New formulation of the Fourier modal method for crossed surface-relief gratings

Li, Lifeng

doi:10.1364/josaa.14.002758

Cited by 966 publications

(563 citation statements)

References 17 publications

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“…32 We will determine the effective propagation constant in the SCiC by using the S-parameter retrieval method. 33,34 The complex reflection and transmission coefficients are numerically calculated by the Fourier modal method 35 where 31ϫ 31 Fourier orders were retained to achieve convergent results. By inversion of these scattering data the effective propagation constant k = k z and the effective impedance Z can be determined.…”

Section: Homogeneitymentioning

confidence: 99%

High symmetry versus optical isotropy of a negative-index metamaterial

et al. 2010

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Optically isotropic metamaterials ͑MMs͒ are required for the implementation of subwavelength imaging systems. At first glance one would expect that their design should be based on unit cells exhibiting a cubic symmetry being the highest crystal symmetry. It is anticipated that this is a sufficient condition since it is usually assumed that light does not resolve the spatial details of MM but experiences the properties of an effective medium, which is then optically isotropic. In this work we challenge this assumption by analyzing the isofrequency surfaces of the dispersion relation of the split cube in carcass negative index MM. We show that this MM is basically optically isotropic but not in the spectral domain where it exhibits negative refraction. The primary goal of this contribution is to introduce a tool that allows to probe a MM against optical isotropy.

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Section: Homogeneitymentioning

confidence: 99%

High symmetry versus optical isotropy of a negative-index metamaterial

et al. 2010

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“…We performed calculations with a Fourier modal method in which all modes, including the evanescent modes, are obtained through an eigenvalue problem of the Fourier components of the fields [21,22]. Figure 5 shows the real and imaginary parts of the wave vector k g for the different AR investigated normalized to the wave vector of the fundamental beam in vacuum.…”

Section: Prl 97 146102 (2006) P H Y S I C a L R E V I E W L E T T E mentioning

confidence: 99%

Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays

et al. 2006

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The influence of hole shape on the nonlinear optical properties of metallic subwavelength hole arrays is investigated. It is found that the amount of second harmonics generated can be enhanced by changing the hole shape. In part this increase is a direct result of the effect of hole shape on the linear transmission properties. Remarkably, in addition to enhancements that follow directly from the linear properties of the array, we find a hot hole shape. For rectangular holes the effective nonlinear response is enhanced by more than 1 order of magnitude for one particular aspect ratio. This enhancement can be attributed to slow propagation of the fundamental wavelength through the holes which occurs close to the hole cutoff. Metal nanostructures are known to greatly enhance electromagnetic fields in certain geometries. Therefore they can also boost nonlinear optics. Surface-enhanced Raman scattering (SERS) [1], for instance, makes use of nobel metal nanoparticles to amplify the spectroscopic Raman signature of even a single molecule [2]. Sharp nanosize tips [3] provide a more controlled route to enhance the optical field. Another powerful example of nonlinear enhancement is a single circular hole, surrounded by an ordered plasmonic structure [4]. In addition to the use of single structures, ensembles of multiple nanostructures or extended metal objects can also be used to induce nonlinear enhancement randomly positioned metal nanoclusters show nonlinear effects [5]. A popular example of multiple nanostructures acting together is a subwavelength hole array which exhibits extraordinary optical transmission [6] in the linear regime. Calculations indicate that the local field enhancement associated with the transmission through the holes is exceptionally large [7]. Blair and co-workers showed that second-harmonics generation (SHG) on a hole array is possible [8].

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“…When combined with a supercell technique, the approach can also handle PC waveguides and cavities [17][18][19][20]. Second, is exhibits excellent numerical convergency and accuracy due to the incorporation of many advanced Fourier-analysis skills [14,18,21,22], and the numerical burden is logarithmatically proportional to the sample length of a finite PC structure. Third, the approach can also handle metallic materials and PC structures that exhibit loss of power to the background [15,18].…”

Section: Introductionmentioning

confidence: 99%

Principles of the plane-wave transfer-matrix method for photonic crystals

2005

Science and Technology of Advanced Materials

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We introduce the principle of the plane-wave transfer-matrix method, a theoretical tool that we have recently developed systematically to solve optical problems of photonic crystals (PCs). In this formulation, the electromagnetic fields are expanded into superposition of plane waves associated with the crystal lattice, which facilitates access to many advanced Fourier analysis techniques. We briefly discuss the standard application of the TMM to solution of transmission, reflection and absorption spectra for a finite PC slab and photonic band structures for an infinite PC. Then we push the formulation further to handle wave propagation in semi-infinite PC crystal structures. The three-dimensional wood-pile PC is taken as an example to show the power of the theory. q

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New formulation of the Fourier modal method for crossed surface-relief gratings

Cited by 966 publications

References 17 publications

High symmetry versus optical isotropy of a negative-index metamaterial

High symmetry versus optical isotropy of a negative-index metamaterial

Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays

Principles of the plane-wave transfer-matrix method for photonic crystals

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