Optical properties of nanostructured metamaterials

Abstract

We present a very efficient recursive method to calculate the effective optical response of nanostructured metamaterials made up of particles with arbitrarily shaped cross sections arranged in periodic two-dimensional arrays. We consider dielectric particles embedded in a metal matrix with a lattice constant much smaller than the wavelength. Neglecting retardation our formalism allows factoring the geometrical properties from the properties of the materials. If the conducting phase is continuous the low frequency behavior is metallic. If the conducting paths are nearly bloqued by the dielectric particles, the high frequency behavior is dielectric. Thus, extraordinary-reflectance bands may develop at intermediate frequencies, where the macroscopic response matches vacuum. The optical properties of these systems may be tuned by adjusting the geometry.Sketch of a nanostructured metamaterial slab with a dielectriclike or metallic-like behavior depending on the frequency of the incoming light.

Magnetic Response of Metamaterials

“…The analogy of the macroscopic wave operator with the Green's function allow us to apply the well‐known Haydock method to recursively generate an orthonormal basis in which our operator can be expressed as a tridiagonal matrix . Choosing an initial state |0⟩ normalized under the metric and corresponding to a plane wave with wavevector k and polarization e , one can generate new states by recursively acting with our “Hamiltonian.” Given the states |0⟩, |1⟩, |2⟩…| n ⟩, we generate the state | n + 1⟩ from where the Haydock coefficients a n and b n are chosen to satisfy …”

Keller’s theorem revisited

“…with a moderate damping characterized by the mean collision frequency γ=0.01ω p . We calculate ò M and  M for these systems employing an efficient procedure [19,20,[25][26][27]] based on HRM [28] and implemented in the Photonic computational package [29].…”

“…In section 3 we develop some applications of the theory. Namely, we show that the normal and parallel response functions of a superlattice are determined one from the other; we test the compliance of effective medium theories to Keller's condition; we test the accuracy of an efficient computational scheme based on Haydock's recursive method (HRM) calculation [19][20][21] for the calculation of the macroscopic response of periodic systems; we discuss the relation among the dielectric resonances of a system and that of its reciprocal system and we explore the corresponding microscopic fields [22]; we test the accuracy of numerical computations for ensemble members of disordered systems; and we illustrate how Keller's theorem may be used to increase the accuracy of rough approximate theories. Finally, section 4 is devoted to conclusions.…”

Optical and electrical properties of nanostructured metallic electrical contacts

“…Material composition, geometry, and order, affect the optical properties of the system. 5,6 Fabrication of nanostructured films with ordered patterns designed to tune optical properties in the visible (VIS) range requires high resolution lithography, employing interferometry of electronic beams 7,8 or similar techniques. A relative simple alternative is to use random composite films.…”

“…12 In the present work, we employ a computationally efficient recursive formalism for the calculation of an effective dielectric response of nanostructured films when the length-scale of the inhomogeneities of the film are much smaller than the wavelength, thus neglecting retardation. 5,6,13 This non-retarded recursive method (RM) is applicable 14 to nano-textured inhomogeneities with scales up to one order of magnitude below the nominal wavelength. Analyzing the optical and electrical properties of semicontinuous Ag films with a graded thickness we have searched for an optimum film, with an adequate conductivity in the low frequency range and a relatively high transmittance in the VIS.…”