Linear and nonlinear homogenized composite mediums as metamaterials

Electromagnetics

Volumn 25, Issue 5, 2005, Pages 461-481

  Mackay, Tom G ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Bianisotropy; Cubic nonlinearity; Group velocity; Strong property fluctuation theory; Voigt waves

Indexed keywords

ANISOTROPY; ELECTROMAGNETISM; MAXWELL EQUATIONS; PERTURBATION TECHNIQUES; VECTORS; WAVE PROPAGATION;

BIANISOTROPY; CUBIC NONLINEARITY; GROUP VELOCITY; STRONG-PROPERTY-FLUCTUATION THEORY; VOIGT WAVES;

COMPOSITE MATERIALS;

EID: 22944488568     PISSN: 02726343     EISSN: None     Source Type: Journal    
DOI: 10.1080/02726340590957425     Document Type: Article

References (68)

1. Born, M., & E. Wolf. 1980. Principles of optics, 6th ed. Oxford, UK: Pergamon.
2. Boyd, R. W. 2003. Nonlinear optics, 2nd ed. London: Academic Press.
3. Boyd, R. W., R. J. Gehr, G. L. Fischer, & J. E. Sipe. 1996. Nonlinear optical properties of nanocomposite materials. Pure Appl. Opt. 5:505-512.
4. Bruggeman, D. A. G. 1935. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen, I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann. Phys. Lpz. 24:636-664.
5. Chen, H.C. 1983. Theory of electromagnetic waves. New York: McGraw-Hill.
6. Engheta, N., D. L. Jaggard, & M. W. Kowarz. 1992. Electromagnetic waves in Faraday chiral media. IEEE Trans. Antennas Propagat. 40:367-374.
7. Frisch, U. 1970. Wave propagation in random media. In Probabilistic methods in applied mathematics, Vol. 1, ed. A. T. Bharucha-Reid. London: Academic Press.
8. Genchev, Z. D. 1992. Anisotropic and gyrotropic version of Polder and van Santen's mixing formula. Waves Random Media 2:99-110.
9. Gerardin, J., & A. Lakhtakia. 2001. Conditions for Voigt wave propagation in linear, homogeneous, dielectric mediums. Optik 112:493-495.
10. Hagedorn, R. 1964. Introduction to field theory and dispersion relations. Oxford, UK: Pergamon.
11. Hashin, Z., & S. Shtrikman. 1962. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33:3125-3131.
12. Hu, L., & Z. Lin. 2003. Imaging properties of uniaxially anisotropic negative refractive index materials. Phys. Lett. A 313:316-324.
13. Jackson, J. D. 1999. Classical electrodynamics, 3rd ed. New York: Wiley.
14. Kärkkäinen, M. K. 2003. Numerical study of wave propagation in uniaxially anisotropic Lorentzian backward-wave slabs. Phys. Rev. E 68:026602.
15. Lakhtakia, A. 1994. Beltrami fields in chiral media. World Scientific: Singapore.
16. Lakhtakia, A., ed. 1996. Selected papers on linear optical composite materials. Bellingham, WA: SPIE Optical Engineering Press.
17. Lakhtakia, A. 1998. Incremental Maxwell Garnett formalism for homogenizing particulate composite media. Microw. Opt. Technol. Lett. 17:276-279.
18. Lakhtakia, A. 2001. Application of strong permittivity fluctuation theory for isotropic, cubically nonlinear, composite mediums. Opt. Commun. 192:145-151.
19. Lakhtakia, A. 2004. On the genesis of Post constraint in modern electromagnetism. Optik 115: 151-158.
20. Lakhtakia, A., & T. G. Mackay. 2004. Towards gravitationally assisted negative refraction of light by vacuum. J. Phys. A: Math. Gen. 37:L505-L510; corrigendum 37:12093.
21. Lakhtakia, A., M. W. McCall, & W. S. Weiglhofer. 2003. Negative phase-velocity mediums. In Introduction to complex mediums for optics and electromagnetics, ed. W. S. Weiglhofer & A. Lakhtakia. Bellingham, WA: SPIE Press.
22. Lakhtakia, A., & B. Shanker. 1993. Beltrami fields within continuous source regions, volume integral equations, scattering algorithms, and the extended Maxwell-Garnett model. Int. J. Appl. Electromag. in Mater. 4:65-82.
23. Lakhtakia, A., & W. S. Weiglhofer. 1996. Constraint on linear, spatiotemporally nonlocal, spatiotemporally nonhomogeneous constitutive relations. Int. J. Infrared Millim. Waves 17:1867-1878.
24. Lakhtakia, A., & W. S. Weiglhofer. 2000. Maxwell Garnett formalism for weakly nonlinear, bianisotropic, dilute, particulate composite media. Int. J. Electron. 87:1401-1408.
25. Lakhtakia, M. N., & A. Lakhtakia. 2001. Anisotropic composite materials with intensity-dependent permittivity tensor: The Bruggeman approach. Electromagnetics 21:129-138.
26. Lax, B., & K. J. Button. 1962. Microwave ferrites and ferrimagnetics. New York: McGraw-Hill.
27. 2 composite films measured on a femtosecond time scale. Appl. Phys. Lett. 72:1817-1819.
28. Mackay, T.G. 2003a. Geometrically derived anisotropy in cubically nonlinear dielectric composites. J. Phys. D: Appl. Phys. 36:583-591.
29. Mackay, T. G. 2003b. Homogenization of linear and nonlinear complex composite materials. In Introduction to complex mediums for optics and electromagnetics, ed. W. S. Weiglhofer and A. Lakhtakia. Bellingham, WA: SPIE Press.
30. Mackay, T.G. 2004. Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites. Waves Random Media 14:485-498.
31. Mackay, T. G., & A. Lakhtakia. 2003. Voigt wave propagation in biaxial composite materials. J. Opt. A: Pure Appl. Opt. 5:91-95.
32. Mackay, T. G., & A. Lakhtakia. 2004a. Correlation length facilitates Voigt wave propagation. Waves Random Media 14:L1-L11.
33. Mackay, T. G., & A. Lakhtakia. 2004b. Enhanced group velocity in metamaterials. J. Phys. A: Math. Gen. 37:L19-L24.
34. Mackay, T.G., & A. Lakhtakia. 2004c. A limitation of the Bruggeman formalism for homogenization. Opt. Commun. 234:35-42.
35. Mackay, T. G., & A. Lakhtakia. 2004d. Negative phase velocity in a uniformly moving, homogeneous, isotropic, dielectric-magnetic medium. J. Phys. A: Math. Gen. 37:5697-5711.
36. Mackay, T. G., & A. Lakhtakia. 2004e. Plane waves with negative phase velocity in Faraday chiral mediums. Phys. Rev. E 69:026602.
37. Mackay, T. G., A. Lakhtakia, & W. S. Weiglhofer. 2000. Strong-property-fluctuation theory for homogenization of bianisotropic composites: Formulation. Phys. Rev. E 62:6052-6064; erratum: 63:049901 (2001).
38. Mackay, T. G., A. Lakhtakia, & W. S. Weiglhofer. 2001a. Ellipsoidal topology, orientation diversity and correlation length in bianisotropic composite mediums. Arch. Elektron. Übertr. 55:243-251.
39. Mackay, T. G., A. Lakhtakia, & W. S. Weiglhofer. 2001b. Homogenisation of similarly oriented, metallic, ellipsoidal inclusions using the bilocal-approximated strong-property-fluctuation theory. Opt. Commun. 197:89-95.
40. Mackay, T. G., A. Lakhtakia, & W. S. Weiglhofer. 2001c. Third-order implementation and convergence of the strong-property-fluctuation theory in electromagnetic homogenization. Phys. Rev. E 64:066616.
41. Mackay, T. G., A. Lakhtakia, & W. S. Weiglhofer. 2002. Homogenisation of isotropic, cubically nonlinear, composite mediums by the strong-permittivity-fluctuation theory: Third-order considerations. Opt. Commun. 204:219-228.
42. Mackay, T. G., A. Lakhtakia, & W. S. Weiglhofer. 2003. The strong-property-fluctuation theory for cubically nonlinear, isotropic chiral composite mediums. Electromagnetics 23:455-479.
43. Maxwell Garnett, J. C. 1904. Colours in metal glasses and in metallic films. Phil. Trans. R. Soc. Lond. A 203:385-420.
44. McCall, M. W., A. Lakhtakia, & W. S. Weiglhofer. 2002. The negative index of refraction demystified. Eur. J. Phys. 23:353-359.
45. Michel, B. 1997. A Fourier space approach to the pointwise singularity of an anisotropic dielectric medium. Int. J. Appl. Electromagn. Mech. 8:219-227.
46. Michel, B., & A. Lakhtakia. 1995. Strong-property-fluctuation theory for homogenizing chiral particulate composites. Phys. Rev. E 51:5701-5707.
47. Michel, B., A. Lakhtakia, & W. S. Weiglhofer. 1998. Homogenization of linear bianisotropic particulate composite media - Numerical studies. Int. J. Appl. Electromag. Mech. 9:167-178; erratum: 10:537-538 (1999).
48. Michel, B., A. Lakhtakia, W. S. Weiglhofer, & T. G. Mackay. 2001. Incremental and differential Maxwell Garnett formalisms for bi-anisotropic composites. Compos. Sci. Technol. 61:13-18.
49. Michel, B., & W. S. Weiglhofer. 1997. Pointwise singularity of dyadic Green function in a general bianisotropic medium. Arch. Elektr. Übertrag. 51:219-223; erratum: 52:310 (1998).
50. Post, E. J. 1997. Formal structure of electromagnetics. New York: Dover.
51. Ryzhov, Yu. A., & V. V. Tamoikin. 1970. Radiation and propagation of electromagnetic waves in randomly inhomogeneous media. Radiophys. Quantum Electron. 14:228-233.
52. Shelby, R. A., D. R. Smith, & S. Schultz. 2001. Experimental verification of a negative index of refraction. Science 292:77-79.
53. Schelm, S., G. B. Smith, G. Wei, A. Vella, L. Wieczorek, K.-H. Muller, & B. Raguse. 2004. Double effective medium model for the optical properties of self-assembled gold nanoparticle films cross-linked with alkane dithiols. Nano Lett. 4:335-339.
54. Sherwin, J. A., & A. Lakhtakia. 2002. Bragg-Pippard formalism for bianisotropic particulate composites. Microwave Opt. Tech. Lett. 33:40-44.
55. Smith, G. B. 2003. Nanostructured thin films. In Introduction to complex mediums for optics and electromagnetics, ed. W. S. Weiglhofer and A. Lakhtakia. Bellingham, WA: SPIE Press.
56. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, & S. Schultz. 2000. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84:4184-4187.
57. Sølna, K., & G. W. Milton. 2002. Can mixing materials make electromagnetic signals travel faster? SIAM J. Appl. Math. 62:2064-2091.
58. Tsang, L., & J. A. Kong. 1981. Scattering of electromagnetic waves from random media with strong permittivity fluctuations. Radio Sci. 16:303-320.
59. Veselago, V.O. 1968. The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp. 10:509-514.
60. Veselago, V. G. 2003. Electrodynamics of media with simultaneously negative electric permittivity and magnetic permeability. In Advances in electromagnetics of complex media and metamaterials, ed. S. Zouhdi, A. Sihvola, & M. Arsalane. Dordrecht, The Netherlands: Kluwer.
61. Voigt, W. 1902. On the behaviour of pleochroitic crystals along directions in the neighbourhood of an optic axis. Phil. Mag. 4:90-97.
62. Walser, R. M. 2003. Metamaterials: An introduction. In Introduction to complex mediums for optics and electromagnetics, ed. W. S. Weiglhofer and A. Lakhtakia. Bellingham, WA: SPIE Press.
63. Ward, L. 1995. The optical constants of bulk materials and films, 2nd ed. Bristol, UK: Adam Hilger.
64. Weiglhofer, W. S., & A. Lakhtakia. 1998. The correct constitutive relations of chiroplasmas and chiroferrites. Microw. Opt. Technol. Lett. 17:405-408.
65. Weiglhofer, W. S., A. Lakhtakia, & B. Michel. 1997. Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium. Microw. Opt. Technol. Lett. 15:263-266; erratum: 22:221 (1999).
66. Weiglhofer, W. S., A. Lakhtakia, & B. Michel. 1998. On the constitutive parameters of a chiroferrite composite medium. Microwave Opt. Technol. Lett. 18:342-345.
67. Weiglhofer, W. S., & T. G. Mackay. 2000. Numerical studies of the constitutive parameters of a chiroplasma composite medium. Arch. Elektr. Übertrag. 54:259-265.
68. Zhuck, N. P. 1994. Strong-fluctuation theory for a mean electromagnetic field in a statistically homogeneous random medium with arbitrary anisotropy of electrical and statistical properties. Phys.Rev.B 50:15636-15645.