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Subwavelength Focusing Properties of Diffractive Photonic Crystal Lens

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Diffractive Optics and Nanophotonics

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Abstract

Subwavelength focusing properties of diffractive photonic crystal lens was considered. It was shown that photonic crystal lens design has not an unique solution and at least of three different types of photonic crystal lens are possible with spatial resolution at focus equal to FWHM = 0.48λ. PhC diffractive lens with mode transformation are also discussed. It was shown the lens focuses radiations to a spot smaller than the diffraction limit with FWHM = 0.35λ. In the second part we suggest a metamaterial based structure whose properties are determined not only by its inner geometry but also by its entire 3D shape. The example of metacuboid are described. We evaluate the potential of this structure to control both the size and the location of the field enhancement (photonic jet). Effect of EM strong localization in photonic crystal is described.

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Notes

  1. 1.

    It could be noted that a partial lensing effect, light concentration resembling a photonic jet (see Chap. 4), at some conditions may be obtained in PhC lens, as it was noted by Antonakakis et al. [5].

  2. 2.

    The authors [17] considered only a rectangular PhC Mikaelian lens and derived the air hole radii of each row from the assumption that the optical path length along the line which crosses the holes from the center should be equivalent to that of the ideal Mikaelian lens. The main limitation of this approach is that it can be applied only to a rectangular lattice PhC Mikaelian lens with varying air hole radius.

  3. 3.

    I.V. Minin, O.V. Minin. Diffractive photonic crystal lens of millimetre waves. Patent of Russia 152929.

  4. 4.

    The authors would like to thanks to Borislav Vasić, Institute of Physics Belgrade, Serbia, for help in simulations.

References

  1. Minin, O. V., & Minin, I. V. (2004). Diffractional optics of millimeter waves. Bristol: Institute of Physics Publishing.

    Book  MATH  Google Scholar 

  2. Minin, I. V., Minin, O. V., Gagnon, N., & Petosa, A. (2007). Investigation of the resolution of phase correcting Fresnel lenses with small focal length-to-diameter ratio and subwavelength focus. In Proceeding of the EMTS 2007, Canada, Ottawa (URSI), July 26–28, 2007.

    Google Scholar 

  3. Joannopoulos, J. D., Meade, R. D., & Winn, J. N. (1995). Photonic crystals: molding the flow of light. Princeton: Princeton University Press.

    MATH  Google Scholar 

  4. Sakoda, K. (2005). Optical properties of photonic crystals (2nd ed.). New York: Springer.

    Google Scholar 

  5. Antonakakis, T., Craster, R. V., & Guenneau, S. (2013). Asymptotics for metamaterials and photonic crystals. Proceedings of the Royal Society of London A, 469, 20120533.

    Article  ADS  MathSciNet  Google Scholar 

  6. Goss Levi, B. (1999). Progress made in near-field imaging with light from a sharp tip. Physics Today, 52, 18.

    Google Scholar 

  7. Flück, E., van Hulst, N. F., Vos, W. L., & Kuipers, L. (2003). Near-field optical investigation of three-dimensional photonic crystals. Physical Review E, 68, 015601.

    Article  ADS  Google Scholar 

  8. Li, C., Holt, M., & Efros, A. L. (2006). Far-field imagimg by the Veselago lens made of a photonic crystal. Journal of the Optical Society B, 23(3), 490–497.

    Article  ADS  Google Scholar 

  9. Daschner, F., Knöchel, R., Foca, E., Carstensen, J., Sergentu, V. V., Föll, H., & Tiginyanu, I. M. (2006). Photonic crystals as host material for a new generation of microwave components. Advances in Radio Science, 4, 17–19.

    Article  ADS  Google Scholar 

  10. Minin, I. V., Minin, O. V., Triandaphilov, Y. R., & Kotlyar, V. V. (2008). Subwavelength diffractive photonic crystal lens. Progress in Electromagnetics Research B (PIER B), 7, 257–264.

    Google Scholar 

  11. Minin, I. V., Minin, O. V., Triandaphilov, Y. R., & Kotlyar, V. V. (2008). Focusing properties of two types of diffractive photonic crystal lens. Optical Memory & Neural Networks (Information Optics), 17(3), 244–248.

    Article  Google Scholar 

  12. Minin, I. V., Minin, O. V., Triandaphilov, Y. R., & Kotlyar, V. V. (2008). Subwavelength diffractive photonic crystal lens. In Proceedings of the 2008 China-Japan Joint Microwave Conference (pp. 756–757). Shanghai, China, September 10–12, 2008.

    Google Scholar 

  13. Minin, I. V., Minin, O. V., Triandaphilov, Y. R., & Kotlyar, V. V. (2008). Subwavelength Diffractive photonic crystal lens. In Proceedings of the International Conference on Mathematical Physics and Its Applications—Steklov Mathematical Institute of the Russian Academy of Sciences (p. 128). Samara State University. Samara, Russia, September 8–13, 2008.

    Google Scholar 

  14. Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation, AP-14, 302–307.

    Google Scholar 

  15. Umashankar, K. R., & Taflove, A. (1982). A novel method to analyze electromagnetic scattering of complex objects. IEEE Transactions on Electromagnetic Compatibility, 24(4), 397–405.

    Google Scholar 

  16. Berenger, J. P. (1994). A perfectly matched layer for the absorption of electromagnetic waves. Computational Physics, 114, 185–200.

    Google Scholar 

  17. Triandafilov, Y. R., & Kotlyar, V. V. (2007). Photonic-crystal Mikaelian lens. Computer Optics, 31(3), 27–31.

    Google Scholar 

  18. Luo, C., Johnson, S. G., Joannopoulos, J. D., & Pendry, J. B. (2002). All-angle negative refraction without negative effective index. Physical Review B, 65, 201104(R).

    Article  ADS  Google Scholar 

  19. Fang, Y., & Shen, T. (2007). Diverse imaging of photonic crystal be the effects of channeling and partial band gap. Optik, 118, 100–102.

    Article  ADS  Google Scholar 

  20. Fang, Y.-T., & Sun, H.-J. (2005). Imaging by photonic crystal using reflection and negative refraction. Chinese Physics Letters, 22(10), 2674–2676.

    Article  ADS  Google Scholar 

  21. Li, Z.-Y., & Lin, L.-L. (2003). Evaluation of lensing in photonic crystal slabs exhibiting negative refraction. Physical Review B, 68, 245110.

    Article  ADS  Google Scholar 

  22. Luo, C., Johnson, S. G., Joannopoulos, J. D., & Pendry, J. B. (2003). Subwavelength imaging in photonic crystals. Physical Review B, 68, 045115.

    Article  ADS  Google Scholar 

  23. Kiasat, Y., Szabo, Zs., & Li, E. P. (2013). Sub-wavelength imaging with non-spherical plasmonic nano-particles. In Proceedings Of the 4th International Conference on Metamaterials, Photonic Crystals and Plasmonics (pp. 49–50). Sharjah, United Arab Emirates, March 18–22, 2013.

    Google Scholar 

  24. Meriakri, V. V. & Nikitin, I. P. (1989). Man-made dielectric with dispersion in the millimeter wavelength band. Quasioptical devices in millimeter and sub-millimeter wavelength ranges. In Proceedings of IRE (pp. 65–70). Har’kov.

    Google Scholar 

  25. Petosa, A., Ittipiboon, A., & Thirakoune, S. (2002). Perforated dielectric resonator antennas. Electronics Letters, 38(24), 1493–1495.

    Article  Google Scholar 

  26. Zhang, Y., & Kishk, A. A. (2007). Analysis of dielectric resonator antenna arrays with supporting perforated rods. In 2nd European Conference on Antennas and Propagation, EuCAP 2007 (pp. 1–5).

    Google Scholar 

  27. Fabre, N., Fasquel, S., Legrand, C., Melique, X., Muller, M., Francois, M., et al. (2006). Towards focusing using photonic crystal flat lens. Opto-Electronics Review, 14(3), 225–232.

    Article  ADS  Google Scholar 

  28. Pacheco-Peña, V., Beruete, M., Minin, I. V., & Minin, O. V. (2014). Terajets produced by 3D dielectric cuboids. Applied Physics Letters, 105, 084102.

    Article  ADS  Google Scholar 

  29. Joannopoulos, J., Meade, R., & Winn, J. (1995). Photonic crystals. Princeton: Princeton University Press.

    Google Scholar 

  30. Lourtioz, J.-M., Benisty, H., Berger, V., Gerard, J.-M., Maystre, D., & Tchelnokov, A. (2008). Photonic crystals. Towards nanoscale photonic devices. Berlin: Springer.

    Google Scholar 

  31. Ehrhardt, M. (Ed.), Wave propagation in periodic media. Analysis, numerical techniques and practical applications. Sharjah: Bentham Science Publishers.

    Google Scholar 

  32. Gong, Q., & Hu, X. (2014). Photonic crystals: principles and applications (366 p). New York: CRC Press.

    Google Scholar 

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Authors and Affiliations

  1. Tomsk State University, Novosibirsk, Russia

    Igor Minin

  2. Tomsk State University, Novosibirsk, Russia

    Oleg Minin

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  1. Igor Minin
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Correspondence to Igor Minin .

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Minin, I., Minin, O. (2016). Subwavelength Focusing Properties of Diffractive Photonic Crystal Lens. In: Diffractive Optics and Nanophotonics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-24253-8_3

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