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.
References
[1]
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.
[2]
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.
[3]
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.
[4]
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.
[5]
L. Tsang and J. A. Kong, “Scattering of Electromagnetic Waves: Advanced Topics,” Wiley Series in Remote Sensing, Wiley, New York, 2001.
[6]
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.
[7]
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.
[8]
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.
[9]
E. J. Post, “Formal Structure of Electromagnetics,” North- Holland Publications, Amsterdam, 1962.
[10]
A. Lakhtakia,V. K. Varadan and V. V. Varadan, “Time- Harmonic Electromagnetic Fields in Chiral Media,” Springer, Berlin, 1989.
[11]
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.
[12]
M. Born and E. Wolf, “Principles of Optics,” Pergamon Press, Oxford, 1965.
[13]
P. Hillion, “Light Beam Shifts in Total Reflection,” Optics Communications,Vol. 266, No. 1, 2006, pp. 336-341.
[14]
E. T. Whittaker and G. N. Watson, “A Course of Modern Analysis,” University Press, Cambridge, 1962.
[15]
A. Erdelyi, “Higher Transcendental Functions,” McGraw- Hill, New York, Vol. 3, 1955.
[16]
P. Hillion, “Theoy of Electromagnetic Wave Propagation in a Longitudinally Periodic Cylinder,” European Physical Journal B, Vol. 62, No. 4, 2008, pp. 477-480.
[17]
J. Zhang. M. T. Albelda, Y. Liu and J. W. Canary, “Chiral Nanotechnology,” Chirality, Vol. 17, No. 7, 2005, pp. 404-420.
[18]
C. Inserra, V. Tournat and V. Gusev, “A Method of Con- trolling Wave Propagation in Initially Spatially Periodic Media,” Europhysics Letters, Vol. 78, No. 4, 2007, p. 44001.
[19]
J. D. Joannopoulos, R. D. Meade and J. N. Wynn, “Pho- tonic Crystals,” University Press, Princeton, 1995.
[20]
C. Lopez, “Material Aspects of Photonic Crystals,” Ad- vanced Materials, Vol. 15, No. 20, 2003, pp. 1679-1704.
[21]
B. Van Der Pol and H. Bremmer, “Operational Calculus,” Academic Press, Cambridge, 1959.
[22]
M. Neviere and E. Popov, “Light Propagation in Periodic Media,” Marcel Dekker, Basel, 2005.
[23]
C. A. Poland, R. Duffin, I. Kinloch, A. Maynard, et al., “Carbon Nanotubes Introduced into the Abdominal Cavity of Mice Show Asbestos-Like Pathogenicity in a Pilot Study,” Nature Nanotechnology, Vol. 3, 2008, pp. 423-428.
[24]
S. Kawata, “Near-Field Optics and Surface Plasmon Polariton,” Springer, Berlin, 2001.
[25]
[N. Yamaguchi, “High Order Bragg Diffraction by Dielectric Grating,” Electronics and Communications in Japan, Vol. 69, No. 8, 2007, pp. 112-121.
