp: 12760–12772

Electromagnetic energy transport in finite photonic structures

M. de Dios-Leyva, C. A. Duque, and J. C. Drake-Pérez  »View Author Affiliations

Optics Express, Vol. 22, Issue 11, pp. 12760-12772 (2014)

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We have derived, for oblique propagation, an equation relating the averaged energy flux density to energy fluxes arising in the process of scattering by a lossless finite photonic structure. The latter fluxes include those associated with the dispersion relation of the structure, reflection, and interference between the incident and reflected waves. We have also derived an explicit relation between the energy flux density and the group velocity, which provides a simple and systematical procedure for studying theoretically and experimentally the properties of the energy transport through a wide variety of finite photonic structures. Such a relation may be regarded as a generalization of the corresponding one for infinite periodic systems to finite photonic structures. A finite, N-period, photonic crystal was used to illustrate the usefulness of our results.

© 2014 Optical Society of America

OCIS Codes
(260.2160) Physical optics : Energy transfer
(160.5293) Materials : Photonic bandgap materials
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: February 24, 2014
Revised Manuscript: April 21, 2014
Manuscript Accepted: April 22, 2014
Published: May 19, 2014

M. de Dios-Leyva, C. A. Duque, and J. C. Drake-Pérez, "Electromagnetic energy transport in finite photonic structures," Opt. Express 22, 12760-12772 (2014)

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]
  3. K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001). [CrossRef]
  4. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, NJ, 2008).
  5. L. Brillouin, Wave Propagation and Group Velocity (Academic Press, 1960).
  6. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  7. S. Foteinopoulou, C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects,” Phys. Rev. B 72,165112 (2005). [CrossRef]
  8. G. Torrese, J. Taylor, H. P. Schriemer, M. Cada, “Energy transport through structures with finite electromagnetic stop gaps,” J. Opt. A: Pure Appl. Opt. 8, 973–980 (2006). [CrossRef]
  9. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970). [CrossRef]
  10. P. Y. Chen, R. C. Mc Phedran, C. M. de Sterke, C. G. Poulton, A. A. Asatryan, L. C. Botten, M. J. Steel, “Group velocity in lossy periodic structured media,” Phys. Rev. A 82,053825 (2010). [CrossRef]
  11. P. Yeh, “Electromagnetic propagation in birefringent layered media,” J. Opt. Soc. Am. 69, 742–756 (1979). [CrossRef]
  12. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. J. Bloemer, C. M. Bowden, J. M. Haus, M. Bertolotti, “Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures,” Phys. Rev. E 63,036610 (2001). [CrossRef]
  13. W. Frias, A. Smolyakov, A. Hirose, “Non-local energy transport in tunneling and plasmonic structures,” Opt. Express 19, 15281–15296 (2011). [CrossRef] [PubMed]
  14. R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002). [CrossRef]
  15. N. Le Thomas, R. Houdré, “Group velocity and energy transport velocity near the band edge of a disordered coupled cavity waveguide: an analytical approach,” J. Opt. Soc. Am. B 27, 2095–2101 (2010). [CrossRef]
  16. M. de Dios-Leyva, J. C. Drake-Pérez, “Group velocity and nonlocal energy transport velocity in finite photonic structures,” J. Opt. Soc. Am. B 29, 2275–2281 (2012). [CrossRef]
  17. H. G. Winful, “Group delay, stored energy, and the tunneling of evanescent electromagnetic waves,” Phys. Rev. E 68,016615 (2003). [CrossRef]
  18. R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, 1992).
  19. M. de Dios-Leyva, O. E. González-Vasquez, “Band structure and associated electromagnetic fields in one-dimensional photonic crystals with left-handed materials,” Phys. Rev. B 77,125102 (2008). [CrossRef]
  20. J. M. Bendickson, J. P. Dowling, M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996). [CrossRef]
  21. M. Centini, C. Sabilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: Applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999). [CrossRef]
  22. E. P. Wigner, “Lower Limit for the Energy Derivative of the Scattering Phase Shift,” Phys. Rev. 98, 145–147 (1955). [CrossRef]
  23. M. de Dios-Leyva, J. C. Drake-Pérez, “Properties of the dispersion relation in finite one-dimensional photonic crystals,” J. Appl. Phys. 109,103526 (2011). [CrossRef]
  24. H. Daninthe, S. Foteinopoulou, C. M. Soukoulis, “Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photonics and Nanostructures-Fundamentals and Applications 4, 123–131 (2006). [CrossRef]
  25. A. R. Davoyan, A. A. Sukhorukov, I. V. Shadrivov, Y. S. Kivshar, Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79,013820 (2009). [CrossRef]
  26. G Torrese, J. Taylor, T. J. Hall, P. Mégret, ”Effective-medium theory for energy velocity in one-dimensional finite lossless photonic crystals,” Phys. Rev. E 73,066616 (2006). [CrossRef]

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