We propose a semianalytical method to model, in both two and three dimensions (2D and 3D, respectively), the radiation emission of quantum emitters (QEs) interacting with nanopatterned structures. We then investigate the emission from QEs near a hyperbolic metamaterial (HMM) with a metallic cylindrical grating on its top and a poly(methyl methacrylate) substrate embedded with QEs on its bottom. The optimization of the cylindrical grating is carried out first using a 2D model (due to its low computational cost), followed by a performance study based on a 3D model. We show that an appropriate choice of grating parameters (period, height, and fill factor) allows not only the control of the QE emission direction but also the increase of both the Purcell factor and the total power coupled from the HMM into free space. In addition, the proposed method provides a detailed mapping of both the Purcell factor and the radiated power as a function of position, enabling us to understand how the QE location affects its behavior. Furthermore, we demonstrate that the QEs with the highest Purcell factor (viz., perpendicularly polarized ones) contribute more to the power radiated into the far field than previously expected. We also show that, in addition to a high Purcell factor of about 145, perpendicularly polarized QEs radiate up to 2 times more power if placed 10 nm from the HMM as they would in free space.
Gated tunable materials-based devices have proven efficient structures to dynamically control quantum emitters’ (QEs) photonic density of states. The active permittivity control enabled by these materials allows manipulating the coupling and dissipation of evanescent modes radiated by the QE, hence controlling the emission parameters. In this sense, we propose here the design and optimization of a plasmonic device coupled with nanoantennas capable of dynamically manipulating the QEs’ emission at visible wavelengths using a thin gated doped titanium nitrate layer. We explore the use of metallic cubic and bow-tie antennas and study their unique characteristics related to enhancing the QEs’ emission. For the nanoantenna geometrical parameters optimization, we propose a discrete-dipole-approximation (DDA) method to accurately calculate all the radiation parameters of a QE embedded in a layered medium coupled to a nanoantenna. This technique allows calculating the decay behavior of QEs arbitrarily distributed, which is only feasible with knowledge of the Purcell factor and quantum efficiency mapped for all possible positions, easily achieved with the proposed model. We show that by employing the proposed DDA, the time required for optimizing and building those maps to evaluate the device’s response is drastically reduced (98%) compared to conventional numerical techniques. Using the DDA to optimize the antenna allowed the device’s quantum efficiency to be enhanced from 1.8% (no nanoantenna) to 8% and 10.5% using the cubic and bow-tie nanoantenna, respectively. In addition, the nanoantenna helps decrease the QE lifetime by a factor of approximately 2, allowing faster modulation speeds. Finally, our modeling and findings can be used to pave the way for the design of new gated optical modulators coupled with nanoantennas for applications that require amplitude modulation.
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