Selected literature on electromagnetic characterisation of nanostructured materials Print E-mail

Overviews on electromagnetic characterization of nanostructured materials

C. Simovski, On electromagnetic characterization and homogenization of nanostructured metamaterials (review article), J. Optics, vol. 13, 013001, 2011.

C. R. Simovski, Material Parameters of Metamaterials (a review), Optics and Spectroscopy, vol. 107, no. 5, pp. 726–753, 2009.

C.R. Simovski, S.A. Tretyakov, History of metamaterials, in: F. Capolino ed. Handbook of Metamaterials, vol. 1, Introductory chapter, CRC Press, Boca Raton-London, 2009.

Homogenization models for unbounded metamaterials



A. Alu, First-Principle Homogenization Theory for Periodic Metamaterial Arrays, arXiv:1012.1351v1, 6.12.2010.

A. Alu, Restoring the Physical Meaning of Metamaterial Constitutive Parameters, arXiv:1012.1353v1, 6.12.2010.

C. Fietz, G. Shvets, Physica B 405, 2930, 2010.

D.R. Smith, Analytic expressions for the constitutive parameters of magnetoelectric metamaterials, Physical Review E, 81, 036605, 2010.

A. Ludwig and K.J. Webb, Accuracy of effective medium parameter extraction procedures for optical metamaterials, Phys. Rev. B 81, 113103, 2010.

C. Fietz and G. Shvets, Homogenization theory for simple metamaterials modeled as one-dimensional arrays of thin polarizable sheets, Phys. Rev. B 82, 205128, 2010.

C.R. Simovski and S.A. Tretyakov, On effective electromagnetic parameters of artificial nanostructured magnetic materials, Photonics and Nanostructures - Fundamentals and Applications, vol. 8, pp. 254–263, 2010.

R.A. Shore, R.D. Yaghjian, IEICE Transactions on Communications E91.B (2010) 1819

C.R. Simovski, S.A. Tretyakov, Material parameters and field energy in reciprocal composite media, in: F. Capolino ed., Handbook of Metamaterials, vol. 1, chapter 1, CRC Press, Boca Raton-London, 2009.

G. Bouchitte, C. Bourel and D. Felbacq, Comptes Rendus, Acad. Sci. Paris, Ser. I 347(2009) 571.

V. M. Agranovich and Yu. N. Gartstein, Electrodynamics of metamaterials and the Landau–Lifshitz approach to the magnetic permeability, Metamaterials, vol. 3 pp. 1-9, 2009.

Shore R A and Yagjian A D (2009) Travelling waves in three dimensional periodic arrays of two different alternating magnetodielectric spheres IEEE Trans. Antennas Propag. 57, 3077

Ya. A. Urzhumov and G. Shvets, Solid State Communications 146 (2008) 208.

Petschulat J, Menzel C, Chipouline A, Rockstuhl C, Tnnermann A, Lederer F and Pertsch T (2008) Multipole Approach to Metamaterials Phys. Rev. A 78, 043811

Ekinci Y, Christ A, Agio M, Martin O J F, Solak H H and Loffler J F (2008) Electric and magnetic resonances in coupled Au particle pairs, Opt. Express 16, 13287

Baena J.D., Jelinek R, Marques R.M. and Silveirinha M.G. (2008) Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials, Phys. Rev. A, 78, 013842

Shore RA and Yagjian A D (2007) Travelling waves in two and three dimensional periodic arrays of lossless scatterers, Radio Sci. 42, RS6S21

M.G. Silveirinha, Generalized Lorentz-Lorenz formulas for microstructured materials, Physical Review B 76, 245117, 2007.

Guenneau S, Zolla F and Nicolet A (2007) Homogenization of three-dimensional photonic crystals with heterogeneous permittivity and permeablity, Waves in Random Complex Media, 17, 653.

A. I. Cabuz, D. Felbacq, and D. Cassagne, Phys. Rev. Lett. 98 (2007) 037403.

Cherednichenko K D and Guenneau S (2007) Bloch wave homogenization for spectral asymptotic analysis of the periodic Maxwell operator, Waves in Random Complex Media, 17, 571.

G. Eleftheriades, K.G Balmain, Negative-Refraction Metamaterials: Fundamental Principles and Applications, Wiley: NY, 2006. Chapter 8, 313-317.

N. Engheta, R. Ziolkowski, Metamaterials Physics and Engineering Explorations, NY: J. Wiley and Sons, 2006. Chapter 5.

D. Smith and J. B. Pendry, JOSA B, 23 (2006) 391.

M.G. Silveirinha, Nonlocal homogenization model for a periodic array of eps-negative rods, Physical Review E 73, 046612, 2006.

A. I. Cabuz, D. Felbacq, and D. Cassagne, Phys. Rev. Lett. 98 (2007) 037403.

D. Felbacq, G. Bouchitte, Opt. Lett. 30 (2005) 10.

Shvets G and Urzhumov Y A (2005) Electric and magnetic properties of sub-wavelength plasmonic crystals J. Opt. A: Pure Appl. Opt. 7, S23

D. Felbacq, G. Bouchitte, Phys. Rev. Lett. 94 (2005) 183902.

M.G. Silveirinha, Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters, Physical Review B 75, 115104, 2007.

M.G. Silveirinha, C.A. Fernandes, Homogenization of 3-D-connected and nonconnected wire metamaterials, IEEE Transactions on Microwave Theory and Techniques, vol. 53, pp. 1418-1430, 2005.

Bouchitte G. and Felbacq D. (2006) Homogenization of the wire photonic crystals: the case of small volume fraction, SIAM J. Appl. Math., 66, 2061

Felbacq D. and Bouchitte G. (2005) Theory of mesoscopic magnetism in photonic crystals, Phys. Rev. Lett., 94, 183902

G. Bouchitte, D. Felbacq, Comptes Rendus, Acad. Sci. Paris, Ser. I 339 (2004) 337.

Poulton C G, Guenneau S and Movchan A B (2004) Non-commuting limits and effective properties for electromagnetism in conical incidence, Phys. Rev. B 69, 195112

J.B. Pendry, A.J. Holden, D.J. Robins, and W.J. Stewart, IEEE Trans. MTT, 47 (1999) 2075

J.B. Pendry, A.J. Holden, D.J. Robins, and W.J. Stewart, J. Phys. Condens. Matter, 10 (1998) 4785

Restrictions of standard characterization approaches and novel characterization approaches for finite-thickness metamaterials

S. Kim, E. F. Kuester, C. L. Holloway, A.D. Scher, J. Baker-Jarvis, Boundary effects  on the determination of metamaterial parameters from normal incidence re°ection and transmission measurements, submitted to IEEE Trans. Antennas Propag., available at

D. Morits and C. Simovski, Electromagnetic characterization of planar and bulk metamaterials: A theoretical study, Phys. Rev. B 82, 165114, 2010.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, Validity of effective material parameters for optical fishnet metamaterials, Phys. Rev. B, vol. 81, p. 035320, 2010.

D.A. Powell, Yu.S. Kivshar, Applied Physics Letters 97 (2010) 091106

A. Andryieuski, R. Malureanu, A.V. Lavrinenko, Optics Express 18 (2010) 15498

C.R. Simovski, Extraction of local material parameters of meta-materials from experimental or simulated data, in: F. Capolino ed., Handbook of Metamaterials, vol. 1, chapter 4, CRC Press, Boca Raton-London, 2009

Silveirinha M G, Baena J D, Jelinek L and Marques R (2009) Nonlocal homogenization of an array of cubic particles made of resonant rings Metamaterials 3, 115

A. D. Scher and E. F. Kuester, Metamaterials 3 (2009) 4455

V. M. Agranovich ancd Yu. N. Gartstein, Metamaterials, 3 (2009) 1.

A.D. Scher and E. F. Kuester, Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles, Metamaterials, vol. 3, pp. 44–55, 2009.

A.D. Scher and E.F. Kuester, Boundary effects in the electromagnetic response of a metamaterial in the case of normal incidence, PIER B, vol. 14, pp. 341-381, 2009.

W. Smigaj and B. Gralak, Phys. Rev. B 77 (2008) 235445.

C.R. Simovski, S.A. Tretyakov, Local constitutive parameters of metamaterials from an effective-medium perspective, Phys. Rev. B, vol. 75, 195111(1-9), 2007.C.R. Simovski. Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices, Metamaterials, vol. 1, no. 2, pp. 62-80, 2007.

C.R. Simovski, Application of the Fresnel formulas for reflection and transmission of electromagnetic waves beyond the quasi-static approximation, Radiotechnika i Elektronika (Journal of Communication Technology and Electronics), vol. 52, No. 9, 953-971, 2007 (data of the English version) (ask the author)

P. Ikonen, E. Saenz, R. Gonzalo, C. Simovski and S. Tretyakov, Mesoscopic effective material parameters for thin layers modeled as single and double grids of interacting loaded wires, Metamaterials, vol. 1, no. 2, pp. 89-105, 2007.

Silveirinha M G and Fernandes C (2007) Transverse-average field approach for the characterization of thin metamaterial slabs Phys. Rev. E 75, 036613

Marques R, Baena J D, Beruete M, Falcone F, Lopetegi T, Sorolla M, Martyn F and Garcia J (2005) Ab initio analysis of frequency selective surfaces based on conventional and complementary split ring resonators, J. Opt. A: Pure Appl. Opt., 7, S38

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, IEEE Transactions on Antennas and Propagation 51 (2003) 2641.

P.A. Belov, R. Marques, M.G. Silveirinha, I.S. Nefedov, C.R. Simovski, S.A. Tretyakov, Physical Review B, vol. 70, 113103 (1-5) 2003

E.F. Kuester, M.A. Mohamed, M. Piket-May, C.L. Holloway, IEEE Trans. Antennas Propag. 51 (2003) 2641

Shvets G. (2002) Photonic approach to making a surface wave accelerator, AIP Conf. Proc. 647, 371

Effective material parameters for nanostructured materials using standard homogenization and characterization methods

Woodley J and Mojahedi M (2010) On the signs of the imaginary parts of the effective permittivity and permeability in metamaterials, J. Opt. Soc. Am. B, 27, 1016

C. R. Simovski and S. A. Tretyakov, Model of isotropic resonant magnetism in the visible range based on core-shell clusters, Phys. Rev. B, vol. 79, p. 045111, 2009

C Tserkezis, J. Phys.: Condens. Matter 21 (2009) 155404.

Garcia-Meca C, Ortuno R, Rodriguez-Fortuno F J, Marti J and Martinez A (2009) Negative refractive index metamaterials aided by extraordinary optical transmission Opt. Lett. 34, 1603

Decker M, Linden S and Wegener M (2009) Coupling effects in low-symmetry planar split-ring resonator arrays, Opt. Lett. 34, 101579

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, Retrieving effective parameters for metamaterials at oblique incidence, Physical Review B 77, 195328, 2008.

Ekinci Y, Christ A, Agio M, Martin O J F, Solak H H and Loffler J F (2008) Electric and magnetic resonances in arrays of coupled gold nanoparticle in-tandem pairs Opt. Express, 16, 13287

Drachev V P, Chettiar U K, Kildishev A V, Yuan H-K, Cai W and Shalaev V M (2008) The Ag dielectric function in plasmonic metamaterials, Opt. Express 16, 1186

B. Kante, A. de Lustrac, J.-M. Lourtioz, F. Gadot, Engineering resonances in infrared metamaterials, Opt. Express 16 (2008) 6774

Zhou J, Koschny T, Kafesaki M and Soukoulis C M (2008) Size dependence and convergence of the retrieval parameters of metamaterials Photon. Nanostruct. 6, 96

Liu N, Guo H, Fu L, Kaiser S, Schweizer H and Giessen H (2008) Three-dimensional photonic metamaterials at optical frequencies Nature Mater. 7, 31

Gundogdu T F, Katsarakis N, Kafesaki M, Penciu R S, Konstantinidis G, Kostopoulos A, Economou E N and Soukoulis C M (2008) Negative index short-slab pair and continuous wires metamaterials in the far infrared regime Opt. Express 16, 9173

E. Lidorikisa, S. Egusa and J. D. Joannopoulos, J. Appl. Phys. 101 (2007) 054304.

Kafesaki M., Tsiapa I., Katsarakis N., Koschny Th., Soukoulis C.M. and Economou E.N. (2007) Left-handed metamaterials: the fishnet structure and its variations Phys. Rev. B 75, 235114

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, F. Lederer, The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach, Opt. Express 15 (2007) 8871

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, T. Ren, J. Mock, S.-Y. Cho, N. M. Jokerst, and D. R. Smith., Appl. Phys. Lett. 90, 092508 (2007).

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements, Phys. Rev. B 75, 115114, 2007.

A. Sarychev, V. Shalaev, Electrodynamics of Metamaterials, Singapore: World Scientific Publishing, 2007, chapter 5

D. R. Smith, D. Schurig, and J. J. Mock, Phys. Rev. E 74 (2006) 036604.

Zhou J, Koschny T and Soukoulis1 CM (2007) Magnetic and electric excitations in split ring resonators, Opt. Express, 15, 17881

D.R. Smith, D.C. Vier, T. Koschny, C.M. Soukoulis, Electromagnetic parameter retrieval from inhomogeneous metamaterials, Physical Review E 71 (2005) 036617.

Th. Koschny, P. Markoš, E.N. Economou, D.R. Smith, D.C. Vier, and C.M. Soukoulis, Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials, Phys. Rev. B 71, 245105 (2005)

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, H. Giessen, Resonances of split-ring resonator metamaterials in the near infrared, Appl. Phys. B 84 (2006) 219

A.N. Grigorenko, Negative refractive index in artificial metamaterials, Optics Letters 31 (2006) 2483

Zhang S, Fan W, Panoiu N C, Malloy K J, Osgood R M and Brueck S R J (2006) Optical negative-index bulk metamaterials consisting of 2D perforated metal–dielectric stacks J. Opt. Soc. Am. B 23, 434

V.V. Varadan and A.R. Tellakula,, Effective properties of split-ring resonator metamaterials using measured scattering parameters: E®ect of gap orientation, J. Appl. Phys. 100 (2006) 034910.

Zhou J, Zhang L, Tuttle G, Koschny Th and Soukoulis C M (2006) Negative index materials using simple short wire pairs Phys. Rev. B 73, 041101

Dolling G, Wegener M, Enkrich C and Linden S (2006) A low-loss negative index metamaterial at telecommunication wavelengths Opt. Lett. 31, 1800

Shalaev V M, Cai W, Chettiar U K, Yuan H, Sarychev A K, Drachev V P and Kildishev A V (2005) Negative refractive index in optics of metal–dielectric composites Opt. Lett. 30, 3356

Dolling G, Enkrich C, Wegener M, Soukoulis C M and Linden S (2006) Low-loss negative-index metamaterial at telecommunication wavelengths Science 312, 892

Linden S, Enkrich C, Dolling G, Klein M W, Zhou J, Koschny T, Soukoulis CM, Burger S, Schmidt F and Wegener M (2006) Photonic metamaterials: magnetism at optical frequencies, IEEE J. Sel. Top. Quantum Electron. 12, 1097

Rockstuhl C, Zentgraf T, Guo H, Liu N, Etrich C, Loa I, Syassen K, Kuhl J, Lederer F and Giessen H (2006) Resonances of split-ring resonator metamaterials in the near infrared, Appl. Phys. B, 84, 219

Alu A, Salandrino A and Engheta N (2006) Negative effective permeability and left-handed materials at optical frequencies, Opt. Express, 14, 1557

Dolling G, Enkrich C, Wegener M, Zhou J F, Soukoulis C.M.and Linden S (2005) Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials, Opt. Lett. 30, 3198

K. Aydin, I. Bulu, K. Guven,M. Kafesaki, C.M. Soukoulis, E. Ozbay, Investigation of magnetic resonances for different split-ring resonator parameters and designs, New J. of Physics 7 (2005) 168.

S. Anantha Ramakrishna, Rep. Prog. Phys. 68 (2005) 449.

S. Zhang, W. Fan, B.K. Minhas, A. Frauenglass, K. J. Malloy, S. R.J. Brueck, Midinfrared resonant magnetic nanostructures exhibiting a negative permeability, Phys. Rev. Lett. 94 (2005) 037402

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, Th Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Magnetic response of split-ring resonators in the far infrared frequency regime, Optics Letters 30 (2005) 1348.

S. Zhang, W. Fan, N. C. Panoiu, K. M. Malloy, R.M. Osgood, and S. R. J. Brueck, Experimental demonstration of near-infrared negative-index metamaterials, Phys. Rev. Lett. 95 (2005) 137404

Zhang S, Fan W, Minhas BK, Frauenglass A, Malloy KJ and Brueck SRJ (2005) Midinfrared resonant magnetic nanostructures exhibiting a negative permeability, Phys. Rev. Lett. 94, 037402

C. Enkrich, S. Linden, M. Wegener, S. Burger, L. Zswchiedrich, F. Schmidt, J. Zhou, T. Koschny and C. M. Soukoulis, Magnetic metamaterials at telecommunication and visible frequencies, Phys. Rev. Lett. 95 (2005) 203901.

H. Chen, L. Ran,J. Huangfu, X.M. Zhang, K. Chen, T.M. Grzegorczyk, and J.A. Kong, Left-handed materials composed of only S-shaped resonators, Phys Rev E 70 (2004) 057605.

T. J. Yen, W. J. Padilla, N. Fang, D.C. Vier, D.R. Smith, J.B. Pendry, D.N. Basov, Terahertz Magnetic Response from Arti¯cial Materials, Science 303 (2004) 1494

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, C. M. Soukoulis, Magnetic Response of Metamaterials at 100 Terahertz, Science 306 (2004) 1351

K.C. Huang, M.L. Povinelli, and J.D. Joannopoulos, Applied Physics Lett. 85 (2004) 543.

D.R. Smith, P. Kolinko, and D. Schurig, J. Opt. Soc. Am. B 21 (2004) 1032.

X. Chen, T. Grzegorczyk, B.-E. Wu, J. Pacheko, and J. A. Kong, Robust method to retrieve the constitutive effective parameters of metamaterials, Phys. Rev. E, 70 (2004) 016608.

S. O Brien, D. McPeake, S.A. Ramakrishna, and J.B. Pendry, Phys. Rev. B, 69 (2004) 241101.

N. Katsarakis, T. Koschny, M. Kafesaki, E.N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B, 70 (2004) 201101(R).

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, Appl. Phys. Lett. 84, (2004) 2943.

C.R. Simovski, B. Sauviac, Physical Review E, Vol. 70, 046607 (1-11), 2004.

Koschny T, Markos P, Smith D R and Soukoulis C M (2003) Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials, Phys. Rev. E, 58, 065602

C.R. Simovski, S. He, Physics Letters A 311 (2003) 254

P.A. Belov, C.R. Simovski, S.A. Tretyakov, Physical Review E, vol. 67, 056622(1-8), 2003.

P. Markos and C. M. Soukoulis,, Numerical studies of left-handed materials and arrays of split ring resonators, Phys. Rev. E 65 (2002) 036622.

S. O'Brien and J.B. Pendry, J. Phys. Condens. Matter, 14 (2002) 4035.

D.R. Smith, S. Schultz, P. Markos and C. Soukoulis, Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients, Phys. Rev. B. 65 (2002) 195104.

S. O'Brien and J.B. Pendry, J. Phys.: Condens. Matter, 14 (2002) 6383.


Standard electromagnetic characterization approaches (measurement techniques and retrieval of material parameters for samples of effectively continuous media)


K. Kadiroglu and U.C. Hasar, A highly accurate microwave method for permittivity determination using corrected scattering parameter measurements, J. of Electromagnetic Waaves and Applic., vol. 24, 2179-2189, 2010.

J. Sheen, Meas. Sci. Technol. 20 (2009) 042001

Kh. Chalapat, K. Sarvala, J. Li, G.S. Paraoanu, IEEE Transactions on Microwave Theory and Techniques 57 (2009) 2257

H.-C. Scheer, in: H.S. Nalwa(Ed.), Handbook of Thin Film Materials, vol. 5, Academic Press, New York 2002, 160

V.S. Merkulov, Optics and Spectroscopy 103 (2007) 629

G. E. Jellison, Thin Solid Films 450 (2004) 42

J. P. Rolland, J. Am. Chem. Soc. (2004) 126 (8), 2322

J. Krupka, IEEE Trans. Microw. Theory Techn. 47 (1999)

G.E. Jellison, Thin Solid Films 313/314 (1998) 193

J.H. Fendler, F.C. Meldrum, Advanced Materials, 7 (1995) 607

J. Baker-Jarvis, E.J. Vanzura, and W.A. Kissick IEEE Trans. Microw. Theory Tech., 38 (1990) 1096.

D.K. Ghodgaonkar, V.V. Varadan, V.K. Varadan, Freespace measurement of complex permittivity and complex
permeability of magnetic materials at microwave frequencies, IEEE Trans Instrum Meas 1990, 39(2), 387–394.

D.K. Ghodgaonkar, V.V. Varadan, V.K. Varadan, Freespace measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies, IEEE Trans Instrum Meas 1990, 39(2), 387–394.

L.P. Lighthart, A fast computational technique for accurate permittivity determination using transmission line methods, IEEE Trans. on MTT, vol. 31, no. 3, pp. 249-254, 1983.


S.S. Stuchly and M. Matuszewski, A combined total reflection-transmission method in application to dielectric spectroscopy, IEEE Trans. Instrum. Meas., vol. IM-27, no. 3, pp. 285-288, 1978.


W.B. Weir, Automatic measurement of complex dielectric constant and permeability at microwave frequencies, IEEE Proceedings, vol. 62, no. 1, pp. 33-36, 1974.


A.M. Nicolson, G.F. Ross, Measurement of intrinsic properties of materials by time-domain techniques, IEEE Transactions on Instrumentation and Measurement IM-19 (1970) 377–382.

A.M. Nicolson, G.F. Ross, Measurement of intrinsic properties of materials by time-domain techniques, IEEE Transactions on Instrumentation and Measurement IM-19 (1970) 377–382.

A.M. Nicolson and G.F. Ross, IEEE Trans. Instrum. Meas., 17 (1968) 395.

M. Sucher, Handbook of Microwave Measurements, vol 2, Brooklyn Polytechnic Press 1963

S.B. Cohn, Microwave measurements on metallic delay media, Proc. IRE, vol. 41, pp. 1177-1183, 1953.


H. Schopper, Z. Phys. 132 (1952) 146

Classical works on surface effects influencing the electromagnetic characterization of layers


O. S. Heavens, Optical Properties of Thin Solid Films (Dover Publications, New York, 1991).


T. B. A. Senior, Combined Resistive and Conductive Sheets, IEEE Trans. Antennas Propag. 33, 577-579, 1985


Philpott, M. R.; Sherman, P. G. Excitons and polaritons in monomolecular layers. Phys. Rev. B (1975) 12, 5381–5394.


M. E. Philpott, Reflection of light by a semi-infinite dielectric, J. Chem. Phys. 60, 1410-1419, 1974.


G.D. Mahan, G. Obermair, Polaritons at Surfaces, Phys. Rev. 183, 834–841,1969


J. Brown and J.S. Seeley, The fields associated with an interface between free space and an artificial dielectric, Proc. IEE (London), vol. 105C, pp. 465-471, 1958


B. A. SotskiÑ– and F. I. Fedorov, Optika i Spektroskopia 4 (2), 365 (1958) [in Russian].


D. V. Sivukhin, Sov. Phys. JETP 3, 269 (1956)


D. V. Sivukhin, Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 21, 267 (1951) [in Russian].


D.V. Sivukhin, Molecular theory of the reflection and refraction of light, Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 18 (1948) 976–994 [in Russian].


W. Shockley, Phys. Rev. 56, 317 (1939).


C. Strachan, Proc. Camb. Phil. Soc. 29, 116 (1933).


I. E. Tamm, Z. Phys. 76, 849 (1932).


C. V. Raman and L. A. Ramdas, Philos. Mag. 3, 220 (1927).


C. V. Raman and L. A. Ramdas, Proc. Roy. Soc. (London), Ser. A 108, 561 (1925).


C. Maclaurin, Proc. Roy. Soc. (London), Ser. A 76, 149 (1905).


P. K. L. Drude, Theory of Optics (Longmans, London, 1902).


P. Drude, Wied. Ann. 43, 146 (1891).



Classical homogenization models for natural and composite media (long-wavelength limt)


Jackson J D (1999) Classical Electrodynamics 3rd ed. (New York: Wiley)


J. Schwinger, L. L. De Raad, K. Milton, and W. Tsai, Classical Electrodynamics (Perseus Books, Reading,


Collin R E (1991) Field Theory of Guided Waves (New York: IEEE Press), chapter 12


B.U. Felderhof and R.B. Jones, Effective dielectric constant of dilute suspension of spheres, Phys. Rev. B, 39, 5669-5677, 1989


Draine, B. T. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. (1988), 333, 848–872.


B. Cichocki and B.U. Felderhof, Dielectric Constant of Polarizable, Nonpolar Fluids and Suspensions, Journal of Statistical Physics, Vol. 53, 500-512, 1988


B.U. Felderhof and R.B. Jones,  Multipolar Corrections to the Clausius-Mossotti Formula for the Effective Dielectric Constant of a Polydisperse Suspension of Spheres, Z. Phys. B - Condensed Matter 62, 231-237, 1986


Landau L D and Lifshits E M (1984) Electrodynamics of Continuous Media 2nd edn (Oxford: Pergamon)


McPhedran R C and McKenzie D R (1978) The conductivity of lattices of spheres: I. The simple cubic lattice Proc. R. Soc. London A 359, 45


McKenzie D R, McPhedran R C and Derrick G H (1978) The conductivity of lattices of spheres: II The body-centred cubic lattice Proc. R. Soc. A 362, 211


J. Sipe and J. V. Kranendonk, Phys. Rev. A 9, 1806 (1974).


Purcell, E. M.; Pennypacker, C. R. Scattering and Absorption of Light by Nonspherical Dielectric Grains. Astrophys. J. (1973) 186, 705–714.


E. A., Lupashko, V. K. Miloslavskii, I. N. Shklyarevskii, Use of the Kramers-Kronig dispersion relationships to calculate the phase of the wave reflected from thin dielectric layers, Opt. Spectrosc. 29, 419-422,1970.


J. S. Toll, Causality and the Dispersion Relation: Logical Foundations, Phys. Rev. 104, 1760-1770, 1956.


Born M and Huang K (1954) Dynamic Theory of Crystal Lattices (Oxford: Oxford University Press)


Lorentz H A (1916) The Theory of Electrons and its Applications to the Phenomena of Light and Radiant Heat (Leipzig: Teubner)


Lorentz H A (1910) On the scattering of light by molecules, Proc. R. Netherlands Acad. Arts Sci. 13 92


Rayleigh Lord (1892) On the influence of obstacles arranged in regular order upon the properties of the medium Phil. Mag. 34, 481