Guidelines for Engineering Directional Polariton Launchers

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Guidelines for Engineering Directional Polariton Launchers

Rafael A. Mayer, Flávio H. Feres, Francisco C.B. Maia, Ingrid D. Barcelos, Alexander S. McLeod, Aleksandr Rodin, and Raul O. Freitas

Phys. Rev. Applied 18, 034089 – Published 30 September 2022

Abstract

Nanophotonic devices based on two-dimensional crystals enable various technological applications, ranging from biosensing to quantum communication. In those devices, plasmonic antennas have been extensively explored in the photon-polariton conversion, as they allow field confinement within subdiffraction volumes. Despite the wide-reaching potential of polaritonics, essential rules for engineering polariton launchers are still to be developed, as the influence of the antenna geometry and source parameters on the polariton directivity is unknown. Here, we address this issue by combining concepts of radio-frequency antenna design with established polariton modeling. As an input for the model, we simulate hyperbolic phonon polariton waves in hexagonal boron nitride launched by metallic antennas. By adapting a Fresnel and Fraunhofer field regions formalism to polaritonics, we optimize the model accuracy and graphically represent several launching parameters as radiation patterns. Furthermore, we demonstrate how our framework can be applied to real antennas by employing it to experimental near-field images of polaritons reported in the literature. Our results show that the antenna geometry, its resonance order, and the angle of incidence of the light can strongly influence the polariton-wave pattern in the crystal. We foresee that our framework can add to further studies approaching optimized polariton launching and help the engineering of nanophotonic chips.

Received 2 May 2022
Revised 15 July 2022
Accepted 15 August 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.034089

Physics Subject Headings (PhySH)

Integrated optics Nanoantennas Nanophotonics Plasmonics Polaritons

2-dimensional systems

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Rafael A. Mayer ^1,2,*, Flávio H. Feres^1,2, Francisco C.B. Maia ¹, Ingrid D. Barcelos ¹, Alexander S. McLeod ³, Aleksandr Rodin ^4,5, and Raul O. Freitas ^1,†

¹Brazilian Synchrotron Light Laboratory, Brazilian Center for Research in Energy and Materials, Campinas, São Paulo 13083-100, Brazil
²Institute of Physics Gleb Wataghin, State University of Campinas, Campinas, São Paulo 13083-859, Brazil
³School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁴Yale-NUS College, 16 College Avenue West 138527, Singapore
⁵Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546 Singapore

^*rafael.mayer@lnls.br
^†raul.freitas@lnls.br

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Vol. 18, Iss. 3 — September 2022

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Images

Figure 1
(a) The parameters of the rod and disk antennas on top of $h$ -BN/ $Ca F$ $_{2}$ . (b) The simulation setup of an antenna illuminated by $p$ -polarized light at an angle of incidence $θ$ . The antenna converts a portion of the radiation into HPhP in the $h$ -BN and scatters the other portion to the far field. A monitor located above the antenna records the $Re [E_{z}]$ fields. (c) $| E_{z} |$ field profile at the cross section of a rod antenna with $L = 3 μ m$ when illuminated at normal incidence ( $θ = 0^{\circ}$ ) at $ω = 1400 {cm}^{- 1}$ . The $x$ axis is rescaled for a clearer visualization.
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Figure 2
(a) The $Re [E_{z}]$ distribution for $ω = 1480 {cm}^{- 1}$ of HPhPs launched by disk antennas. (b) The HPhP $r_{d}$ patterns for different $D$ and $θ$ values. The scale in (a) represents $2 μ m$ . The averaged detectable distance (c) and the directivity of the disks (d) as a function of $D$ . The gray dashed lines indicate the disk diameters of $D = 2.6$ , $5.5$ , and $8.5 μ m$ .
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Figure 3
Simulated HPhP wave fronts revealed by electric field contour lines for rod antennas of (a) $L = 1 μ m$ and $ω = 1420 {cm}^{- 1}$ and (b) $L = 5 μ m$ and $ω = 1500 {cm}^{- 1}$ , at $θ = 0^{\circ}$ . (c) $Re [E_{z}]$ profiles along the diagonal (inset dashed blue line) and on-axis (inset dashed red line) directions, for $L = 3 μ m$ and $ω = 1440 {cm}^{- 1}$ . The inset shows the $Re [E_{z}]$ distribution with the diagonal (blue) and on-axis (red) directions, highlighted as dashed lines. (d) The red points indicate $Δ λ_{p}^{on - axis} (r_{0})$ [Eq. (4)] for the on-axis direction. The blue dashed line represents the fitted exponential curve for the $Δ λ_{p}^{diag .} (r_{0})$ data points in the diagonal direction (blue points). The small open circle indicates the position $r_{0}$ where $Δ λ_{p}^{i} = 10 %$ for this case. (e) $r_{0} (Δ λ_{p}^{diag .} = 10 %)$ as a function of $L^{2} / λ_{p}$ for different values of $L$ and $ω$ . A linear fit is represented as a black dashed line. (f) An illustration of the field regions of HPhP waves launched by a rod antenna. The inset in the Fraunhofer region ( $r_{f, p} < λ_{p}$ ) indicates that, in this region, the launching properties can be described in polar coordinates, while in the Fresnel region ( $r_{f, p} > ℓ$ ), the field profile should be modeled in directions that are perpendicular to the contour of the antenna.
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Figure 4
The launching properties of rod antennas, for $L = 1 μ m$ (b)–(d), $2 μ m$ (e), $3 μ m$ (f), and $4 μ m$ (g) under normal illumination $(θ = 0^{\circ})$ and $ω = 1480 {cm}^{- 1}$ . For $L = 1 μ m$ , the launching properties are graphically represented as polar plots, a choice based on the field regions criterion in Fig. 3. A schematic of the rod antenna in polar plot (a) helps the visualization of the analyzed directions. For the other antenna lengths, the launching properties are represented in Cartesian plots, as vectors that are perpendicular to the antenna contours. A and f are represented in color scale, while ${\vec{r}}_{d}$ is represented as gray arrows that are scaled with the dimensions of the antennas.
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Figure 5
(a) A $r_{d}$ polar plot retrieved via the model from the real-space $| S_{2} |$ s-SNOM image at $1430 {cm}^{- 1}$ . (b) $A$ , $f$ , and $r_{d}$ patterns calculated from the s-SNOM amplitude near-field image measured at $1515 {cm}^{- 1}$ . In (a) and (b), the scale bars represent $2 μ m$ . The size of the $r_{d}$ arrows in (b) follows the image scale. (c),(d) Experimental s-SNOM amplitude profiles extracted along the dashed blue lines indicated in (a) and (b), respectively. The solid blue lines indicate the amplitude profiles calculated using the model. The vertical red dashed line indicates $r_{d}$ for these antenna and frequency configurations. $2 δ$ represents twice the standard deviation of the s-SNOM signal outside the waves zone and it is applied on the definition of $r_{d}$ . The s-SNOM data in (a) and (b) are obtained from Ref. [15], with the permission of the authors.
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