FOCUSING, IMAGING AND FOURIER TRANSFORMING WITH A LARGE NUMERICAL APERTURE, DIELECTRIC FLAT PHOTONIC CRYSTAL LENS IN METAMATERIAL REGIME

Öz An untraditional Gradient Index Photonic Crystal (GRIN PC) is employed within the long wavelength regime to exhibit focusing, imaging and Fourier Transforming. A very large numerical aperture is aimed by breaking the paraxial wave approximation and the slowly changing refractive index assumption. This untraditional GRIN PC is shown to exhibit very similar lensing characteristics as its analytically solvable counterparts demonstrate. The results suggest that Fourier Transforming together with Fractional Fourier Transforms can be obtained from the present design. The performance of the GRIN PC lens is very much dependent on the excitation source as it is expected from GRIN optics and adiffractional propagating beams over large distances can be obtained.

Anahtar Kelimeler:

Graded Index Photonic Crystal (GRIN) lens, Fractional Fourier Transform, Fourier Optics, Adiffractional beam propagation

PDF

___

J.B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett., 85/18 (2000) 3966–3969.

D.R. Smith, J.B. Pendry and M.C.K. Wiltshire, Metamaterials and Negative Refractive Index, Science, 305/5685 (2004) 788-792.

A. Grbic and G.V. Eleftheriades, Subwavelength focusing using a negative-refractive-index transmission line lens, IEEE Antennas Wirel. Propag. Lett., 2 (2003) 186-189.

K. Aydin, I. Bulu and E. Ozbay, Subwavelength resolution with a negative-index metamaterial superlens, Appl. Phys. Lett., 90 (2007) 254102.

[5] D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr and D.R. Smith, Metamaterial Electromagnetic Cloak at Microwave Frequencies, Science, 314/5801 (2006) 977-980.

R. Liu, C. Ji, J.J. Mock, J.Y. Chin, T.J. Cui, D.R. Smith, Broadband Ground-Plane Cloak, Science, 323/5912 (2009) 366-369.

D. Sell, J. Yang, E.W. Wang, T. Phan, S. Doshay and J.A. Fan, Ultra-High-Efficiency Anomalous Refraction with Dielectric Metasurfaces, ACS Photonics, 5/6 (2018) 2402-2407.

C. Argyropoulos, N.M. Estakhri, F. Monticone and A. Alù, Negative refraction, gain and nonlinear effects in hyperbolic metamaterials, Opt. Express, 21 (2013) 15037-15047.

W. Liang, Z. Li, Y. Wang, W. Chen and Z. Li, All-angle optical switch based on the zero reflection effect of graphene–dielectric hyperbolic metamaterials, Photon. Res., 7 (2019) 318-324.

J. Noonan and T.G. Mackay, On electromagnetic surface waves supported by an isotropic chiral material, Opt. Commun., 434 (2019) 224-229.

T. Gric and O. Hess, Disorder in Metamaterials Chapter 12, Advanced Thermoelectric Materials (editted by C.R. Park), (John Wiley & Sons, Inc., 2019)

M. Takeda, A. Tsuchiyama, M. Okada, S. Matsui, T. Inoue and K. Aizawa, Improvement of focusing characteristics of a surface plasmonic lens for UV wavelength, Jpn. J. Appl. Phys., 56 (2017) 09NC02.

W.T. Chen, A.Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, F. Capasso, A broadband achromatic metalens for focusing and imaging in the visible, Nat. Nanotechnol., 13 (2018) 220−226.

N. Kundtz and D.R. Smith, Extreme-angle broadband metamaterial lens, Nat. Mater., 9 (2010) 129–132.

H. Kurt and D.S. Citrin, Graded index photonic crystals, Opt. Express, 15 (2007) 1240-1253.

D. Schurig, J.B. Pendry and D.R. Smith, Calculation of material properties and ray tracing in transformation media, Opt. Express, 14 (2006) 9794-9804.

A.O. Cakmak, E. Colak, H. Caglayan, H. Kurt and E. Ozbay, High efficiency of graded index photonic crystal as an input coupler, J. Appl. Phys., 105/10 (2009) 103708.

A.E. Serebryannikov, A.O. Cakmak, E. Colak, H. Caglayan, H. Kurt and E. Ozbay, Multiple slow waves and relevant transverse transmission and confinement in chirped photonic crystals, Opt. Express, 22 (2014) 21806-21819.

M. Gumus, I.H. Giden and H. Kurt, Broadband self-collimation in C2 symmetric photonic crystals, Opt. Lett., 43/11 (2018) 2555-2558.

D. Luo, G. Alagappan, X.W. Sun, Z. Raszewski and J.P. Ning, Superbending effect in two-dimensional graded photonic crystals, Opt. Commun., 282/2 (2009) 329–332.

E. Centeno, D. Cassagne and J.-P. Albert, Mirage and superbending effect in two dimensional graded photonic crystals, Phys. Rev. B, 73/23 (2006) 235119–235123.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne and J. M. Lourtioz, Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect, Appl. Phys. Lett. 92(13), 133501 (2008).

C. Gomez-Reino, M.V. Perez and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

G. Lubkowski, R. Schuhmann and T. Weiland, Extraction of Effective Metamaterial Parameters by Parameter Fitting of Dispersive Models, Microw. Opt. Technol. Lett., 49 (2007) 285-288.

B.D.F. Casse, W.T. Lu, Y.J. Huang and S. Sridhar, Nano-optical microlens with ultrashort focal length using negative refraction, Appl. Phys. Lett., 93 (2008) 053111.

C. G. Parazzoli, R.B. Greegor, J.A. Nielsen, M.A. Thompson, K. Li, A.M. Vetter, M.H. Tanielian and D.C. Vier, Performance of a negative index of refraction lens, Appl. Phys. Lett., 84 (2004) 3232-3234.

T. Driscoll, D.N. Basov, A.F. Starr, P.M. Rye, S. Nemat-Nasser, D. Schurig and D.R. Smith, Freespace microwave focusing by a negative-index gradient lens, Appl. Phys. Lett., 88 (2006) 081101.

R.B. Greegor, C.G. Parazzoli, J.A. Nielsen, M.A. Thompson, M.H. Tanielian and D.R. Smith, Simulation and testing of a graded negative index of refraction lens, Appl. Phys. Lett., 87 (2005) 091114.

D. R. Smith, J. J. Mock, A. F. Starr and D. Schurig, Gradient index metamaterials, Phys. Rev. E, 71 (2005) 36609.

O. Paul, B. Reinhard, B. Krolla, R. Beigang and M. Rahm, Gradient index metamaterial based on slot elements, Appl. Phys. Lett., 96 (2010) 241110.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui and D. R. Smith, Gradient index circuit by waveguided metamaterials, Appl. Phys. Lett., 94 (2009) 073506.

R. Liu, Q. Cheng, J. Y. Chin, J. J. Mock, T. J. Cui and D. R. Smith, Broadband gradient index microwave quasi-optical elements based on non-resonant metamaterials, Opt. Express, 17 (2009) 21030-21041.

U. Levy, M. Nezhad, H.-C. Kim, C.-H. Tsai, L. Pang and Y. Fainmann, Implementation of a graded-index medium by use of subwavelength structures with graded fill factor, J. Opt. Soc. Am. A, 22 (2005) 724-733 (2005).

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham and Y. Fainman, Inhomogenous Dielectric Metamaterials with Space-Variant Polarizability, Phys. Rev. Lett., 98 (2007) 243901.

M. Lu, B.K. Juluri, S.-C.S. Lin, B. Kirally, T. Gao and T.J. Huang, Beam aperture modifier and beam deflector using graded-index photonic crystals, J. Appl. Phys., 108 (2010) 103505.

H.-W. Wang and L.-W. Chen, High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals, J. Opt. Soc. Am. B, 28 (2011) 2098-2104.

H.-W. Wang and L.-W. Chen, A cylindrical optical black hole using graded index photonic crystals, J. Appl. Phys., 109 (2011) 103104.

M. Yin, X.Y. Tian, H.X. Han and D.C. Li, Free-space carpet-cloak based on gradient index photonic crystals in metamaterial regime, Appl. Phys. Lett., 100 (2012) 124101.

B. Vasic, G. Isic, R. Gajic and K. Hingerl, Controlling electromagnetic fields with graded photonic crystals in metamaterial regime, Opt. Express, 18 (2010) 20321-20333.

Z.L. Mei, J. Bai and T.J. Cui, Gradient index metamaterials realized by drilling hole arrays, J. Phys. D: Appl. Phys., 43 (2010) 055404.

B. Vasic, R. Gajic and K. Hingerl, Graded photonic crystals for implementation of gradient refractive index media, J. Nanophoton., 5 (2011) 051806.

B. Vasic and R. Gajic, Self-focusing media using graded photonic crystals: Focusing, Fourier transforming and imaging, directive emission and directional cloaking, J. Appl. Phys., 110 (2011) 053103.

B. Saleh and M. Teich, Fundamentals of photonics (New York, Wiley, 1991).

R. Weinstock, Calculus of Variations with Applications to Physics and Engineering (New York: Dover Publications, 1974).

M. Turduev, I.H. Giden and H. Kurt, Design of flat lens-like graded index medium by photonic crystals: Exploring both low and high frequency regimes, Opt. Comm., 339 (2015) 22-33.

H.M. Ozaktas and D. Mendlovic, Fractional Fourier optics, J. Opt. Soc. Am. A, 12 (1995) 743-751.