We demonstrate an improvement of the plane wave expansion method treating two-dimensional photonic
crystals by applying Fourier factorization with generally elliptic polarization bases. By studying one example
of periodically arranged cylindrical elements, we compare our approach to the classical Ho method in which the
permittivity function is simply expanded without changing coordinates, and to the normal vector method using
a normal-tangential polarization transform. The compared calculations clearly show that our approach yields
the best convergence properties owing to the complete continuity of our distribution of polarization bases.
The rigorous coupled wave theory dealing with optics of discontinuous two-dimensional (2D) periodic structures
is reformulated by using the complex Fourier factorization method, which is a generalized implementation of the
fast Fourier factorization rules. The modified approach yields considerably improved convergence properties, as
shown on three samples of 2D gratingsmade as periodically arranged cylindrical holes on the top of quartz, silicon,
and gold substrates. The method can also be applied to the calculation of 2D photonic band-gap structures or
nonperiodic cylindrical devices, and can be generalized to elements with arbitrary cross-sections.
The characteristic matrix T and total matrix M have been determined for isotropic prism coupling gap and anisotropic
one with magnetic ordering in linear magneto-optical approximation. On the base of these matrices the reflection and
transmission coefficients of structure have been specified. The effect of gap thickness, index of refraction and linear
transverse anisotropy of coupling media is discussed. Special attention is devoted to the ultra-thin approximation.
We report on the development of an analytical theory and a method of experimental observation of dynamic properties of magnetic vortices excited in cylindrical ferromagnetic discs magnetostatically coupled into arrays. The theory, based on Thiele's equation of motion and the approximative rigid-vortex model, enables us to determine the eigenfrequencies of the vortices' harmonic oscillation within pairs [J. Shibata et al., Phys. Rev. B 67, 224404 (2003)] and large arrays [J. Shibata and Y. Otani, Phys. Rev. B 70, 012404 (2004)] of the discs, the latter being a proposal to design a new type of artificial crystals with magnonic band structures. Then we briefly describe the basic principles of our time-resolved Kerr microscope and show the capabilities of our method to detect all the features studied theoretically. Finally we present an experimental example of observation of the dynamic evolution of short-pulse magnetic field excitation of a vortex weakly coupled within an array of cylindrical Permalloy discs.
Spectroscopic ellipsometry (SE) with microscopic measurement spot is applied to extract geometrical parameters of a bi-periodic array of holes patterned on the top of an Si wafer, namely the holes' diameter and depth, while the period of the patterning is assumed same as the value intended by the manufacturer. The SE response of the structure is simulated by the rigorous coupled-wave analysis implemented as the Airy-like internal reflection series, whose detailed description for the case of 2D gratings is provided with a brief demonstration of its convergence properties. The result of the extraction by SE is compared with results obtained by scanning electron microscopy (SEM) with reasonable agreement. The difference between some of the SE, SEM, and nominal parameters are discussed and the possibility to increase the accuracy of SE-based metrology is suggested.
The rigorous coupled wave analysis (RCWA) implemented as the Airy-like internal reflection series (AIRS) is applied in a theoretical analysis of the optical response of diffraction gratings. Detailed theoretical description of the RCWA with respect to the AIRS implementation is provided, including the application of Li's Fourier factorization rules and the recursive algorithm for sliced relief gratings. Numerical analysis of convergence properties including computation time is demonstrated for structures made of transparent, semiconductor, or metallic materials.
Roman Antos, Martin Veis, Eva Liskova, Mitsuru Aoyama, Jaroslav Hamrle, Takashi Kimura, Pavol Gustafik, Masahiro Horie, Jan Mistrik, Tomuo Yamaguchi, Stefan Visnovsky, Naomichi Okamoto
Spectroscopic ellipsometry (SE) and magneto-optical (MO) spectroscopy are applied to analyze three sets of shallow magnetic gratings. The experimental data of SE are used to extract geometrical parameters of several samples. A half-micrometer thick transparent interlayer present between the periodic magnetic wires and the substrate in one of the sets of the samples is used to increase the sensitivity of SE and MO measurements. Thanks to this sensitivity the geometrical parameters can be extracted together with the material composition of the magnetic film. In order to interpret the magneto-optical Kerr effect (MOKE) measurement, three theoretical approaches are used in the simulations, the rigorous coupled-wave method (CWM), the local mode method (LMM), and a new approach based on comparing CWM with LMM with defining a 'quality factor' of the grating with respect to the wire edges. Using the MOKE spectra in the 0th and -1st diffraction orders, one set of the samples made with a protection capping is analyzed with respect to the native-oxidation process. The quality factor of these samples is extracted from MOKE in the -1st diffraction order for p-polarized incidence. The monitoring system based on both SE and MOKE is rated as highly sensitive and precise, and with accurate determination of the optical and magneto-optical constants it could by applied in multi-parameter fitting.
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