Optical fano resonances in photonic crystal slabs near diffraction threshold anomalies

Akimov, Alexey; Gippius, N. A.; Tikhodeev, S. G.

doi:10.1134/s0021364011080029

Cited by 21 publications

(30 citation statements)

References 15 publications

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“…(a) Structure geometry with parameters as specified in Refs. [16,21]. The structure consists of a periodic grating (dark gray) of a material with refractive index 2.5, embedded into a substrate with permittivity ε (unperturbed case: ε = 2.25), and air on top.…”

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confidence: 99%

First-order perturbation theory for changes in the surrounding of open optical resonators

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2019

Opt. Lett.

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The single-mode approximation of the resonant state expansion has proven to give accurate first-order approximations of resonance shifts and linewidth changes when modifying the material properties inside open optical resonators. Here, we extend this first-order perturbation theory to modifications of the material properties in the surrounding medium. As a side product of our derivations, we retrieve the already known analytical normalization condition for resonant states. We apply our theory to two example systems: A metallic nanosphere and a one-dimensional photonic crystal slab.Nanophotonic structures such as photonic crystals or plasmonic nanoparticles compromise optical resonances with strong electromagnetic near-fields. Consequently, even tiny changes in the the surrounding materials can have significant influence on the resonances frequencies. This is the key to various kinds of optical sensing applications [1-7]. Fig. 1 displays exemplarily a metallic sphere, around which the surrounding permittivity is changed from ε to ε + ∆ε, thus shifting the resonance wavenumber from k m to k ν .The modeling of such systems often relies on extensive numerical simulations, which can be rather inefficient, since in many practical cases, the variations in the material properties are extremely small. In contrast, perturbative theories are particularly suited for these cases. They are based on the eigenmodes of the system, also known as resonant states (RS) or quasi-normal modes [8][9][10][11], and have proven to be very efficient for all kinds of perturbations inside or in close proximity to nanophotonic resonators [8,[12][13][14][15][16][17]. However, a general rigorous way to incorporate perturbations of the surrounding medium into the theory is missing so far. The main difficulty arises from the fact that nanophotonic systems exhibit RS that radiate to the far field, so that their field distributions grow with distance to the resonator [15,16,18]. Hence, conventional perturbative formulations for bound states, e.g., known from quantum mechanics, cannot be applied. Several normalization schemes have been developed in recent years (for details, see Refs. [9,10,19] and references therein), but no theory exists so far for perturbations in the exterior. In this Letter, we derive such a theory for homogeneous and isotropic perturbations.The frequency representation of Maxwell's equations [Gaussian units, time dependence exp(−iωt)] can be written as [19]

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confidence: 99%

First-order perturbation theory for changes in the surrounding of open optical resonators

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Weiß²

2019

Opt. Lett.

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“…Such continua are generally known in the theory of quasi-guided modes in photonic crystal structures 35 as potential sources of Wood-Rayleigh anomalies in optical spectra. [36][37][38][39][40] Technically, they are caused in that case by the presence of square roots in the photon dispersion of light propagated and Bragg scattered inside the photonic crystal. In the case of a dielectric cylinder, which is used for the RSE in 2D, the continuum originates mathematically from the cut in the cylindrical Hankel functions solving Maxwell's equations outside the cylinder.…”

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confidence: 99%

Resonant state expansion applied to two-dimensional open optical systems

2013

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The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution.

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“…An interesting deflection of LSPR on an air Rayleigh anomaly is observed in p polarization. This resonance can be described according to the paper [65]. Chapter 5…”

Section: Optical Modes In Waveguides Of Various Thicknessmentioning

confidence: 99%

Fourier modal method for the description of nanoparticle lattices in the dipole approximation

2019

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Rigorous coupled-wave analysis (RCWA) is a very effective tool for the studying optical properties of multilayered vertically invariant periodic structures. However, it fails to deal with arrays of small particles because of high gradients in a local field. In this thesis, we implement discrete dipole approximation (DDA) for the construction of scattering matrices of arrays of resonant nanoparticles. This strongly speeds up the calculations and therefore provides an opportunity for thorough consideration of various layered structures with small periodic inclusions in terms of the RCWA. We study in detail three main stages of the method: calculation of polarizability tensor of a single nanoparticle, effective polarizability of this particle in a lattice and corresponding scattering matrix of the layer for further integration in the conventional RCWA approach. We demonstrate the performance of the proposed method by considering plasmonic lattices embedded in a homogeneous ambiance and placed inside and onto optical waveguides and compare our results with experimental papers. Such phenomena as localized surface plasmon resonances (LSPRs) and lattice plasmon resonances (LPRs) are observed as well as their hybridization with photonic guided modes. High accuracy and fast convergence of our approach are shown by a comparison with other computational approaches. Typical limits of applicability of our approximate method are determined by an exploration of the dependence of its error on the parameters of the structure. This paper is an extended version of our article [1].

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Optical fano resonances in photonic crystal slabs near diffraction threshold anomalies

Cited by 21 publications

References 15 publications

First-order perturbation theory for changes in the surrounding of open optical resonators

First-order perturbation theory for changes in the surrounding of open optical resonators

Resonant state expansion applied to two-dimensional open optical systems

Fourier modal method for the description of nanoparticle lattices in the dipole approximation

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