Abstract

We study the quality factor variation of three-dimensional Metal-Insulator-Metal nanoresonators when their volume is shrunk from the diffraction limit (λ/2n)3 down to a deep subwavelength scale (λ/50)3. In addition to rigorous fully-vectorial calculations, we provide a semi-analytical expression of the quality factor Q obtained with a Fabry-Perot model. The latter quantitatively predicts the absorption and radiation losses of the nanoresonator and provides an in-depth understanding of the mode lifetime that cannot be obtained with brute-force computations. In particular, it highlights the impact of slow-wave effects on the Q-factor as the size of the resonator is decreased. The Fabry-Perot model also evidences that, unexpectedly, wave retardation effects are present in metallic nanoparticles, even for deep subwavelength dimensions in the quasi-static regime.

Highlights

  • Optical nanoresonators with ultra-small volumes are a key ingredient for numerous nanophotonics applications

  • We study the quality factor variation of three-dimensional Metal-Insulator-Metal nanoresonators when their volume is shrunk from the diffraction limit (λ /2n)3 down to a deep subwavelength scale (λ /50)3

  • Confining light in three-dimensional (3D) volumes well below the diffraction limit can be achieved by taking advantage of the large wavevectors of surface plasmon polaritons (SPPs) that result from the coupling between light and free electrons in metals [10]

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Summary

Introduction

Optical nanoresonators with ultra-small volumes are a key ingredient for numerous nanophotonics applications. We study the resonance with the lowest energy supported by a single 3D MIM resonator, see Fig. 1 This fundamental resonance is crucial in the context of ultra-small resonators because it has no cut-off and can be scaled down to deep subwavelength dimensions in the quasi-static regime. The authors in [26] overlooked the importance of slow-wave effects and derived a Q-factor expression that is not consistent with the asymptotic value derived in the quasi-static limit for metallic nanoparticles of arbitrary shape [37] We correct this discrepancy by properly taking into account slow-wave effects in the Fabry-Perot model. For ultrasmall resonators, the Fabry-Perot model correctly predicts the quality factor saturation toward the asymptotic value obtained in the quasi-static limit [37]

Magnetic resonance of a single 3D MIM resonator
Fabry-Perot model of the resonance
Fabry-Perot equations: phase-matching condition and quality factor
Analysis of the Q-factor increase
Fabry-Perot model in the quasi-static limit
Findings
Conclusion
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