Abstract
Composite materials have recently found wide industrial use. This in turn demands development of more sophisticated descriptions of an interaction of electromagnetic waves with such inhomogeneous systems. Commonly, for this aim the macroscopic Maxwell equations are employed. These equations are obtained by homogenization (averaging) of the microscopic Lorentz equations and contain additional unknown fields: magnetic field \(\vec H\) and electrical induction \(\vec D\). To complete the system, one needs to introduce, so-called, constitutive relations connecting these new fields with the averaged values of the electric \(\vec E\) and magnetic \(\vec B\) fields. Although there exists a well developed theory of constitutive relations for materials without dispersion and with temporal dispersion, we still have run into obstacles while describing system with spatial dispersion. This communication is devoted to some issues of spatial dispersion problem.
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References
Landauer, R. (1978) Electrical conductivity in inhomogeneous media, in J.C. Garland and D.B. Tanner (Eds.), Proc. of AIP Conference, 40, New York,American Institute of Physics, 2–45.
Bergman, D. J., Stroud, D. (1992) Physical properties of macroscopically inhomogeneous media, Solid. St. Phys., 46, 148–269.
Lagarkov, A. N., Sarychev, A. K., Smychkovich, Yu. R., and Vinogradov, A. P. (1992) Effective medium theory for microwave dielectric constant and magnetic permeability of conducting stick composites, J. Electro. Waves Applic. 6, 1159–1176.
Sanchez-Palencia, E. (1980) Non-Homogeneous Media and Vibration Theory, Springer Verlag, New York.
Bakhvalov, N. S., Panasenko G. P. (1989) Homogenization. Averaging processes in periodic media, in Mathematical Problems in the Mechanics of Composite Materials, Kluwer Academic Publisher, Dordrecht.
Velikhov, E. P., Dykhne, A. M., (1963) in Proc. VI Int. Symp. Ion. Phen. in Gases, Paris, 511.
Brekhovskikh, I. M. (1960) Waves in Layered Media Academic Press, New York.
Vinogradov, A.P., Panina, L. V., Sarychev, A.K. (1989) Method for calculating the dielectric constant and magnetic permeability in percolating systems, Sov. Phys. Dokl. 34, 530–532.
Schelkunoff, S. A. and Priis, H. T. (1952) Antenna Theory and Practice, Wiley, New York.
Lewin, L (1975) Theory of Waveguides., Newnes-Butterworths, London.
Jaggard, D. L., Mickelson, A. R., and Papas, C. H. (1979) On electromagnetic waves in chirai media, Appl. Phys. 18, 211–216.
Lakhtakia, A., Varadan, V. K., Varadan, V.V. (1989) Time-harmonic Electromagnetic Fields in Chirai Media, Lecture Notes in Physics 335, Springer, New York.
Lindell, I. V., Sihvola, A.H., Tretyakov, S.A., Viitanen A.J. (1994) Electromagnetic Waves in Chirai and Bi-Isotropic Media, Artech House, Boston.
Kukolev, I. V., Lagarkov, A.N., Matitsin, S. M., Rosanov, K. N., and Vinogradov A. P. (1992) Investigation of effective magnetic permeability of inhomogeneous dielectric materials at microwaves, in Proc. of the Material Research Society Spring Meeting, San Francisco No. L6.14.
Landau, L.D., Lifehitz, E.M. (1982) Electrodynamics of Continuous Media, Pergamon Press, New York.
Born, M. (1933) Optik, Springer, Berlin (in German).
Golubkov, A.A., Makarov, V.A. (1995) Boundary conditions for electromagnetic field on the surface of media with weak spatial dispersion, Uspekhi Fizicheskikh Nauk 165, 339–346 (in Russian)
Silin, V.P., Rukhadze, A.A. (1961) Electromagnetic Properties of Plasma and Plasma-like Media, GosAtomIzdat, Moscow (in Russian).
Ryazanov, I.M. (1987) Electrodynamics of Condensed Matter, (in Russian).
Vinogradov, A.P. (1993) Microscopic properties of a chiral object, in Ari Sihvola, Sergei Tretyakov, Igor Semchenko (Eds.) Proc. Int. Seminar on Electrodynamics of Chiral and Bianisotropic Media Bianisotropics’93, Helsinki University of Technology, Electromagnetics Laboratory Report 159.
Stanley, H.E. (1971) Introduction to Phase Transitions and Critical Phenomena, Clarendon Press, Oxford.
Rytov, S.M. (1955) J. Experimental and Theoretical Physics (JETF), 29, 5 (in Russian)
Vinogradov, A.P., Romanenko, V.E. (1995) Artificial magnetics based on racemic helix inclusions, in A. Sihvola et al. (Eds.), Proc. of 4th Intl. Conf. on Chiral, Bi-isotropic and Bi-anisotropic Media, CEIRAL’95, The Pennsylvania State University, State College, pp. 143–148.
Ryghov, Yu.A., Tamoikin, V.V. (1970) Radiation and transmitance of electromagnetic waves in randomly inhomogeneous media, Radifizika, 13, 356 (in Russian).
Hoppe, D.J., Rahmat-Samii, Y. (1995) Impedance Boundary Conditions in Electromagnetics, Taylor & Francis, Washington.
Senior, T. B. A., Volakis, J.L. (1995) Approximate Boundary Conditions in Electromagnetics, The IEE Press, London.
Agranovich, V.M., Yudson, V.I. (1973) Boundary conditions in media with spatial dispersion, Opt. Com. 7, 121–124.
Maradudin, A.A., Mills, D.L. (1973) Effect of spatial dispersion on the properties of a semi-infinite dielectric, Phys. Rev. B 7, 2787–2810.
Agarwal, G.S., Pattanayak, D.N., Wolf, E. (1974) Phys. Rev. B 8, 1447–1463.
Birman, J.L. (1982) Chapter 2, in J.L. Birman (Ed.) Excitons, North Holland Co.
Agranovich, V.M., Ginzburg, V.L. (1966) Spatial Dispersion in Crystal Optics and the Theory of Excitons, Interscience, New York.
Busarov, I.G., Lagarkov, A.N., Sterlina, I.G., Vinogradov, A.P. (1992) Interaction of electromagnetic waves with heterogeneous systems. Non-Presnels type of reflection, in Proc. of the International Conference STATPHYS 18, Berlin, pp. 269–280.
Vinogradov A.P., Lagarkov, A.N., Romanenko, V.E. (1996) Effects of spatial dispersion in composite materials at mw range, Doclady Acdemii Nauk, 349, 182–184 (in Russian).
Stewart, J.E., Gallaway, W.S. (1962) Diffraction anomalies in grating spectrophotometers Applied Optics 1, 421–427.
Hessel, A., Oliner, A.A. (1965) A new theory of Wood’s anomalies on optical gratings, Applied Optics 4, 1275–1281.
Palmer, C.H., Evering, F.C., and Nelson, F.M. (1965) Diffraction anomalies for gratings of rectengular profile, Appl. Opt. 4, 1271–1278.
Botten, L.C., Craig, M.S., McPhedran, R.C., Adams, J. L., and Andrewartha, J. R. (1981) The finitely conducting lamellar diffraction grating, Optica Acta 28, 1087–1101.
Botten, L.C., Craig, M.S., McPhedran, R. C. (1981) Highly conducting lamellar diffraction gratings, Optica Acta 8, 1103–1109.
McPhedran, R.C., Waterworth, M.D. (1972) A theoretical demonstration of properties of grating anomalies (S-polarization), Optica Acta 19, 877–891.
McPhedran, R.C., Botten, L.C., Craig, M.S., Neviere, M., and Maystre, D., (1982) Lossy lamellar gratings in the quasistatic limit, Optica Acta 29, 289–294.
Burckhardt, C.B. (1966) Diffraction of a plane wave at a sinusoidally stratified dielectric grating, J. Opt. Soc. of Am. 56, 1502–1511.
Kaspar, F.G. (1973) Diffraction by thick, periodically stratified grating with complex dielectric constant, J. Opt. Soc. of Am. 63, 37–45.
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Lagarkov, A.N., Vinogradov, A.P. (1997). Non-Local Response of Composite Materials in Microwave Range. In: Priou, A., Sihvola, A., Tretyakov, S., Vinogradov, A. (eds) Advances in Complex Electromagnetic Materials. NATO ASI Series, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5734-6_9
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DOI: https://doi.org/10.1007/978-94-011-5734-6_9
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