Wave Propagation in Nanocomposite Materials
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Abstract
Electromagnetic wave propagation is first analyzed in a composite material mde of chiral nano-inclusions embedded in a dielectric, with the help of Maxwell-Garnett formula for permittivity and permeability and its reciprocal for chirality. Then, this composite material appears as an homo-geneous isotropic chiral medium which may be described by the Post constitutive relations. We analyze the propagation of an harmonic plane wave in such a medium and we show that two different modes can propagate. We also discuss harmonic plane wave scattering on a semi-infinite chiral composite medium. Then, still in the frame of Maxwell-Garnett theory, the propagation of TE and TM fields is investigated in a periodic material made of nano dots immersed in a dielectric. The periodic fields are solutions of a Mathieu equation and such a material behaves as a diffraction grating.
- M. Khan, A. K. Sood, F. L. Deepak and C. N. R. Rao, “Nanorotors Using Asymmetric in Organic Nanorods in an Optical Trap,” Nanotechnology, Vol. 17, No. 11, 2006, pp. S287-S290.
- X. M. Guo, C. Jiang and T. S. Shi, “Prepared Chiral Nanorods of a Cobalt,” Inorganic Chemistry, Vol. 46, No. 12, 2007, pp. 4766-4768.
- J. C. Maxwell-Garnett, “Colours in Metal Glasses and Metallic Films,” Philosophical Transactions of the Royal Society of London A, Vol. 203, No. 359-371, 1904, pp. 385-420.
- C. A. Grimes, “Calculation of the Effective Electromag-netic properties of Granular Materials,” in: A. Lakhtakia, Ed., Essays on the Formal Aspects of Electromagnetic Theory, World Scientific, Singapore, 1993, pp. 699-746.
- L. Tsang and J. A. Kong, “Scattering of Electromagnetic Waves: Advanced Topics,” Wiley Series in Remote Sensing, Wiley, New York, 2001.
- P. Mallet, C. A. Guerin and A. Sentenac, “Maxwell-Gar- nett Mixing Rule in the Presence of Multiple Scattering,” Physical Review B, Vol. 72, No. 1, 2005, p. 014205.
- B. Shanker and A. Lakhtakia, “Extended Maxwell-Garnett Model for Chiral-in-Chiral Composites,” Journal of Physics D: Applied Physics, Vol. 26, No. 10, 1993, pp. 1746- 1758.
- A. Lakhtakia, V. K. Varadan and V. V. Varadan, “On the Maxwell-Garnett Model of Chiral Composite,” Journal of Materials Research, Vol. 8, No. 4, 1993, pp. 917-922.
- E. J. Post, “Formal Structure of Electromagnetics,” North- Holland Publications, Amsterdam, 1962.
- A. Lakhtakia,V. K. Varadan and V. V. Varadan, “Time- Harmonic Electromagnetic Fields in Chiral Media,” Springer, Berlin, 1989.
- S. Bassiri, C. H. Papas and N. Engheta, “Electromagnetic Wave Propagation through a Dielectric-Chiral Interface and through a Chiral Slab,” Journal of the Optical Society of America A, Vol. 5, No. 9, 1988, pp. 1450-1459.
- M. Born and E. Wolf, “Principles of Optics,” Pergamon Press, Oxford, 1965.
- P. Hillion, “Light Beam Shifts in Total Reflection,” Optics Communications,Vol. 266, No. 1, 2006, pp. 336-341.
- E. T. Whittaker and G. N. Watson, “A Course of Modern Analysis,” University Press, Cambridge, 1962.
- A. Erdelyi, “Higher Transcendental Functions,” McGraw- Hill, New York, Vol. 3, 1955.
- P. Hillion, “Theoy of Electromagnetic Wave Propagation in a Longitudinally Periodic Cylinder,” European Physical Journal B, Vol. 62, No. 4, 2008, pp. 477-480.