Semianalytical Model for Design and Analysis of Grating-Assisted Radiation Emission of Quantum Emitters in Hyperbolic Metamaterials

Abstract

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.

Hyperbolic Metamaterials and Metasurfaces: Fundamentals and Applications

“…However, due to the limitation of dissipation and large impedance mismatch in bulk HMMs, it has been demonstrated theoretically and experimentally that the emission rate and intensity will be higher within the HMMs than near the interface. For example, using nanopatterned Ag–Si multilayer HMMs, the spontaneous recombination rate in InGaN/GaN quantum wells (QWs) can be enhanced to ≈160‐fold in broadband .…”

“…Compared with other optical metamaterials, like chiral and split ring resonator–based metamaterials, HMMs have advantages of relative ease of fabrication at optical frequencies, broadband nonresonant and 3D bulk responses, and flexible wavelength tunability. As a result, HMMs have attracted widespread interest and become a good multifunctional platform for many exotic applications, such as optical negative refraction and light beam steering, subdiffraction‐limited imaging and nanolithography, spontaneous and thermal emission engineering, ultrasensitive optical, biological, and chemical sensing, omnidirectional and broadband optical absorption …”

Polarization-sensitive beam steering from quantum emitters coupled with birefringent metamaterials

“…Furthermore, the anomalous dispersion of periodically patterned structures enables beam steering in quantum emitters via near-field coupling of optical resonances. Owing to recent advances in monolayer transition metal chalcogenides with a direct band gap, theoretical and experimental research has explored 1D periodic grooves [10], two-dimensional (2D) photonic crystals [11,12], and hyperbolic metamaterials [13][14][15][16][17]. For example, Zhang et al reported unidirectional radiation with a narrow divergence angle from monolayer MoS 2 by exploiting Fano resonance in 2D freestanding photonic crystal slabs [11].…”

“…Various attempts based on birefringent hyperbolic metamaterials have been made to steer the direction of light. Mota et al demonstrated theoretically that Ag∕TiO 2 hyperbolic metamaterials lead to polarizationindependent vertical radiation from quantum emitters [13]. Jacob et al theoretically reported that quantum emitters placed on hyperbolic dispersive substrates lead to directional surface plasmon waves [14].…”

Vertical beaming of incoherent quantum emitters via the near-field coupling of Fano resonance

“…To induce a more dramatic beaming effect, one-dimensional (1D) grating surfaces [12], two-dimensional (2D) photonic crystal cavities [13][14][15], hyperbolic metamaterials [16], and even single nanowires [17] that serve as photonic dispersionengineered structures have been extensively studied. The idea of achieving directional emission from quantum emitters by coupling with optical resonances was studied over past decades; in previous literatures, periodic air holes were directly incorporated into quantum emitters so that they simultaneously served as photonic crystals [18,19].…”