volume | PIER Journals

Abstract

In this part, we develop an efficient algorithm for the computation of the complete transmitted and reflected electromagnetic fields in generic 2D arrays of carbon nanotubes (CNTs). The method relies on first approaching individual CNTs using an effective-boundary condition based on a proper quantum conductivity model. An exact eigenmode solution is obtained for this problem for both single-wall and multi-wall CNTs, which then is integrated with Floquet mode theory to handle periodic arrays of CNTs. The algorithm's convergence rate is accelerated using special methods and then applied to the analysis and design of various multi-layered CNT-based photonic crystals. It is shown that the proposed method can clearly demarcate the intrinsic resonances due to electronic transitions in individual CNTS and new sets of geometric resonances produced by the array environment. The algorithm can be used to analyze measured optical spectra of CNT composites and to design new optical bandgap devices.

1. Iijima, S., "Helical microtabules of graphitic carbon," Nature, Vol. 354, 56-58, 1991.
doi:10.1038/354056a0

2. Meyyappan, M., Carbon Nanoyubes: Sceince and Applications, CRC Press, 2005.

3. Poole, C. P. and F. J. Owens, Introduction to Nanotechnology, Wiley-Interscience, 2003.

4. Smalley, R. E., M. S. Dresselhaus, G. Dresselhaus, and P. Avouris, Carbon Nanotubes: Synthesis, Structure, Properties and Applications, Springer, 2001.

5. Kempa, K., et al. "Photonic crystals based on periodic arrays of aligned carbon nanotubes," Nano Letters, Vol. 3, No. 1, 13-18, 2003.
doi:10.1021/nl0258271

6. Lidorikis, E. and A. C. Ferrari, "Photonics with multiwall carbon nanotube arrays," ACS Nano, Vol. 3, No. 5, 1238-1248, 2009.
doi:10.1021/nn900123a

7. Butt, H., Q. Dai, T. D. Wilkinson, and G. A. J. Amaratunga, "Negative index photonic crystal lenses based on carbon nanotube arrays," Photonics and Nanostructures --- Fundamentals and Applications, Vol. 10, No. 4, 499-505, October 2012.
doi:10.1016/j.photonics.2012.04.003

8. Slepyan, G. Y., et al. "Electronic and electromagnetic properties of nanotubes," Phys. Rev. B, Vol. 57, No. 16, 9485-9497, April 1998.
doi:10.1103/PhysRevB.57.9485

9. Slepyan, G. Y., et al. "Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions, and surface wave propagation," Phys. Rev. B, Vol. 60, No. 24, 17136-17149, December 1999.
doi:10.1103/PhysRevB.60.17136

10. Slepyan, G. Ya., M. V. Shuba, and S. A. Maksimenko, "Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas," Phys. Rev. B, Vol. 73, 195416-19526, May 2006.
doi:10.1103/PhysRevB.73.195416

11. Mikki, S. M. and A. Kishk, "Theory of optical scattering by carbon nanotubes," Microwave & Optical Technology Letters, Vol. 49, No. 10, 2360-2364, October 2007.
doi:10.1002/mop.22768

12. Mikki, S. M. and A. A. Kishk, "Derivation of the dielectric tensor of carbon nanotubes using lattice dynamics formalism," Progress In Electromagnetics Research B, Vol. 9, 1-26, 2008.
doi:10.2528/PIERB08082301

13. Mikki, S. and A. Kishk, "Electromagnetic scattering by multi-wall carbon nanotube using effective-boundary condition approach," IEEE Antennas & Propagation/URSI International Symposium, 2008.

14. Mikki, S. M. and A. A. Kishk, "Electromagnetic scattering by multi-wall carbon nanotubes using effective-boundary condition approach: Theory and applications," Progress In Electromagnetics Research B, Vol. 17, 49-67, 2009.
doi:10.2528/PIERB09040605

15. Mikki, S.M. and A. A. Kishk, "A symmetry-based formalism for the electrodynamics of nanotubes," Progress In Electromagnetics Research, Vol. 86, 111-134, 2008.
doi:10.2528/PIER08081704

16. Mikki, S. M. and A. A. Kishk, "Various homogenization formalisms for carbon nanotube composites," International URSI Meeting, Ottawa, July 21-26, 2007.

17. Mikki, S. M. and A. Kishk, "Mean-field electrodynamic theory of aligned carbon nanotube composites," IEEE Trans. Antennas Progat., Vol. 57, No. 5, 1412-1419, May 2009.
doi:10.1109/TAP.2009.2016687

18. Chew, W. C., Waves and Fields in Inhomogeneous Media, re-print Ed., IEEE Press, 1999.
doi:10.1109/9780470547052

19. Kushta, K. and K. Yausumoto, "Electromagnetic scattering from periodic arrays of two circular cylinders per unit cell," Progress In Electromagnetics Research, Vol. 29, 69-85, 2000.
doi:10.2528/PIER99103101

20. Yausumoto, K. and K. Yoshitomi, "Efficient calculation of lattice sums for free-space periodic Green’s functions," IEEE Trans. Antennas & Propagation, Vol. 47, 1050-1055, June 1999.
doi:10.1109/8.777130

21. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, 1965.

22. Collins, P. G., "Defects and disorder in carbon nanotubes," Oxford Handbook of Nanoscience and Technology: Frontiers and Advances, A. V. Narlikar, & Y. Y. Fu, (Eds.), Oxford Univ. Press, Oxford, 2009.

23. Nho, H. W., Y. Kalegowda, H.-J. Shin, and T. H. Yoon, "Nanoscale characterization of local structures and defects in photonic crystals using synchrotron-based transmission soft X-ray microscopy," Scientific Reports, Vol. 6, 24488, 2016.
doi:10.1038/srep24488

24. Liew, S. F., S. Knitter, W. Xiong, and H. Cao, "Photonic crystals with topological defects," Phys. Rev. A, Vol. 91, 023811, February 6, 2015.

Prof. Said Mikki

Dr. Ahmed A. Kishk