Graded photonic crystals for implementation of gradient refractive index media

Gradient refractive index lens-like media are implemented using two-dimensional graded photonic crystals. They were considered as effectively homogeneous media in the long-wavelength approximation. Specified distribution of the gradient refractive index was realized using rods with spatially varying radii and applied for a design of a focusing and imaging lens. The validity of the proposed method was confirmed using full-wave numerical simulations. Planar versions of the presented lenses can find applications in integrated nanophotonics.

[1]  T. A. Birks,et al.  Hamiltonian optics of nonuniform photonic crystals , 1999 .

[2]  David Cassagne,et al.  Mirage and superbending effect in two-dimensional graded photonic crystals , 2006 .

[3]  Chii-Chang Chen,et al.  Focusing of electromagnetic waves by periodic arrays of air holes with gradually varying radii. , 2006, Optics express.

[4]  Ari Sihvola,et al.  Electromagnetic mixing formulas and applications , 1999 .

[5]  Carlos Gómez-Reino,et al.  Design of GRIN optical components for coupling and interconnects , 2008 .

[6]  Carsten Rockstuhl,et al.  Designing optical elements from isotropic materials by using transformation optics , 2010 .

[7]  Hamza Kurt,et al.  Graded index photonic crystals. , 2007, Optics express.

[8]  J. Arriaga,et al.  Photonic crystals as optical components , 1999 .

[9]  Masaya Notomi,et al.  Self-collimating phenomena in photonic crystals , 1999 .

[10]  Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method. , 2004 .

[11]  M. Lipson,et al.  Silicon nanostructure cloak operating at optical frequencies , 2009, 0904.3508.

[12]  E. Centeno,et al.  Graded photonic crystals. , 2005, Optics letters.

[13]  G. Bartal,et al.  An optical cloak made of dielectrics. , 2009, Nature materials.

[14]  M. Adams,et al.  Optical waves in crystals , 1984, IEEE Journal of Quantum Electronics.

[15]  J. Pendry,et al.  Hiding under the carpet: a new strategy for cloaking. , 2008, Physical review letters.

[16]  R. Gajić,et al.  Controlling electromagnetic fields with graded photonic crystals in metamaterial regime. , 2010, Optics express.

[17]  Yeshaiahu Fainman,et al.  Implementation of a graded-index medium by use of subwavelength structures with graded fill factor. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  Wounjhang Park,et al.  Graded negative index lens by photonic crystals. , 2008, Optics express.

[19]  Kurt Busch,et al.  Transport properties of random arrays of dielectric cylinders , 1998 .

[20]  J. Lee,et al.  Direct visualization of optical frequency invisibility cloak based on silicon nanorod array. , 2009, Optics express.

[21]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[22]  Y. Fainman,et al.  Inhomogenous dielectric metamaterials with space-variant polarizability. , 2007, Physical review letters.

[23]  F. S. Roux,et al.  Planar photonic crystal gradient index lens, simulated with a finite difference time domain method , 2006 .

[24]  Ekmel Ozbay,et al.  The focusing effect of graded index photonic crystals , 2008 .

[25]  Ekmel Ozbay,et al.  High efficiency of graded index photonic crystal as an input coupler , 2009 .

[26]  Steven G. Johnson,et al.  All-angle negative refraction without negative effective index , 2002 .