Photonic Gap Antennas Based on High-Index-Contrast Slot Waveguides

Optical antennas made of low-loss dielectrics have several advantages over plasmonic antennas, including high radiative quantum efficiency, negligible heating, and excellent photostability. However, due to weak spatial confinement, conventional dielectric antennas fail to offer light-matter interaction strengths on par with those of plasmonic antennas. We propose here an all-dielectric antenna configuration that can support strongly confined modes ($V\sim {10}^{-4}{\lambda }_0^3$) while maintaining unity antenna quantum efficiency. This configuration consists of a high-index pillar structure with a transverse gap that is filled with a low-index material, where the contrast of indices induces a strong enhancement of the electric field perpendicular to the gap. We provide a detailed explanation of the operational principle of such photonic gap antennas (PGAs) based on the dispersion relation of symmetric and asymmetric horizontal slot waveguides. To discuss the properties of PGAs, we consider silicon pillars with air or the polymer CYTOP as the gap material. We show by full-wave simulations that PGAs with an emitter embedded in the gap can enhance the spontaneous emission rate by a factor of approximately $1000$ for air gaps and approximately $400$ for CYTOP gaps over a spectral bandwidth of $\mathrm{\Delta }\lambda \approx 300\mathrm{nm}$ at $\lambda =1.25\mu \mathrm{m}$. Furthermore, the PGAs can be designed to provide unidirectional out-of-plane radiation across a substantial portion of their spectral bandwidth. This is achieved by setting the position of the gap at an optimized off-centered position of the pillar so as to properly break the vertical symmetry of the structure. We also demonstrate that, when acting as receivers, PGAs can lead to a near-field intensity enhancement by a factor of approximately $3000$ for air gaps and approximately $1200$ for CYTOP gaps.

Figure 1

Photonic gap antennas (PGAs) and the dispersion relation of their infinite-length waveguide counterparts. (a) A perspective view of different PGA structures: a symmetric rectangular PGA (left) and an asymmetric elliptical PGA (right). (b) A perspective view of an infinite-length (along $x$) conventional silicon waveguide (left), a symmetric slot waveguide (center), and an asymmetric slot waveguide (right). (c) The dispersion relation for the two lowest quasi-TM eigenmodes (electric field along the $z$ axis), showing the normalized real angular frequency, $\mathrm{Re}(\omega )/{\omega }_0,\mathrm{where}{\omega }_0=2\pi (235)\mathrm{THz}$, as a function of the normalized propagation constant, $k_x\ell /2\pi ,\mathrm{where}\ell =250\mathrm{nm}$. These relations are plotted for the conventional silicon waveguide (red), the symmetric slot waveguide (black), and the asymmetric slot waveguide (blue). The corresponding cross sections are shown as insets in (d). The waveguides are composed of silicon, with an air gap, with a gap thickness of 2 nm. The height (including the gap) and width of the waveguide cross sections are 582 nm (along $z$) and 240 nm (along $y$), respectively. The solid gray lines show the light lines for bulk air and silicon. The vertical dashed line at $k_x\ell /2\pi =0.5$ intersects the dispersion curves of the waveguides at their respective resonant frequencies for a finite-length ($\ell =250\mathrm{nm}$) of the structure along the $x$ axis. (d) An enlarged portion of the dispersion relation in (c), identified by a rectangle, highlighting changes due to the incorporation of the gap layer.

Figure 2

The normalized $E_z$ of the eigenmode profiles for the infinite-length waveguides in Fig. 1 and SER enhancement factors for the corresponding PGAs (finite-length waveguide sections). The $E_z$ components for the ${\mathrm{TM}}_0$ (red) and ${\mathrm{TM}}_1$ (blue) modes are shown at their respective resonant frequencies for (a) the conventional silicon waveguide, (c) the symmetric slot waveguide, and (e) the asymmetric slot waveguide. (b),(d),(f) The SER enhancement factors versus the frequency for the corresponding finite-length ($\ell =250\mathrm{nm}$) waveguide structures of (a), (c), and (e), respectively. The vertical dashed lines in (b), (d), and (f) are at the resonant frequencies of the ${\mathrm{TM}}_0$ (red) and the ${\mathrm{TM}}_1$ (blue) mode calculated from the dispersion relation illustrated in Figs. 1 and 1.

Figure 3

The design and emission properties of elliptical PGAs. (a) A perspective view of the asymmetric elliptical PGA ($t_1/t_2=3$) with design parameters (in nanometers) $w_1=240$, ${\ell }_1=300$, $t_1=435$, $t_2=145$, and $g=2\mathrm{nm}$. The emitter is $\hat{\mathit{z}}$ oriented and positioned within the gap layer 124 nm away from the vertical central axis of the structure along the $x$ axis. (b) SER enhancement factors versus frequencies for the asymmetric PGA in (a) and the symmetric PGA with $t_1/t_2=1$ ($t_1+t_2$ constant). (c) The electric field distribution in the central $x$-$z$ plane of the asymmetric PGA for the ${\mathrm{TM}}_0$ (left) and ${\mathrm{TM}}_1$ (right) modes. (d) The F:B ratio as a function of the frequency for asymmetric and symmetric PGAs.

Figure 4

The radiation properties of an asymmetric PGA with $t_1/t_2=1.76$ and SER enhancement factors for different gap thicknesses and materials. The total thickness of silicon ($t_1+t_2$), $w_1$ and ${\ell }_1$ are the same as in Fig. 3. (a) The F:B ratio (left axis) and directivity (right axis) versus the frequency for the PGA with a 2-nm air gap. The insets show the radiation patterns of the PGA in the $x$-$z$ plane at the corresponding frequencies, with their maximum directivity normalized to 0 dB. (b) SER enhancement factors versus the frequency for the PGA with air gaps (red) and CYTOP gaps (blue) of thickness $g=2\mathrm{nm}$ (solid lines) and $g=5\mathrm{nm}$ (dashed lines).

Figure 5

The extinction cross sections and electric field enhancement factors of PGAs with a CYTOP gap. (a) The extinction cross section (${\sigma }_{\mathrm{ext}}={\sigma }_{\mathrm{sca}}$) versus the frequency. (b) The field enhancement factor $|{\mathbf{E}}_{\max }|/|{\mathbf{E}}_{\mathrm{inc}}|$ as a function of the frequency for elliptical PGAs, where the gap position and thickness are varied. The combined thickness of silicon ($t_1+t_2$), $w_1$, and ${\ell }_1$ are the same as for the PGA in Fig. 3. (c) The near-field intensity distribution for the asymmetric PGA ($t_1/t_2=3$) with $g=2\mathrm{nm}$ on a plane parallel to $x$-$y$ plane and passing through the center of the gap layer. (d) The intensity distribution within the gap layer along the $x$ axis at $y=0$. The upper line of the shaded region represents the intensity profile at the center of the gap ($z=0$), whereas the lower bound represents the intensity profile near the CYTOP-$\mathrm{Si}$ boundaries ($z=-g/2,g/2$). The field intensity increases from the bottom CYTOP-$\mathrm{Si}$ boundary to the center of the gap and decreases in a similar pattern up to the top CYTOP-$\mathrm{Si}$ boundary.