Nanostructured metamaterials: advances in the calculation of their optical properties
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Abstract
This article aims to present the work that has been done in recent years in the field of nanostructured meta-materials. Mainly, the work done in the Center for Optical Research A.C. in conjunction with the Institute of Physics of the UNAM. These works have focused on the development of new theoretical models that explain the optical properties of nanostructured systems. In addition, these models have been implemented within high-performance computational packages, which has allowed the realization of precise numerical calculations, which allow to know the physical quantities with which a material can be characterized; in this case, nanostructured meta-materials. Mostly, these numerical calculations have been focused on the computation of the dielectric function and non-linear susceptibility, being of great importance to be able to predict its value precisely because they are two fundamental quantities in the understanding of the interaction of light with matter. In addition to this theoretical-numerical development, some results obtained throughout this time are shown, where you can observe the versatility and flexibility of calculations as well as the importance of having such methodologies in material prediction, description and design “measure” of the needs. Finally, the future perspectives of this research are presented, as well as some of the most important challenges in this regard.
Article Details
Mundo Nano. Revista Interdisciplinaria en Nanociencias y Nanotecnología por Universidad Nacional Autónoma de México se distribuye bajo una Licencia Creative Commons Atribución-NoComercial 4.0 Internacional.
Basada en una obra en http://www.mundonano.unam.mx.
References
Bergman y Dunn. (1992). Bulk effective dielectric constant of a composite with a periodic microgeometry. Physical Review. B, Condensed Matter, 45(23): 13262-71, junio 15. http://dx.doi.org/10.1103/physrevb.45.13262
Brudny, V. L., Mochán, W. L., Maytorena. J. A. Mendoza, B. S. (2003). Second harmonic generation from a collection of nanoparticles. Physica Status Solidi (b), 240(3): 518-26, diciembre 1. http://dx.doi.org/10.1002/pssb.200303855
Cortes, E. et al. (2010). Optical properties of nanostructured metamaterials. Physica Status Solidi (b), 247(8): 2102-7. https://doi.org/10.1002/pssb.200983941
Datta, S., C. T. Chan, K. M. Ho y C. M. Soukoulis. (1993). effective dielectric constant of periodic composite structures. Physical Review B, 48(20): 14936-43, noviembre 15. http://dx.doi.org/10.1103/PhysRevB.48.14936
Decker, M., M. W. Klein, M. Wegener y S. Linden. (2007). Circular dichroism of planar chiral magnetic metamaterials. Optics Letters, 32(7): 856-58, abril 1. http://dx.doi.org/10.1364/OL.32.000856
Haydock, R. (1980). The recursive solution of the Schrödinger equation. Computer Physics Communications, 20(1): 11-16, septiembre 1. http://dx.doi.org/10.1016/0010-4655(80)90101-0
Keller, J. B. (1963). Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. Journal of Applied Physics, 34(4): 991-93, abril 1. http://dx.doi.org/10.1063/1.1729580
Keller, J. B. (1964). A theorem on the conductivity of a composite medium. Journal of Mathematical Physics, 5(4): 548-549.
Klein, Matthias W., Martin Wegener, Nils Feth and Stefan Linden. (2007). OSA Experiments on second- and third-harmonic generation from magnetic metamaterials. Optics Express, 15(8): 5238-5247. OSA | The Optical Society. (Consultado septiembre 2, 2019). https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-15-8-5238&id=132271
Krasnok, A., Mykhailo Tymchenko y Andrea Alù. (2018). Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Materials Today, 21(1): 8-21, enero 1. http://dx.doi.org/10.1016/j.mattod.2017.06.007
Krokhin, A., P. Halevi y J. Arriaga. (2002). Long-wavelength limit (homogenization) for two-dimensional photonic crystals. Physical Review B, 65(11): 115208, marzo 7. http://dx.doi.org/10.1103/PhysRevB.65.115208
Linden S., Enkrich C., Wegener M., Zhou J., Koschny T., Soukoulis C. M. (2004). Magnetic response of metamaterials at 100 terahertz. Science, 306(5700): 1351-53, noviembre 19, Nueva York, N.Y. http://dx.doi.org/10.1126/science.1105371
Liu, Zhaowei, Lee H., Xiong Y., Sun C., Zhang X. (2007). Farfield optical hyperlens magnifying sub-diffraction-limited objects. Science, 315(5819): 1686, marzo 23, Nueva York, N. Y. http://dx.doi.org/10.1126/science.1137368
Markel, Vadim A. (2016). Introduction to the Maxwell Garnett approximation: tutorial. Journal of the Optical Society of America A, 33(7): 1244, julio 1. http://dx.doi.org/10.1364/JOSAA.33.001244
McPhedran, R. C. y G. W. Milton. (1981). Bounds and exact theories for the transport properties of inhomogeneous media. Applied Physics A, 26(4): 207-20, diciembre 1. http://dx.doi.org/10.1007/BF00617840
Mendoza, Bernardo S. y W. Luis Mochán. (2016). Tailored optical polarization in nano structured metamaterials, Physical Review B, 94(19), noviembre 21. http://dx.doi.org/10.1103/PhysRevB.94.195137
Mendoza, Bernardo S. y W. Luis Mochán. (2012). Birefringent nanostructured composite materials. Physical Review B, 85(12): 125418, marzo 14. http://dx.doi.org/10.1103/PhysRevB.85.125418
Meza, Ulises R. Bernardo S. Mendoza y W. Luis Mochán. (2019). Second-harmonic generation in nanostructured metamaterials. Physical Review B, 99(12): 125408, marzo 6. http://dx.doi.org/10.1103/PhysRevB.99.125408
Milton, G. W. (1981). Bounds on the complex permittivity of a two-component composite material. Journal of Applied Physics, 52(8): 5286-93, agosto 1. http://dx.doi.org/10.1063/1.329385
Mochán, W. Luis y Rubén G. Barrera. (1985). Electromagnetic response of systems with spatial fluctuations. I. General formalism. Physical Review B, 32(8): 4984-4988, octubre 15. http://dx.doi.org/10.1103/PhysRevB.32.4984
Mochán, W. Luis y Rubén G. Barrera. (1985). Electromagnetic response of systems with spatial fluctuations. II. Applications. Physical Review B, 32(8): 4989-5001, octubre 15. http://dx.doi.org/10.1103/PhysRevB.32.4989
Mochán, W. Luis, Bernardo S. Mendoza y Irina Solís. (2014). Second harmonic generation in nanostructured metamaterials. En Latin America Optics and Photonics Conference. Cancún: OSA. LM2C.2. http://dx.doi.org/10.1364/LAOP.2014.LM2C.2
Mochán, W. Luis, Guillermo P. Ortiz y Bernardo S. Mendoza. (2010). Efficient homogenization procedure for the calculation of optical properties of 3D nanostructured composites. Optics Express, 18(21): 22119, octubre 11. http://dx.doi.org/10.1364/OE.18.022119
Nevard, J. y Joseph B. Keller. (1985). Reciprocal relations for effective conductivities of anisotropic media. Journal of Mathematical Physics, 26(11): 2761-65, noviembre 1. http://dx.doi.org/10.1063/1.526697
Ortiz, Guillermo P. et al. (2009). Effective optical response of metamaterials. Physical Review B, 79(24): 245132, junio 26. http://dx.doi.org/10.1103/PhysRevB.79.245132
PDL: Minuit -a PDL Interface to the Minuit librarymetacpan.org. (Consultado septiembre 2, 2019). https://metacpan.org/pod/PDL::Minuit
Pendry, J. B. (2000). Negative refraction makes a perfect lens. Physical Review Letters, 85(18): 3966-69, octubre 30. http://dx.doi.org/10.1103/PhysRevLett.85.3966
Plum, E. et al. (2007). Giant optical gyrotropy due to electromagnetic coupling. Applied Physics Letters, 90(22): 223113, mayo 28. http://dx.doi.org/10.1063/1.2745203
Popov, A. K. y V. M. Shalaev. (2006). Negative-index metamaterials: second-harmonic generation, manley–rowe relations and parametric amplification. Applied Physics B, 84(1): 131-37, julio 1. http://dx.doi.org/10.1007/s00340-006-2167-4
Schaich, W. L. y A. Liebsch. (1988). Nonretarded hydrodynamic-model calculation of second-harmonic generation at a metal surface. Physical Review B, 37(11): 6187-92, abril 15. http://dx.doi.org/10.1103/PhysRevB.37.6187
Sergio G. Rodrigo, V. Laliena y L. Martín-Moreno. (2015). Second-harmonic generation from metallic arrays of rectangular holes. Journal of the Optical Society of America B, 32(1): 15, enero 1.
Smith, David R. et al. (2000). Composite medium with simultaneously negative permeability and permittivity. Physical Review Letters, 84(18): 4184-87, mayo 1. http://dx.doi.org/10.1103/PhysRevLett.84.4184
Smith, David R. y John B. Pendry. (2006). Homogenization of metamaterials by field averaging (invited paper). Journal of the Optical Society of America B, 23(3): 391, marzo 1. http://dx.doi.org/10.1364/JOSAB.23.000391
Sözüer, H. S., J. W. Haus y R. Inguva. (1992). Photonic bands: Convergence problems with the plane-wave method. Physical Review B, 45(24): 13962-72, junio 15. http://dx.doi.org/10.1103/PhysRevB.45.13962
Tao, Ruibao, Zhe Chen y Ping Sheng. (1990). First-principles Fourier approach for the calculation of the effective dielectric constant of periodic composites. Phys. Rev. B, 41(4): 2417-20, febrero 1. http://dx.doi.org/10.1103/PhysRevB.41.2417
Veselago, Viktor G. (1968). The electrodynamics of substances with simultaneously negative values of and μ. Soviet Physics Uspekhi, 10(4): 509. http://dx.doi.org/10.1070/PU1968v010n04ABEH003699