Evgeny Popov

Staircase approximation validity for arbitrary-shaped gratings

An electromagnetic study of the staircase approximation of arbitrary shaped gratings is conducted with three different grating theories. Numerical results on a deep aluminum sinusoidal grating show that the staircase approximation introduces sharp maxima in the local field map close to the edges of the profile. These maxima are especially pronounced in TM polarization and do not exist with the original sinusoidal profile. Their existence is not an algorithmic artifact, since they are found with different grating theories and numerical implementations. Since the number of the maxima increases with the number of the slices, a greater number of Fourier components is required to correctly represent the electromagnetic field, and thus a worsening of the convergence rate is observed. The study of the local field map provides an understanding of why methods that do not use the staircase approximation (e.g., the differential theory) converge faster than methods that use it. As a consequence, a 1% accuracy in the efficiencies of a deep sinusoidal metallic grating is obtained 30 times faster when the differential theory is used in comparison with the use of the rigorous coupled-wave theory. A theoretical analysis is proposed in the limit when the number of slices tends to infinity, which shows that even in that case the staircase approximation is not well suited to describe the real profile.

Differential theory of diffraction by finite cylindrical objects.

We present a differential theory for solving Maxwell equations in cylindrical coordinates, projecting them onto a Fourier-Bessel basis. Numerical calculations require the truncation of that basis, so that correct rules of factorization have to be used. The convergence of the method is studied for different cases of dielectric and metallic cylinders of finite length. Applications of such a method are presented, with a special emphasis on the near-field map inside a hole pierced in a plane metallic film.

Enhanced transmission of light through a circularly structured aperture

Using the differential theory of light diffraction by finite cylindrical objects, we study light transmission through a small circular aperture in a metallic screen with concentric corrugation around the nanohole. Poynting vector maps in the region below the screen show that the field enhancement compared with an unstructured aperture is obtained with corrugation lying on the entrance face of the screen. Corrugation on the exit face leads to a more directional radiation close to the normal to the screen. The spectral dependence of the transmission shows a sharp maximum linked with surface plasmon excitation.

Optimization of plasmon excitation at structured apertures.

Surface plasmon excitation that is due to a single or a structured circular aperture in a flat metallic screen is investigated theoretically and numerically with a view to enhancing the electric field close to the metallic surface. A systematic study of the homogeneous solution of the electromagnetic scattering problem is made with cylindrical coordinates, expanding Maxwell equations on a Fourier-Bessel basis. A perturbation analysis devoted to simple physical analyses of different types of cylindrical nanostructure is developed for the optimization of plasmon excitation by a normally incident linearly polarized monochromatic plane wave. The conclusions drawn from this analysis agree well with the results of rigorous electromagnetic calculations obtained with the differential theory of diffraction in cylindrical coordinates.

Second-harmonic-generation-induced optical bistability in prism or grating couplers

We deal with second-harmonic generation in chi((2)) nonlinear-optical resonators such as prism or grating couplers. The theoretical study is performed within the framework of a recently developed coupled-mode analysis leading to a set of equations governing the amplitudes of pump and second-harmonic frequency fields. We predict analytically that second-harmonic generation in prism or grating couplers may lead to optical bistability. We believe this to be the first demonstration of such an effect in chi((2)) optical resonators.

Low polarization dependent diffraction grating for wavelength demultimlexing.

A low polarization dependent, high diffraction efficiency grating for wavelength demultiplexer is proposed, manufactured by standard crystallographic etching of Si surface. Light is incident and diffracted inside the wafer, which is covered with reflecting metal. Optimized groove form results in a flat spectral response for TE and TM polarizations.

Fast Fourier factorization method applied to modal analysis of slanted lamellar diffraction gratings in conical mountings

A new formulation of the Fourier modal method that applies fast Fourier factorization [J. Opt. Soc. Am. A 17 (2000) 1773] is presented for slanted lamellar gratings in conical mountings. A new eigenvalue problem in the grating region is derived, and used to study metallic gratings. Comparison of the convergence speed of the numerical results given by the conventional methods and the new one shows a spectacular improvement. The fast Fourier factorization method can be also applied to various volume slanted-fringe gratings with discontinuous permittivity variations.

Almost perfect blazing by photonic crystal rod gratings

A periodic array of dielectric rods or holes, known as two-dimensional photonic crystal, is shown to have blazing properties similar to those of classical diffraction gratings. Several different optogeometric configurations are shown numerically to exhibit an almost perfect blazing in the -1st reflected order with a plateaulike spectral dependence in nonpolarized light.

High-accuracy translation–rotation encoder with two gratings in a Littrow mount

A new type of translation-rotation encoder that makes use of two identical transparent dielectric gratings lighted in a -1-order Littrow mount is proposed. The correct choice of the wavelength-to-groove-spacing ratio produces only two transmitted beams, which interfere with the highest possible visibility in a large range of experimental conditions. Thus this mounting permits high-accuracy encoders to be produced by the use of cheap photoresist or plastic gratings and opens the way to industrial applications in high-precision mechanics, information processing, etc.

T matrix of the homogeneous anisotropic sphere: applications to orientation-averaged resonant scattering

We illustrate some numerical applications of a recently derived semianalytic method for calculating the T matrix of a sphere composed of an arbitrary anisotropic medium with or without losses. This theory is essentially an extension of Mie theory of the diffraction by an isotropic sphere. We use this theory to verify a long-standing conjecture by Bohren and Huffman that the extinction cross section of an orientation-averaged anisotropic sphere is not simply the average of the extinction cross sections of three isotropic spheres, each having a refractive index equal to that of one of the principal axes.