Abstract
In this article we describe a mathematically rigorous proof of Anderson localization of light in randomized periodic media, based on the macroscopic Maxwell equations.
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References
P. W. Anderson, “Absense of Diffusion in Certain Random Lattice,” Phys. Rev. 109, 1492–1505 (1958).
P. W. Anderson, “A Question of Classical Localization. A Theory of White Paint,” Philosophical Magazine B 53, 505–509 (1985).
J. M. Barbaroux, J. M. Combes and P. D. Hislop, “Localization near Band Edges for Random Schrodinger Operators,” Helv. Phys. Acta, to appear.
M. Sh. Birman and M. Z. Solomyak, “L 2 Theory of the Maxwell Operator in Arbitrary Domains,” Russian Math. Surveys, 42:6, 75–96, 1987.
R. Carmona and J. Lacroix, Spectral Theory of Random Schrödinger Operators (Birkhäuser, Boston, USA, 1990).
J. Combes and P. Hislop, “Localization for some Continuous, Random Hamiltonians in d-dimensions,” J. Funct. Anal. 124, 149–180 (1994).
Development and Applications of Materials Exhibiting Photonic Band Gaps, Journal of the Optical Society of America B 10, 280–413 (1993).
L. Deych and A. Lisyansky, “Impurity Localization of Electromagnetic Waves in Polariton Region,” Phys. Rev. Lett., to appear.
H. von Dreifus and A. Klein, “A New Proof of Localization in the Anderson Tight Binding Model,” Commun. Math. Phys. 124, 285–299 (1989).
A. Figotin, “High-contrast Photonic crystals,” in this volume.
A. Figotin and A. Klein, “Localization Phenomenon in Gaps of the Spectrum of Random Lattice Operators,” J. Stat. Phys. 75, 997–1021 (1994).
A. Figotin and A. Klein, “Localization of Electromagnetic and Acoustic Waves in Random Media. Lattice Model,” J. Stat. Phys. 76, 985–1003 (1994).
A. Figotin and A. Klein, “Localization of Classical Waves I: Acoustic Waves,” Commun. Math. Phys. 180, 439–482 (1996).
A. Figotin and A. Klein, “Localization of Classical Waves II: Electromagnetic Waves,” Commun. Math. Phys. 184, 411–441 (1997).
A. Figotin and A. Klein, “Localized Classical Waves Created by Defects,” J. Stat. Phys. 86, 165–177 (1997).
A. Figotin and A. Klein, “Midgap Defect Modes in Dielectric and Acoustic Media,” SIAM J. Appl. Math. (1998).
A. Figotin and A. Klein, “Localization of Light in Lossless Inhomogeneous Dielectrics,” J. Opt. Soc. Am. A 15, 1423–1435 (1998).
A. Figotin and P. Kuchment, “Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model,” SIAM J. Appl. Math. 56, 68–88 (1996).
A. Figotin and P. Kuchment, “Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. II. 2D Photonic Crystals,” SIAM J. Appl. Math. 56, 1561–1620 (1996).
J. Fröhlich and T. Spencer, “Absence of Diffusion in the Anderson Tight Binding Model for Large Disorder or Low Energy,” Commun. Math. Phys. 88, 151–184 (1983).
J. Fröhlich, F. Martinelli, E. Scoppola and T. Spencer, “Constructive Proof of Localization in the Anderson Tight Binding Model,” Commun. Math. Phys. 101, 21–46 (1985).
F. Germinet and S. De Bievre, “Dynamical Localization for Discrete and Continuous Random Schrödinger Operators,” Commun. Math. Phys., to appear.
H. Holden and F. Martinelli, “On Absence of Diffusion near the Bottom of the Spectrum for a Random Schrödinger Operator on L 2(ℝv),” Commun. Math. Phys. 93, 197–217 (1984).
P. M. Hui and N. F. Johnson, “Photonic Band-Gap Materials,” in Solid State Physics, vol. 49, H. Ehrenreich and F. Spaepen, eds., 151–203 (Academic Press, New York, USA, 1995).
S. Jitomirskaya and A. Klein, in preparation.
J. Joannopoulos, R. Meade and J. Winn, Photonic Crystals (Princeton University Press, Princeton, USA, 1995).
S. John, “Localization of Light,” Phys. Today, May 1991, 32–40.
S. John, “The Localization of Light,” in Photonic Band Gaps and Localization, C.M. Soukoulis, ed., NATO ASI Series B., Vol. 308, 1–22 (Plenum, New York, 1993).
W. Kirsch and F. Martinelli, “On the Ergodic Properties of the Spectrum of General Random Operators,” J. Reine Angew. Math. 334, 141–156 (1982).
A. Klein and A. Koines, “A General Framework for Localization of Classical Waves,” in preparation.
A. Klein and M. Seifert, in preparation.
W. Kohler, G. Papanicolaou and B. White, “Localization and Mode Convertion for Elastic Waves in Randomly Layered Media,” Wave Motion 23, 1–22 and 181–201 (1996).
I. M. Lifshits, S. A. Greduskul and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, USA, 1988).
A. Maradudin, E. Montroll and G. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation (Academic Press, New York, 1963).
J. Maynard, “Acoustic Anderson Localization,” in Random Media and Composites, B. V. Kohn and G. W. Milton, eds., 206–207 (SIAM, Philadelphia, USA, 1988).
L. Pastur and A. Figotin, Spectra of Random and Almost-periodic Operators (Springer-Verlag, Heidelberg, USA, 1991).
J. Rarity and C. Weisbuch, eds., Microcavities and Photonic Bandgaps: Physics and Applications (Kluwer Academic Publishers, Dordrecht, Holland, 1995).
B. Shklovskii and A. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, Heidelberg, Germany, 1984).
C. Soukoulis, ed., Photonic Band Gaps and Localization (Plenum, New York, 1993).
C. Soukoulis, ed., Photonic Band Gap Materials (Kluwer Academic Publishers, Dordrecht, Holland, 1996).
C. Soukoulis, “Photonic Band Gap Materials,” in this volume.
P. R. Villeneuve and J. Joannopoulos, “Working at the Speed of Light,” Science Spectra, Number 9, 18–24 (1997).
P. R. Villeneuve and M. Piche, “Photonic Band Gaps in Periodic Dielectric Structures,” Prog. Quant. Electr. 18, 153–200 (1994).
D. Wiersma, P. Bartolini, A. Lagendijk and R. Righini, “Localization of Light in a Disordered Medium,” Nature 390, 671–673 (1997).
D. Wiersma, in this volume.
E. Yablonovitch, T. Gmitter, R. Meade, D. Brommer, A. Rappe and J. Joannopoulos, “Donor and Acceptor Modes in Photonic Periodic Structure,” Phys. Rev. B 44, 13772–13774 (1991).
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Klein, A. (1999). Localization of Light in Randomized Periodic Media. In: Fouque, JP. (eds) Diffuse Waves in Complex Media. NATO Science Series, vol 531. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4572-5_3
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DOI: https://doi.org/10.1007/978-94-011-4572-5_3
Publisher Name: Springer, Dordrecht
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