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Register a new userOn the bandwidth of singular plasmonic resonators in relation to the Chu limit
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Plasmonic nanostructures with singular geometries can exhibit a broadband scattering response that at first glance appears to violate the lower bounds for the radiation quality (Q) factor of small radiators, known as the Chu limit. Here we explore this apparent contradiction, investigating the Q factor of the resonant modes supported by two nearly touching cylinders, and analyze how their fractional bandwidth fares in relation to the Chu limit. We first derive lower bounds for the radiation Q factors of two-dimensional objects of arbitrary cross-section. We then discuss the dissipation and radiation Q factors associated with the plasmonic resonances of a cylinder dimer as a function of its gap size. We show that the radiation Q factor is always larger than the minimum Q and, as long as the peaks in the scattering spectrum are well separated, their bandwidth is equal to the inverse of their Q factor. In the limit of touching cylinders, the resonance spectra transition from discrete to a continuum around an accumulation point, yielding a broadband response for any finite level of material loss. Within any given frequency interval, the response is the result of a multitude of plasmon resonances, each individually obeying the Chu limit. Nevertheless, the connection between the Q factor and the overall bandwidth of the scattering response is lost. Our study sheds light onto the exotic resonant phenomena emerging when plasmonic materials are shaped in singular geometries, and outlines their opportunities and limitations for nanophotonics.
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Strong coupling of plasmonic excitations and dipolar emitters, such as organic molecules, have been studied extensively in the last years. The questions whether strong coupling can be achieved with a single molecule only and how this is unambiguously proven are still under debate. A critical issue of plasmonic in contrast to photonic systems is additional excitonic line broadening, which is often neglected when modeling such systems. This has led to too optimistic design predictions or incorrect interpretation of ambiguous experimental data, for example in models relying on Maxwell solvers without self-consistent incorporation of line broadening effects. In this paper, we present a heuristic modeling approach for strongly coupled systems based on plasmonic nanoparticles and dipolar emitters that accounts for such broadening and elucidates on recent experiments with single emitters. We explicitly focus on a clear and intuitive classical description that utilizes well-established methods, easy to use within typical Maxwell solvers. The heuristic model (i) provides experimentally relevant numbers like emitter densities and spectra (ii) allows to discriminate systems, which can reach the strong coupling regime from those, which can not (iii) allows to identify optimization routes and (iv) nicely matches with experimental findings. In particular, we employ an approach related to quasi normal modes and extinction simulations where the excitonic system is represented by a frequency dependent permittivity. As examples, we investigate two configurations with many, but also single emitters, which have been studied in recent experiments.
In several experiments involving material background, it has been observed that the Chu, Einstein-Laub and Ampere formulations of optical force lead to either different optical forces or wrong total optical force. In order to identify the exact reason behind such significant disagreements, we investigate the optical force in a number of tractor beam and lateral force experiments. We demonstrate that the modified Einstein-Laub or modified Chu formulations, obtained from two mathematical consistency conditions of force calculation, give the time-averaged force that agrees with the experiments. We consider both the chiral and achiral objects embedded in complex material backgrounds. Though the distinct formulations of optical force have been made mathematically equivalent in this work; the aspect of physical consistency of these distinct optical force formulations have also been investigated. It is known that the theory of Minkowski suggests zero bulk force inside a lossless object for which we still do not have any experimental verification. In contrast, both modified Einstein-Laub and modified Chu force formulations suggest non-zero bulk force inside a lossless object. Hence, for a future resolution of this discrepancy, we also suggest a possible experiment to investigate the bulk force and to check the validity of these distinct formulations.
Highly resonant photonic structures, such as cavities and metasurfaces, can dramatically enhance the efficiency of nonlinear processes by utilizing strong optical field enhancement at the resonance. The latter, however, comes at the expense of the bandwidth. Here, we overcome such tradeoff by utilizing time-varying resonant structures. Using harmonics generation as an example, we show that the amplitude and phase format of the excitation, as well as the time evolution of the resonator, can be optimized to yield the strongest nonlinear response. We find the conditions for an efficient synthesis of electromagnetic signals that surpass the cavity bandwidth, and discuss a potential experimental realization of this concept.
We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach currently used in the literature (in regimes where this is possible), and demonstrate several order of magnitude improvement for the calculation run times. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters, since they require an integration over a range of frequencies. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam. In the latter example, we show how to compute the quantum optical parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwells equations and are shown to be in excellent agreement.
Metal nanoparticles are the most frequently used nanostructures in plasmonics. However, besides nanoparticles, metal nanowires feature several advantages for applications. Their elongation offers a larger interaction volume, their resonances can reach higher quality factors, and their mode structure provides better coupling into integrated hybrid dielectric-plasmonic circuits. It is crucial though, to control the distance of the wire to a supporting substrate, to another metal layer or to active materials with sub-nanometer precision. A dielectric coating can be utilized for distance control, but it must not degrade the plasmonic properties. In this paper, we introduce a controlled synthesis and coating approach for silver nanowires to fulfill these demands. We synthesize and characterize silver nanowires of around 70 nm in diameter. These nanowires are coated with nm-sized silica shells using a modified Stober method to achieve a homogeneous and smooth surface quality. We use transmission electron microscopy, dark-field microscopy and electron-energy loss spectroscopy to study morphology and plasmonic resonances of individual nanowires and quantify the influence of the silica coating. Thorough numerical simulations support the experimental findings showing that the coating does not deteriorate the plasmonic properties and thus introduce silver nanowires as usable building blocks for integrated hybrid plasmonic systems.
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