Open Access
Issue
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
Page(s) 1483 - 1519
DOI https://doi.org/10.1051/m2an/2022045
Published online 20 July 2022
  1. H. Ammari, H. Kang and K. Kim, Polarization tensors and effective properties of anisotropic composite materials. J. Differ. Equ. 215 (2005) 401–428. [CrossRef] [Google Scholar]
  2. H. Ammari, H. Kang, S. Soussi and H. Zribi, Layer potential techniques in spectral analysis. part 2: Sensitivity analysis of spectral properties of high contrast band-gap materials. Multiscale Model. Simul. 5 (2006) 646–663. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Ammari, H. Kang and H. Lee, Layer Potential Techniques in Spectral Analysis, American Mathematical Society, 201 Charles Street, Providence, RI (2009). [CrossRef] [Google Scholar]
  4. B.C. Aslan, W.W. Hager and S. Moskow, A generalized eigenproblem for the laplacian which arises in lightning. J. Math. Anal. Appl. 341 (2008) 1028–1041. [CrossRef] [MathSciNet] [Google Scholar]
  5. D.J. Bergman, The dielectric constant of a composite material - a problem in classical physics. Phys. Rep. 43 (1978) 377–407. [CrossRef] [MathSciNet] [Google Scholar]
  6. D.J. Bergman, The dielectric constant of a simple cubic array of identical spheres. J. Phys. C. 12 (1979) 4947–4960. [CrossRef] [Google Scholar]
  7. G. Bouchitté, C. Bourel and D. Felbacq, Homogenization near resonances and artificial magnetism in three dimensional dielectric metamaterials. Arch. Ration. Mech. Anal. 225 (2017) 1233–1277. [Google Scholar]
  8. O.P. Bruno, The effective conductivity of strongly heterogeneous composites. Proc. R. Soc. Lond. A 433 (1991) 353–381. [CrossRef] [Google Scholar]
  9. P.Y. Chen, D.J. Bergman and Y. Sivan, Generalizing normal mode expansion of electromagnetic green’s tensor to open systems. Phys. Rev. Appl. 11 (2019). [Google Scholar]
  10. A. Figotin and P. Kuchment, Band-gap structure of the spectrum of periodic maxwell operators. J. Stat. Phys. 74 (1994) 447–455. [CrossRef] [Google Scholar]
  11. A. Figotin and P. Kuchment, Band-gap structure of spectra of periodic dielectric and acoustic media. 1. scalar model. SIAM J. Appl. Math. 56 (1996) 68–88. [Google Scholar]
  12. A. Figotin, P. Kuchment, Spectral properties of classical waves in high-contrast periodic media. SIAM J. Appl. Math. 58 (1998) 683–702. [Google Scholar]
  13. R. Hempel and K. Lienau, Spectral properties of periodic media in the large coupling limit. Commun. Partial Differ. Equ. 25 (2000) 1445–1470. [Google Scholar]
  14. J.D. Jackson, Classical Electrodynamics. John Wiley & Sons, NY (1962). [Google Scholar]
  15. J.D. Joannopoulos, S.G. Johnson, J.N. Winn and R.D. Meade, Photonic Crystals: Molding the Flow of Light. Princeton University Press, 2nd edition edition (2008). [Google Scholar]
  16. S.G. Johnson and J.D. Joannopoulos, Photonic Crystals, The road from Theory to Practice. Kluwer Acad. Publ. (2002). [Google Scholar]
  17. H. Kang, Layer potential approaches to interface problems. In Inverse Problems and Imaging: Panoramas et synthèses 44. Société Mathématique de France (2013). [Google Scholar]
  18. T. Kato, On the convergence of the perturbation method, 1. Prog. Theor. Phys. 4 (1949) 514–523. [CrossRef] [Google Scholar]
  19. T. Kato, On the convergence of the perturbation method, 2. Prog. Theor. Phys. 5 (1950) 95–101. [CrossRef] [Google Scholar]
  20. T. Kato, Perturbation Theory for Linear Operators. Springer, Berlin Heidelberg, Germany (1995). [CrossRef] [Google Scholar]
  21. D. Khavinson, M. Putinar and H. Shapiro, Poincaré’s variational problem in potential theory. Arch. Ration. Mech. Anal. 185 (2007) 143–184. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Kuchment, The mathematics of photonic crystals. SIAM: Math. Model. Optical Sci. Front. Appl. Math. 22 (2001) 207–272. [CrossRef] [Google Scholar]
  23. P. Kuchment, On some spectral problems of mathematical physics. Contemporary Mathematics (2004). [Google Scholar]
  24. R. Lipton and R. Viator Jr., Bloch waves in crystals and periodic high contrast media. ESAIM: M2AN 51 (2017) 889–918. [CrossRef] [EDP Sciences] [Google Scholar]
  25. R. Lipton and R. Viator Jr., Creating band gaps in periodic media. Multiscale Model. Simul. 15 (2017) 1612–1650. [CrossRef] [MathSciNet] [Google Scholar]
  26. I. Mayergoyz, D. Fredkin and Z. Zhang, Electrostatic (plasmon) resonances in nanoparticles. Phys. Rev. B 72 (2005). [CrossRef] [Google Scholar]
  27. R.C. McPhedran and G.W. Milton, Bounds and exact theories for transport properties of inhomogeneous media. Appl. Phys. A 26 (1981) 207–220. [CrossRef] [Google Scholar]
  28. G.W. Milton, The Theory of Composites. Cambridge University Press, Cambridge (2002). [CrossRef] [Google Scholar]
  29. D. Mitrea, M. Mitrea and J. Pipher, Vector potential theory on nonsmooth domains in r3 and applications to electromagnetic scattering. J. Fourier Anal. Appl. 3 (1996) 131–192. [Google Scholar]
  30. K. Sakoda, Optical Properties of Photonic Crystals. Springer Verlag (2001). [CrossRef] [Google Scholar]
  31. R.E. Slusher and B.J. Eggleton (Editors), Nonlinear Photonic Crystals. Springer Verlag (2003). [CrossRef] [Google Scholar]
  32. B. Sz.-Nagy, Perturbations des transformations autoadjoints dans léspace de hilbert. Comment. Math. Helv. 19 (1946) 347–366. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you