Effective medium approximation of anisotropic lamellar nanogratings based on Fourier factorization

Abstract

Anisotropic lamellar sub-wavelength gratings (nanogratings) are described by Effective Medium Approximation (EMA). Analytical formulas for effective medium optical parameters of nanogratings from arbitrary anisotropic materials are derived using approximation of zeroorder diffraction mode. The method is based on Rigorous Coupled Wave Analysis (RCWA) combined with proper Fourier factorization method. Good agreement between EMA and the rigorous model is observed, where slight differences are explained by the influence of evanescent higher Fourier harmonics in the nanograting. 3292-3302 (1979).

Modeling of magneto-optical properties of lamellar nanogratings

“…The differences between the simple model (2) and the data obtained from fit of rigorous model correspond to effects of higher-order evanescent waves. Differences increases with increasing grating period Λ [8].…”

“…First, a simple EMA model, uses zero-order approximation of the effective parameters assuming that only the zero diffraction order can be found in the grating [6][7][8][9]. Second one is based on the following virtual experiment: The reflectivity and ellipsometric data obtained from the rigorous grating model are fitted to the response from an effective layer described by appropriate parameters.…”

Effective spectral optical functions of lamellar nanogratings

“…At this stage of algorithm the boundary conditions are included also in the representation of the permittivity tensor. If Li factorization rules [15] are used for lamellar grating, the zero order Bloch wave in nanograting corresponds in first approximation to a plane wave with wave number of the zero Fourier harmonic [14] (this wave number can be obtained by assuming expansion with only zero Fourier harmonic -quasi-static limit).…”

“…Recently, quasi-static expressions for the generally anisotropic lamellar gratings were reported in Ref. [14].…”

Spectrally resolved complex transmittance measurements of infrared nanostructured devices

“…11,12 In the present article we describe a way to measure the complex transmittance spectrum, both amplitude and phase, of a material with a sub-mm spatial resolution, which may be used to retrieve their optical properties (effective permittivity or permeability) over the mid-and long-infrared wavelength ranges. 13 …”