2012-06-19
Electric-Field Distributions of Dielectric Single Layers of Spheres with Different Compactness
By
Progress In Electromagnetics Research M, Vol. 25, 13-26, 2012
Abstract
The internal electric-field distribution from single layers of dielectric spheres with high refractive index (n=2.65) has been analyzed for a number of different compactness cases by FDTD (Finite-Difference Time-Domain) method. The field distributions from the transmission spectra were compared with the internal electric-field distribution of the Mie modes of an isolated sphere. In general, the agreement is very good in almost all cases studied. The results show that TE and TM Mie modes are the origin of the resonances in the transmission spectra of the single layers. The resonances of the monolayer attributed to TE11 and TM11 Mie modes are only excited for compactness values lower than 0.38, suggesting a dependence of periodical arrangement effects for these modes. Moreover, the field distribution corresponding to some of the dips in the spectrum cannot be directly attributed to Mie modes (TE21). The result indicates these are formed by degenerated or weakly coupled Mie modes induced by the periodic structure.
Citation
Angel Andueza, Paola Morales, and Joaquín Sevilla, "Electric-Field Distributions of Dielectric Single Layers of Spheres with Different Compactness," Progress In Electromagnetics Research M, Vol. 25, 13-26, 2012.
doi:10.2528/PIERM12042012
References

1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, No. 20, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059        Google Scholar

2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, No. 23, 2486-2489, 1987.
doi:10.1103/PhysRevLett.58.2486        Google Scholar

3. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Cristal, Molding the Flow of Light, Princeton University Press, New Yersey, 2005.

4. Soukoulis, C. M., Photonic Band Gap Materialst, Kluwer Academic Publishers, Dordrecht, 1996.
doi:10.1007/978-94-009-1665-4

5. Miyazaki, H. and K. Ohtaka, "Near-field images of a monolayer of periodically arrayed dielectric spheres," Phys. Rev. B, Vol. 58, No. 11, 6920-6937, 1998.
doi:10.1103/PhysRevB.58.6920        Google Scholar

6. Kondo, T., S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, "Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres," Phys. Rev. B, Vol. 70, No. 23, 1-6, 2004.        Google Scholar

7. Kondo, T., M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, "Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy," Phys. Rev. B, Vol. 3, 331111-331114, 2002.        Google Scholar

8. Kurokawa, Y., Y. Jimba, and H. Miyazaki, "Optical band structure and near-fieldintensity of a periodically arrayed monolayer of dielectric spheres on dielectric substrate of finite thickness," Phys. Rev. B, Vol. 70, No. 15, 1551171-1551179, 2004.
doi:10.1103/PhysRevB.70.155107        Google Scholar

9. Kurokawa, Y., Y. Jimba, and H. Miyazaki, "Internal electric-field intensity distribution of a monolayer of periodically arrayed dielectric spheres," Phys. Rev. B, Vol. 70, No. 15, 1550171-1550175, 2004.
doi:10.1103/PhysRevB.70.155107        Google Scholar

10. Kurokawa, Y., H. Miyazaki, and Y. Jimba, "Light scattering from a monolayer of periodically arrayed dielectric spheres on dielectric substrates," Phys. Rev. B, Vol. 65, No. 20, 2011021-2011024, 2002.
doi:10.1103/PhysRevB.65.201102        Google Scholar

11. Kurokawa, Y., H. Miyazaki, H. T. Miyazaki, and Y. Jimba, "Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres," J. Phys. Soc. Jpn., Vol. 74, No. 3, 924-929, 2005.
doi:10.1143/JPSJ.74.924        Google Scholar

12. Miyazaki, H. T., H. Miyazaki, K. Ohtaka, and T. Sato, "Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope," J. Appl. Phys., Vol. 87, No. 10, 7152-7158, 2000.
doi:10.1063/1.372962        Google Scholar

13. Ohtaka, K., "Scattering theory of low-energy photon diffraction," J. Phys. C, Vol. 13, No. 4, 667-680, 1980.
doi:10.1088/0022-3719/13/4/022        Google Scholar

14. Ohtaka, K., "Energy band of photons and low-energy photon diffraction," Phys. Rev. B, Vol. 19, No. 10, 5057-5067, 1979.
doi:10.1103/PhysRevB.19.5057        Google Scholar

15. Ohtaka, K. and M. Inoue, "Light scattering from macroscopic spherical bodies. I. Integrated density of states of transverse electromagnetic fields," Phys. Rev. B, Vol. 25, No. 2, 677-688, 1982.
doi:10.1103/PhysRevB.25.677        Google Scholar

16. Ohtaka, K., S. Suda, T. Nagano, A. Ueta, T. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, "Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region," Phys. Rev. B, Vol. 61, No. 8, 5267-5279, 2000.
doi:10.1103/PhysRevB.61.5267        Google Scholar

17. Ohtaka, K. and Y. Tanabe, "Photonic band using vector spherical waves. I. Various properties of bloch electric fields and heavy photons," J. Phys. Soc. Jpn., Vol. 65, No. 7, 2265-2275, 1996.
doi:10.1143/JPSJ.65.2265        Google Scholar

18. Ohtaka, K. and Y. Tanabe, "Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field," J. Phys. Soc. Jpn., Vol. 65, No. 7, 2276-2284, 1996.
doi:10.1143/JPSJ.65.2276        Google Scholar

19. Ohtaka, K. and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn., Vol. 65, No. 8, 2670-2284, 1996.
doi:10.1143/JPSJ.65.2670        Google Scholar

20. Sainidou, R., N. Stefanou, I. E. Psarobas, and A. Modinos, "Scattering of elastic waves by a periodic monolayer of spheres," Phys. Rev. B, Vol. 66, No. 2, 243031-243037, 2002.
doi:10.1103/PhysRevB.66.024303        Google Scholar

21. Yano, S., Y. Segawa, J. S. Bae, K. Mizuno, S. Yamaguchi, and K. Ohtaka, "Optical properties of monolayer lattice and three-dimensional photonic crystals using dielectric spheres," Phys. Rev. B, Vol. 66, No. 7, 751191-751197, 2002.
doi:10.1103/PhysRevB.66.075119        Google Scholar

22. Andueza, A., R. Echeverria, and J. Sevilla, "Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness," J. Appl. Phys., Vol. 104, No. 4, 043103, 2008.        Google Scholar

23. Andueza, A. and J. Sevilla, "Non compact single-layers of dielectric spheres electromagnetic behaviour," Opt. Quantum Electron., Vol. 39, No. 4-6, 311-320, 2007.
doi:10.1007/s11082-007-9091-7        Google Scholar

24. Andueza, A., R. Echeverria, P. Morales, and J. Sevilla, "Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness," J. Appl. Phys., Vol. 107, No. 12, 124902, 2010.        Google Scholar

25. Andueza, A., T. Smet, P. Morales, and J. Sevilla, "Disorder effect in the transmission spectra of a noncompact single layer of dielectric spheres derived from microwave spectroscopy," Appl. Opt., Vol. 50, No. 31, 91-97, 2011.
doi:10.1364/AO.50.000G91        Google Scholar

26. Andueza, A., P. Morales, and J. Sevilla, "Photonic band effect in single-layers of high refractive index spheres of different compactness," J. Appl. Phys., Vol. 111, No. 10, 104902, 2012.        Google Scholar

27. Handapangoda, C. C., M. Premaratne, and P. N. Pathirana, "Plane wave scattering by a spherical dielectric particle in motion: A relativistic extension of the Mie theory," Progress In Electromagnetics Research, Vol. 112, 349-379, 2011.        Google Scholar

28. Lidorikis, E., M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett., Vol. 81, No. 7, 1405-1408, 1998.
doi:10.1103/PhysRevLett.81.1405        Google Scholar

29. Shalin, A. S., "Optical antireflection of a medium by nanostructural layers," Progress In Electromagnetics Research B, Vol. 31, 45-66, 2011.        Google Scholar

30. Mie, G., "Die optischen eigenschaften kolloider goldlsungen," Zeitschrift fur Chemie und Industrie der Kolloide, Vol. 2, No. 5, 129-133, 1907.
doi:10.1007/BF01503334        Google Scholar

31. Bohrem, C. F. and D. R. Huffman, Absorption and Scattering of Light by Small Particules, Wiley, New York, 1995.