Vol. 20

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Near Field Focusing Effect and Hyperbolic Dispersion in Dielectric Photonic Crystals

By Natesan Yogesh and Venkatachalam Subramanian
Progress In Electromagnetics Research M, Vol. 20, 179-190, 2011


This paper investigates the near field focusing behavior corresponding to the hyperbolic dispersion regime at the second band of the square lattice photonic crystal (PC). Numerical studies reveal the influence of the corner part negative refraction in the observed focusing effect, though the major part of the refraction is divergent at this hyperbolic regime. It is further observed that the investigated dispersion shows the surface mode behavior when the effective index of the PC slab is higher than the air medium. This aspect may be implemented for the excitation and transfer of near fields for an evanescent wave microscopy.


Natesan Yogesh and Venkatachalam Subramanian, "Near Field Focusing Effect and Hyperbolic Dispersion in Dielectric Photonic Crystals," Progress In Electromagnetics Research M, Vol. 20, 179-190, 2011.


    1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp., Vol. 10, 509-514, 1968.

    2. Silin, R. A., "Possibility of creating plane-parallel lenses," Opt. Spectrosc., Vol. 44, 109, 1978.

    3. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966, 2000.

    4. Ramakrishna, S. A. and T. M. Grezegorczyk, Physics and Applications of Negative Refractive Index Materials, 77-143, CRC Press, Boca Raton, 2009.

    5. Cheng, Q., H.-F. Ma, and T.-J. Cui, "A complementary lens based on broadband metamaterials," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 1, 93-101, 2010.

    6. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light, 2nd Edition, Princeton University Press, Princeton, New Jersey, 2008.

    7. Smith, D. R. and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett., Vol. 90, No. 7, 077405, 2003.

    8. Smith, D. R., P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B, Vol. 21, No. 5, 1032-1043, 2004.

    9. Qiao, S., G. Zheng, H. Zhang, and L.-X. Ran, "Transition behavior of k-surface: From hyperbola to ellipse," Progress In Electromagnetics Research, Vol. 81, 267-277, 2008.

    10. Kong, F., B.-I. Wu, H. Hunag, J. Huangfu, S. Xi, and J. A. Kong, "Lateral displacement of an electromagnetic beam reflected from a grounded indefinite uniaxial slab," Progress In Electromagnetics Research, Vol. 82, 351-366, 2008.

    11. Notomi, M., "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B, Vol. 62, No. 16, 10696-10705, 2000.

    12. Luo, C., S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B, Vol. 65, 201104(R), 2002.

    13. Fang, Y. and T. Shen, "Diverse imaging of photonic crystal be the effects of channeling and partial band gap," Optik, Vol. 118, 100-102, 2007.

    14. Sun, G. and A. G. Kirk, "Analyses of negative refraction in the partial bandgap of photonic crystals," Opt. Express, Vol. 16, No. 6, 4330-4336, 2008.

    15. Tang, Z., R. Peng, Y. Ye, C. Zhao, D. Fan, H. Zhang, and S. Wen, "Optical properties of a square-lattice photonic crystal within the partial band gap," J. Opt. Am. A, Vol. 24, No. 2, 379-384, 2007.

    16. Minin, I. V., O. V. Minin, Y. R. Triandaphilov, and V. V. Kotlyar, "Subwavelength diffractive photonic crystal lens," Progress In Electromagnetics Research B, Vol. 7, 257-264, 2008.

    17. Fang, Y.-T. and H.-J. Sun, "Imaging by photonic crystal using reflection and negative refraction," Chin. Phys. Lett., Vol. 22, No. 10, 2674-2676, 2005.

    18. Li, Z.-Y. and L.-L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B, Vol. 68, 245110, 2003.

    19. Feng, S., L. Ao, and Y.-Q. Wang, "Engineering the near-field imaging of a rectangular-lattice photonic-crystal slab in the second band," Science in China Series G: Physics, Mechanics and Astronomy, Vol. 52, No. 1, 87-91, 2009.

    20. Luo, C., S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B, Vol. 68, 045115, 2003.

    21. Wang, M.-Y., J. Xu, J.Wu, B.Wei, H.-L. Li, T. Xu, and D.-B. Ge, "FDTD study on wave propagation in layered structures with biaxial anisotropic metamaterials," Progress In Electromagnetics Research, Vol. 81, 253-265, 2008.

    22. Smith, D. R., D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett., Vol. 84, No. 13, 2244-2246, 2004.

    23. Whiteman, J. R., The Mathematics of Finite Elements and Applications, John Wiley and Sons, Chichester, 1998. http://www.comsol.com..

    24. Johnson, S. G. and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a plane wave basis," Opt. Express, Vol. 8, No. 13, 173-190, 2001 http://ab-initio.mit.edu/mpb..

    25. Reynolds, A. L., "Translight software,", The University of Glasgow, 2000. Email id: areynolds@elec.gla.ac.uk..

    26. Qiu, M., F2P: Finite-difference Time-domain 2D Simulator for Photonic Devices, http://www.imit.kth.se/info/FOFU/PC/F2P..

    27. Lu, Z., J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. and D. W. Prather Schneider, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett., Vol. 95, 153901, 2005.

    28. Zhang, X., Z. Li, B. Cheng, and D.-Z. Zhang, "Non-near-field focus and imaging of an unpolarized electromagnetic wave through high-symmetry quasicrystals," Opt. Express, Vol. 15, No. 13, 1292-1300, 2007.

    29. Entezar, S. R., A. Namdar, H. Rahimi, and H. Tajalli, "Localized waves at the surface of a single-negative periodic multilayer structure," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 2-3, 171-182, 2009.