From Dark to Bright: First-Order Perturbation Theory with Analytical Mode Normalization for Plasmonic Nanoantenna Arrays Applied to Refractive Index Sensing

Weiß, Thomas; Mesch, Martin; Schäferling, Martin; Gießen, Harald; Langbein, Wolfgang Werner; Muljarov, Egor A.

doi:10.1103/physrevlett.116.237401

Cited by 85 publications

(115 citation statements)

References 42 publications

(32 reference statements)

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“…It should be noted that this formulation of the normalization is slightly different than in most of our previous works on the resonant state expansion [10,[15][16][17][18][19][20][21]25,27,28], which is valid also for magnetic and bianisotropic materials [26]. This formulation can be reduced to our previous results for nonmagnetic materials that are solely described by the electric field, the electric permittivity, and the electric current as a special case.…”

Section: Resonant Statesmentioning

confidence: 86%

“…When normalizing the resonant states appropriately [10,[15][16][17][18][19][20][21]26,27], they can be used together with possible cuts to expand the Green's dyadic with outgoing boundary conditions as follows:…”

Section: Resonant Statesmentioning

confidence: 99%

“…Calculating the derivative is trivial for the first term on the right-hand side. For the second term, we have to differentiate the analytical continuation of F n on the complex k plane, which depends on the geometry of interest [15][16][17]20,21,27].…”

Section: Resonant Statesmentioning

confidence: 99%

“…The resonant states and their field distributions are calculated by the methods described in Refs. [20,50,51]. In the Appendix, we sketch how to use our formalism for single scatterers in three-dimensional space and give more details on the planar periodic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Several approaches have been suggested for the normalization of resonant states [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This includes approximate formulations for highquality modes [23][24][25], the utilization of perfectly matched layers [14] or, equivalently, complex coordinates [11] in the exterior of the system, as well as numerical approaches [20,22].…”

Section: Introductionmentioning

confidence: 99%

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How to calculate the pole expansion of the optical scattering matrix from the resonant states

Weiß

Muljarov

2018

Phys. Rev. B

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We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wave numbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions, or the restriction to geometries, or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wave number with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far-and near-field response based on the physically meaningful resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism.

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Section: Resonant Statesmentioning

confidence: 86%

Section: Resonant Statesmentioning

confidence: 99%

Section: Resonant Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How to calculate the pole expansion of the optical scattering matrix from the resonant states

Weiß

Muljarov

2018

Phys. Rev. B

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Graphene Tunable Plasmon–Phonon Coupling in Mid‐IR Complementary Metamaterial

Chen

Hasan

et al. 2018

Adv Materials Technologies

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concentration monitoring. [1] In order to improve sensing accuracy, the engineered photon-electron oscillation resonant along the interface or confined in the subwavelength metamaterial can be utilized. [2] This collective electromagnetic oscillating behavior known as plasmonic resonance is able to express the unique optical features under different conditions. Among the various types of plasmonic resonances, Fano resonance is characterized by the sharp asymmetric line shape, created by the interference of a narrow discrete state (black or subradiant mode) with the broadband continuum state (bright or super-radiant mode) and is favorable for constructing slow light or nonlinear optical platform to launch the high-Q enhanced applications, such as biochemical sensing. [3][4][5][6] The most popular approach to the excitation of Fano resonance in the mid-infrared frequency range is to break the symmetry of metamaterial geometry. [7][8][9] There are other methods including the multistacking of thin metal and dielectric layers [10] and making use of material intrinsic damping as the subradiant mode. [11][12][13] For example, with the mid-infrared vibrational absorption resonance (phonon band) of silicon dioxide as the dark mode, the strong Fano coupling between the SiO 2 thin film and metamaterial split ring resonator (SRR) is observed such that it leads to mode splitting featured as frequency anticrossing. [13] In the asymmetric SRR metamaterial, polymethyl-methacrylate (PMMA) produced Fano resonance is enhanced as well. [14] The Fano resonance from metamaterial plasmon coupled with the phonon vibration of PMMA is varied through changing metamaterial geometry. [11,15] Moreover, the realization of the ultrasensitive detection of polymer molecule is obtained through matching the polymer phonon resonance with the Fano resonance of periodic nanostructures. [16] The alteration of Fano resonance can be achieved by the individual or simultaneous control of dark and bright resonance. The aforementioned geometry variation of subwavelength metamaterial can be used to shift the broad bright mode resonance. The alternative approaches such as mechanical stress, [17] liquid crystal, [18] micro electromechanical system technology [19] are exploited to either modify the optical properties of the surrounding material or actively reconfigure the structure. Recently, the dynamic manipulation of Fano resonance by graphene electrostatic tuning has been demonstrated by some groups. [20,21] Metamaterial-based plasmonics has become an overwhelming research field due to its enormous potential and versatility in molecular sensing, imaging, and nonlinear optics. This work presents a new tunable plasmonic platform on which the metamaterial resonance is coupled with infrared vibrational bond in the presence of graphene electrostatic modulation. The maximum electric field enhancement factor induced by mode coupling is 14 and the quality factor (Q-factor) of phonon mode is increased approximately by fourfold. The graphene electrostatic modulation b...

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Symmetry‐Protected Dual Bound States in the Continuum in Metamaterials

Cong

Singh

2019

Advanced Optical Materials

258

117

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to access extreme confinement of photons into micro-or nanoscale region [3,10,11] above the light line within the radiation continuum. In general, EM wave is usually interpreted in terms of frequency spectrum, and it propagates as a spectral continuum above the light line in different media. Different orders of resonances may be found in the propagating continuum at specific frequencies described by i n n n 0  ω ω γ = + , where the real part indicates resonance frequencies and the imaginary part indicates the leakage rates of the n-order mode. [12] For a strongly confined mode, the leakage rate is significantly reduced, and goes to zero if photons are perfectly trapped in a so-called bound state in an ideal scenario. [13] However, such a bound state in the continuum (BIC) is not observable from the spectrum due to the nonradiative feature with vanishing spectral linewidth. As an embedded eigenvalue of the photonic system, [14] it becomes visible in the spectrum with a finite leakage rate as a quasi-BIC by introducing external perturbations. Such a BIC-inspired mechanism for light confinement allows a general strategy to access extremely high quality factor (Q, Q = ω 0 /2γ) resonance in optical cavities.Dielectric photonic crystals (PhCs) are an excellent platform to explore the BICs which largely avoid the intrinsic Ohmic loss for extremely high Q generation by exciting displacement current. [15,16] Nevertheless, the geometric size of unit cells in PhCs is usually at the scale of resonance wavelength, and resonant energy is thus loosely confined in the resonator cavity with a relatively large mode volume (V). In this condition, Purcell factor proportional to Q/V is largely reduced in the traditional PhCs despite a large Q, which hinders the efficient spontaneous emission rates in the context of cavity quantum electrodynamics. [17] An efficient approach to densely confine photons is by using metamaterials whose building blocks are in the subwavelength scale, and the resonant mode volume could be further reduced to a deep subwavelength scale by carefully designing the resonator geometry and mode properties. Here, we demonstrate dual symmetry-protected BICs in a subwavelength metamaterial that are independently induced by orthogonal polarizations of incident light. The features of the subwavelength BICs are experimentally observed in the terahertz spectrum by slightly breaking the C 2 symmetry with large Q factors. We also show the inverse square dependence of Q factor on the structural asymmetry parameter which describes a Bound state in the continuum (BIC) is a mathematical concept with an infinite radiative quality factor (Q) that exists only in an ideal infinite array of resonators. In photonics, it is essential to achieve high Q resonances for enhanced light-mater interactions that could enable low-threshold lasers, ultrasensitive sensors, and optical tweezers. Hence, it is important to explore BICs in different photonic systems including subwavelength metamaterials where symmetry-protected dual BICs exist. Th...

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From Dark to Bright: First-Order Perturbation Theory with Analytical Mode Normalization for Plasmonic Nanoantenna Arrays Applied to Refractive Index Sensing

Cited by 85 publications

References 42 publications

How to calculate the pole expansion of the optical scattering matrix from the resonant states

How to calculate the pole expansion of the optical scattering matrix from the resonant states

Graphene Tunable Plasmon–Phonon Coupling in Mid‐IR Complementary Metamaterial

Symmetry‐Protected Dual Bound States in the Continuum in Metamaterials

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