A time domain analysis of wave motions in chiral materials

Mathematische Nachrichten

Volumn 250, Issue , 2003, Pages 3-16

  Athanasiadis, Christodoulos ^a   Roach, Gary F ^b   Stratis, Ioannis G ^a  

^a UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Chiral materials; Time domain; Wave motions

Indexed keywords

EID: 0037289157     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310018     Document Type: Article

References (34)

1. R. A. Adams, Sobolev Spaces (Academic Press, New York, 1975).
2. H. Ammari, K. Hamdache, and J.-C. Nédélec, Chirality in the Maxwell equations by the dipole approximation method, SIAM J. Appl. Math. 59, 2045-2059 (1999).
3. C. Athanasiadis, Costakis, and I. G. Stratis, Electromagnetic scattering by a homogeneous chiral obstacle in a chiral environment, IMA J. Appl. Math. 64, 245-258 (2000).
4. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures (North Holland, Amsterdam, 1978).
5. I. Egorov, Time-domain Green dyadics for temporally dispersive bi-isotropic media, J. Phys. A: Math. Gen. 31, 7363-7378 (1998).
6. D. M. Eidus, The principle of limiting absorption, Math. Sb. 57 (1962); AMS Transl. 47, 157-191 (1965).
7. D. M. Eidus, The principle of limiting absorption, Math. Sb. 57 (1962); AMS Transl. 47, 157-191 (1965).
8. D. M. Eidus, The principle of limiting amplitude, Uspekhi Mat. Nauk. 24, 91-156 (1969); Russ. Math. Surv. 24, 97-167 (1969).
9. D. M. Eidus, The principle of limiting amplitude, Uspekhi Mat. Nauk. 24, 91-156 (1969); Russ. Math. Surv. 24, 97-167 (1969).
10. D. J. Frantzeskakis, A. Ioannidis, G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos, On the error of the optical response approximation in chiral media, Appl. Anal., in press (2003).
11. J. A. Goldstein, Semigroups of Linear Operators and Applications (Oxford University Press, Oxford, 1986).
12. A. Hasegawa, Fundamentals in optical soliton theory in fibers, in: Optical Solitons: Theoretical Challenges and Industrial Perspectives, edited by V. E. Zakharov and S. Wabnitz (EDP Sciences, Les Ulis, Springer-Verlag, Berlin, 1999), p. 1-18.
13. P. Hillion, Spinor form of electromagnetism in non homogeneous media, Int. J. Engng. Sci. 29, 1157-1165 (1991).
14. P. Hillion and A. Lakhtakia, On an initial boundary value problem involving Beltrami-Moses fields in electromagnetic theory, Phil. Trans. R. Soc. London A 344, 235-248 (1993).
15. G. Kristenson and S. Rikte, Transient wave propagation in reciprocal bi-isotropic media at oblique incidence, J. Math. Phys. 34, 1339-1359 (1993).
16. A. Lakhtakia (ed.), Selected Papers on Natural Optical Activity, Milestone Series 15, SPIE Optical (Engineering Press, Bellingham, 1990).
17. A. Lakhtakia, Beltrami Fields in Chiral Media, World Scientific Series in Contemporary Chemical Physics Vol 2 (World Scientific, London, 1994).
18. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, Time Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics No. 335 (Springer-Verlag, Berlin, 1989).
19. R. Leis, Initial Boundary Value Problems of Mathematical Physics (John Wiley & Sons, Chichester, 1986).
20. I. V. Lindell, Methods for Electromagnetic Field Analysis (Clarendon Press, Oxford, 1992).
21. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media (Artech House, Boston, 1994).
22. S. A. Maksimenko, G. Y. Slepyan, and A. Lakhtakia: Gaussian pulse propagation in a linear lossy chiral medium, J. Opt. Soc. Am. A 14, 894-900 (1997).
23. H. E. Moses, Eigenfunctions of the curl operator, rotationally invariant Helmholtz theorem and applications to electromagnetic and fluid dynamics, SIAM J. Appl. Math. 21, 114-144 (1971).
24. H. E. Moses and R. T. Prosser, The general solution of the time dependent Maxwell's equations in an infinite medium with constant conductivity, Proc. R. Soc. London A 43, 493-507 (1990).
25. H. E. Moses, R. Nagem, and G. H. Sandri, The general solution of the three dimensional acoustic equation and of Maxwell's equations in the infinite domain in terms of the asymptotic solution in the wave zone, J. Math. Phys. 33, 86-101 (1992).
26. M. Reed and B. Simon, Methods of Mathematical Physics, Vols 1-4, (Academic Press, New York, 1972 - 1979).
27. G. F. Roach, An Introduction to Linear and Nonlinear Scattering Theory, Pitman Monographs and Surveys in Pure and Applied Mathematics Vol 78 (Longman, Essex, 1995).
28. G. F. Roach and B. Zhang, A transmission problem for the reduced wave equation in inhomogeneous media with an infinite interface, Proc. Roy. Soc. Lond. A436, 121-140 (1992).
29. G. F. Roach and B. Zhang, The limiting amplitude principle for wave propagation with two unbounded media, Proc. Camb. Phil. Soc. 112 (1993), 207-223
30. G. F. Roach and B. Zhang, Spectral representations and scattering theory for the wave equation with two unbounded media, Proc. Camb. Phil. Soc. 113, 423-447 (1993).
31. E. Sanchez-Palencia, Non-homogeneous Media and Vibration Theory, Lecture Notes in Physics No. 127 (Springer-Verlag, Berlin, 1980).
32. I. G. Stratis, Electromagnetic scattering problems in chiral media: a review, Electromagnetics 19, 547-562 (1999).
33. W. S. Weiglhofer and A. Lakhtakia, On causality requirements for material media, AEU Int. J. Electron. Commun. 59, 389-391 (1996).
34. C. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains, Lecture Notes in Mathematics No. 442 (Springer-Verlag Berlin, 1975).