Abstract
In this work, a numerical technique known as integral equation method (IEM) was used to model the optical response of two-dimensional photonic structures of hexagonal lattice with rods that have smooth and rough surfaces, under TM polarization. Photonic structures were modeled by different materials. One of them was formed with dielectric–dielectric media and the other with dielectric–dispersive LHM media. We found that the optical response was modulated by the roughness of the surface of the inclusions. We also observed that the scattering patterns depend on the type of photonic structure and the incidence angle. Additionally, when we consider the two-dimensional photonic structure with rough surfaces, we approach a real physical system and this causes changes in the reflective optical properties. This property is very useful and has multiple applications in waveguides, filters, omnidirectional mirrors, beam splitters, and so on.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008), Chaps. 4–6
A. Mukherjee, A.D. Ariza-Flores, R.F. Balderas-Valadez, V. Agarwal, Controlling the optical properties of composite multilayered photonic structures: effect of superposition. Opt. Express 21, 17324–17339 (2013). https://doi.org/10.1364/OE.21.017324
T.V.K. Karthik, L. Martinez, V. Agarwal, Porous silicon ZnO/SnO2 structures for CO2 detection. J. Alloy. Compd. 731, 853–863 (2017). https://doi.org/10.1016/j.jallcom.2017.10.070
T.F. Krauss, R.M. De La Rue, Photonic crystals in the optical regime: past, present and future. Prog. Quant. Electron. 23, 51–96 (1999). https://doi.org/10.1016/S0079-6727(99)00004-X
A. Mendoza-Suárez, F. Villa-Villa, Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one- and two-dimensional photonic crystals. J. Opt. Soc. Am. B 23, 2249–2256 (2006). https://doi.org/10.1364/JOSAB.23.002249
A.A. Maradudin, T. Michel, A.R. McGurn, E.R. Méndez, Enhanced backscattering of light from a random grating. Annals Phys. 203(2), 255–307 (1990). https://doi.org/10.1016/0003-4916(90)90172-K
H.I. Pérez, C.I. Valencia, E.R. Méndez, J.A. Sánchez-Gil, On the transmission of diffuse light through thick slits. J. Opt. Soc. Am. A 26(4), 909–918 (2009). https://doi.org/10.1364/JOSAA.26.000909
H. Perez-Aguilar, A. Mendoza-Suárez, E.S. Tututi, I.F. Herrera-González, Disordered field patterns in a waveguide with periodic surfaces. Prog. Electromagn. Res. 48, 329–346 (2013). https://doi.org/10.2528/PIERB12120509
T. Nordam, P.A. Letnes, I. Simonsen, A.A. Maradudin, Numerical solutions of the Rayleigh equations for the scattering of light from a two-dimensional randomly rough perfectly conducting surface. J. Opt. Soc. Am. A 31, 1126–1134 (2014). https://doi.org/10.1364/JOSAA.31.001126
A. González-Alcalde, J.P. Banon, O.S. Hetland, A.A. Maradudin, E.R. Méndez, T. Nordam, I. Simonsen, Experimental and numerical studies of the scattering of light from a two-dimensional randomly rough interface in the presence of total internal reflection: optical Yoneda peaks. Opt. Express 24, 25995–26005 (2016). https://doi.org/10.1364/OE.24.025995
S. Hughes, S. Ramunno, J.F. Young, J.E. Sipe, Optical scattering loss due to disorder and fabrication roughness in semiconductor photonic crystal slab waveguides, in International Quantum Electronics Conference IThL5 (2004). https://doi.org/10.1364/IQEC.2004.IThL5
A. Mandatori, M. Bertolotti, C. Sibilia, B.J. Hoenders, M. Scalora, Coherence effects in propagation through one-dimensional photonic bandgap structures with a rough glass interface. J. Opt. Soc. Am. B 24, 2921–2929 (2007). https://doi.org/10.1364/JOSAB.24.002921
H.Y. Wu, M. Schaden, Perturbative roughness corrections to electromagnetic Casimir energies. Phys. Rev. D 89, 105003 (2014). https://doi.org/10.1103/PhysRevD.89.105003
L. Ondič, M. Varga, I. Pelant, J. Valenta, A. Kromka, R.G. Elliman, Silicon nanocrystal-based photonic crystal slabs with broadband and efficient directional light emission. Scientific Reports 7, 5763 (2017). https://doi.org/10.1038/s41598-017-05973-y
R.F. Balderas-Valadez, V. Agarwal, C. Pacholski, Fabrication of porous silicon-based optical sensors using metal-assisted chemical etching. RSC Adv. 6(26), 21430–21434 (2016). https://doi.org/10.1039/C5RA26816H
J.E. Baker, R. Sriram, B.J. Miller, Two-dimensional photonic crystals for sensitive microscale chemical and biochemical sensing. Lab Chip 15, 971–990 (2015). https://doi.org/10.1039/C4LC01208A
Y.X. Zong, J.B. Xia, Photonic band structure of two-dimensional metal/dielectric photonic crystals. J. Phys. D: Appl. Phys. 48(35), 355103 (2015). http://iopscience.iop.org/article/10.1088/0022-3727/48/35/355103/meta
A. Mendoza-Suárez, F. Villa-Villa, J.A. Gaspar-Armenta, Band structure of two-dimensional photonic crystals that include dispersive left handed materials and dielectrics in the unit cell. J. Opt. Soc. Am. B 24, 3091–3098 (2007). https://doi.org/10.1364/JOSAB.24.003091
V. Castillo-Gallardo, L.E. Puente-Díaz, H. Pérez-Aguilar, A. Mendoza-Suárez, F. Villa-Villa, Band structure of two-dimensional photonic crystals that include dispersive left-handed materials with rough surfaces in their lattice. Unpublished
D. Bria, B. Djafari-Rouhani, A. Akjouj, L. Dobrzynski, J.P. Vigneron, E.H. El Boudouti, A. Nougaoui, Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials. Phys. Rev. E 69, 066613 (2004). https://doi.org/10.1103/PhysRevE.69.066613
Acknowledgments
This research was supported by Consejo Nacional de Ciencia y Tecnología through a scholarship for Castillo-Gallardo, Puente-Díaz and Lozano-Trejo. Also, Pérez-Aguilar and Mendoza-Suárez express their gratitude to the Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo for the financial support granted for the development of this research project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Castillo-Gallardo, V., Puente-Díaz, L., Lozano-Trejo, E., Pérez-Aguilar, H., Mendoza-Suárez, A. (2019). Effects of the Roughness in the Optical Response of a 2DPC That Have Dielectric or Dispersive LHM Cylindrical Inclusions: The Triangular Lattice. In: Martínez-García, A., Bhattacharya, I., Otani, Y., Tutsch, R. (eds) Progress in Optomechatronic Technologies . Springer Proceedings in Physics, vol 233. Springer, Singapore. https://doi.org/10.1007/978-981-32-9632-9_5
Download citation
DOI: https://doi.org/10.1007/978-981-32-9632-9_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-32-9631-2
Online ISBN: 978-981-32-9632-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)