The temporal fluctuation of the inverse participation ratio for localized field modes in three-dimensional percolation system

Authors

  • E. Martínez-Sánchez UNIVERSIDAD AUTÓNOMA DE COAHUILA
  • A. Díaz-de-Anda UNIVERSIDAD AUTÓNOMA DE PUEBLA
  • G. Burlak UNIVERSIDAD AUTÓNOMA DE MORELOS
  • R. Muñiz-Valdez UNIVERSIDAD AUTÓNOMA DE COAHUILA

DOI:

https://doi.org/10.31349/RevMexFis.67.285

Keywords:

Optics localization, spanning cluster, random pores, incorporated nanoemitters, FDTD

Abstract

We investigate the structure of the  optical field radiated by the disordered optical nano-emitters randomly incorporated  in three-dimensional cluster of a percolation material. Our numerical studies shown that the temporal variations of the inverse participation ratio (IPR) allow analyzing the extended and localized field structures over a long time range. The properties of IPR and the dynamics of the lasing emitters allow to find the characteristic time scales when the localization of the field in a general three-dimensional disordered system occurs. The studied effect opens new perspectives to control the optical fields localization in modern optical nano-technologies.

References

D.S. Wiersma, P. Bartolini, A. Lagendijk, et al. Localization of light in a disordered medium, Nature 390 (1997) 671, https://doi.org/10.1038/37757.

D. Vollhardt, Localization Effects in Disordered Systems. Festkiirperprobleme 27 (1987) 63.

D.S. Wiersma, Disordered photonics, Nat. Photonics 7 (2013) 188, https://doi.org/10.1038/nphoton.2013.29

D. Vollhardt, P. Wolfle, Scaling Equations from a Self-Consistent Theory of Anderson Localization, Phys. Rev. Lett. 48 (1982) 699, https://doi.org/10.1103/PhysRevLett.48.699

P. Sebbah, D. Sornette, C. Vanneste, Anomalous diffusion in two-dimensional Anderson-localization dynamics, Phys. Rev. B 48 (1993) 12506, https://doi.org/10.1103/PhysRevLett.48.699.

M.M. Sigalas, C.M. Soukoulis, C. T. Chan, et al. Localization of electromagnetic waves in two-dimensional disordered systems, Phys. Rev. B. 53 (1996) 8340, https://doi.org/10.1103/PhysRevB.53.8340.

T. Schwartz, G. Bartal, S. Fishman, et al. Transport and Anderson localization in disordered two-dimensional photonic lattices, Nature 446 (2007) 52, https://doi.org/10.1038/nature05623.

F. Riboli, P. Barthelemy, S. Vignolini, et al. Anderson localization of near-visible light in two dimensions, Opt. Lett. 36 (2011) 127 https://doi.org/10.1364/OL.36.000127.

G. Burlak, E. Martinez-Sanchez, The optical Anderson localization in three-dimensional percolation system, Opt. Commun. 387 (2017) 426, https://doi.org/10.1016/j.optcom.2016.10.068

P. Sebbah, C. Vanneste, Random laser in the localized regime, Phys. Rev. B, 66 (2002) 144202, https://doi.org/10.1103/PhysRevB.66.144202

H. Noh, J. Yang, S.F. Liew, et al. Control of lasing in biomimetic structures with short-range order, Phys. Rev. Lett. 106 (2011) 183901, https://doi.org/10.1103/PhysRevLett.106.183901

D. S. Wiersma, The physics and applications of random lasers, Nat. Phys. 4 (2008) 359, https://doi.org/10.1038/nphys971

G. Burlak, Y.G. Rubo, Mirrorless lasing fromlight emitters in percolating clusters, Phys. Rev. A 92 (2015) 013812, https://doi.org/10.1103/PhysRevA.92.013812

G. Burlak, The Dynamic Three-Dimensional Localization of Fields in Active Percolating Systems, Adv. in Math. Phys. 2019 (2019) 1, https://doi.org/10.1155/2019/5867012

F. Wenger, Inverse Participation Ratio in $2+ epsilon$ Dimensions, Zeitschrift fur Physik B Condens. Matter 36 (1980) 209, https://doi.org/10.1007/BF01325284

X. Jiang, C.M. Soukoulis, Phys. Rev. Lett. 85 (2000) 70, https://doi.org/10.1103/PhysRevLett.85.70

A.E. Siegman, Lasers, (University Science Books, Mill Valley California, 1986),pp. 27-39.

M.A. Noginov, J. Novak, D. Grigsby, et al. Opt. A: Pure Appl. Opt. 8 (2006) S285, https://doi.org/10.1088/1464-4258/8/4/S31

A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Publishers, Boston, London, 2005),pp. 51-327.

H. Cao, Y.G. Zhao, S.T. Ho, et al. Random Laser Action in Semiconductor Powder, Phys. Rev. Lett. 82 (1999) 2278, https://doi.org/10.1103/PhysRevLett.82.2278

J. Sanghera, W. Kim, G. Villalobos, et al. Ceramic Laser Materials, Materials 5 (2012) 258, https://doi.org/10.3390/ma5020258

H. Shinobu, Localization Length and Inverse Participation Ratio of Two Dimensional Electron in the Quantized Hall Effect, Prog. Theor. Phys. 76 (1986) 1210, https://doi.org/10.1143/PTP.76.1210

G. Burlak, Y. Calderon-Segura, Percolation and lasing in real 3D crystals with inhomogeneous distributed random pores, Phys. B. 453 (2014) 8, https://doi.org/10.1016/j.physb.2014.04.030

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Published

2021-07-15

How to Cite

[1]
E. Martínez-Sánchez, A. Díaz-de-Anda, G. Burlak, and R. Muñiz-Valdez, “The temporal fluctuation of the inverse participation ratio for localized field modes in three-dimensional percolation system”, Rev. Mex. Fís., vol. 67, no. 2 Mar-Apr, pp. 285–291, Jul. 2021.

Issue

Vol. 67 No. 2 Mar-Apr (2021): Revista Mexicana de Física

Section

13 Optics

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Copyright (c) 2021 ERIKA MARTINEZ SANCHEZ, ALFREDO DÍAZ DE ANDA, GENADDIY BURLAK, RODRIGO MUÑIZ VALDEZ

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