**3. Bundt plasmonic antenna**

Now we are going to examine a novel optical antenna design that is called Bundt Optenna [25, 26]. Here, the optical antenna is abbreviated as "Optenna" and has a unique shape that looks like a Bundt baking pan. The Bundt Optenna has been featured by scientific media as promising for nanoscale infrared detection devices such as solar cells, telecommunications photodetectors, shortwave cameras, and mid-wave microbolometers [27]. In addition, it can keep plasmonic losses to a minimum while focusing infrared radiation to nanoscale size, thus doing the trick [28].

This Bundt Optenna has many desirable advantages. It has an ultra-broadband optical response covering the near, shortwave, and mid-wave infrared bands with high fractional bandwidth up to 42%. It is polarization insensitive with a wide field of view. It can squeeze both electric and magnetic fields down to 50 nm spot area to enhance optical absorption efficiency within a thin-film detection layer. The power absorption enhancement can reach up to 8 orders of magnitude (i.e. 80 dB). Moreover, it has a compact size with potential applications in energy harvesting, optical communications, and biomedical technology.

**Figure 5** shows a schematic diagram of the Bundt Optenna structure with different cross-sections. It has a gold concentric structure that is filled with air as a dielectric material. The Optenna is built on top of a semiconductor thin-film detection layer above a thick bulk substrate. **Figure 5a** shows a two-dimensional periodic array of the Bundt unit-cells with a periodic separation of "L". A vertical cross-section in a single unit cell is shown in **Figure 5b**. It shows three stages. The first stage consists of a

#### **Figure 5.**

*The schematic diagram of the proposed infrared detection device with Bundt Optenna. (a) a perspective view of 2D periodic Bundt array, (b) a vertical cross-section of unit-cell indicating different stages and the underneath semiconductor layers, (c) a vertical cross-section of unit-cell indicating different dimensions [25].*

coaxial (concentric) conical horn and a middle post. The conical concentric shape allows the Optenna to easily impedance match surrounding free-space, and collect most of the incident radiation due to its relatively large input aperture. In addition, this shape allows for polarization-insensitive operation because of its symmetry around the central axis. The second stage is an annular gold waveguide that matches the optical impedance between the first stage and the third stage. The third stage is a conical gold wedge extending through the thin-film detection layer. It allows the excited SPP to penetrate deep inside the absorbing layer thus increasing the overall absorption area inside the thin-film. **Figure 5c** labels different dimensions on the cross-section of a single unit cell.

The incident free-space infrared radiation is collected by the Bundt array's large aperture. The coaxial horn and post with air-filling dielectric act like a metal–insulator–metal (MIM) waveguide that has a conical flare. This waveguide is end-fire excited by incident free-space radiation and generates SPP on the antenna gold surfaces forming a TE11 mode [29] that propagates along the MIM waveguide. Both the plasmonic electric and magnetic fields are squeezed gradually during propagation until they reach a sub-wavelength nano wide (F = 50 nm) annular area at the first stage output. This area can be found by the following equation:

$$\text{Area} = \pi \times \left[ \left( \frac{B}{2} + F \right)^2 \right] - \left( \frac{B}{2} \right)^2 \tag{1}$$

The "A", "B", "C", and "E" are the dimensions of Bundt's first stage. They are optimized to allow optical-impedance matching between free-space and Bundt coaxial horn. This means the optical bac-reflections are minimized, and in turn forward propagating transmitted signals are maximized. An annular waveguide with a width "F" and length "G" that is filled with air is used as an intermediate second stage. Which matches the optical impedance between the antenna's first stage and third stage (absorbing thin-film). The annular waveguide is an extension of the flared coaxial horn with TE11 propagating squeezed mode. The annular waveguide has multiple reflections between its input and output like a Fabry-Perot resonator. Therefore, the waveguide length "G" is chosen to make the round-trip phase-shift (Δφ) equal to "mπ". This condition can be written as:

$$
\Delta \rho = \mathbb{Z} \times \mathbb{G} \times K + \delta \rho = m \times \pi \tag{2}
$$

The "δφ" is the reflections phase-shift at waveguide input and output, "k" is the propagation constant, and "m" is an integer number. This condition results in constructive interference at waveguide output, and destructive interference of backreflected waves at waveguide input.

The third stage of the Bundt Optenna is a conical gold wedge of length "H", besides the Bundt base on top of the thin-film layer. The third stage acts like a flared MIM waveguide that is excited by the SPP out of the annular waveguide. This SPP spreads inside the absorbing thin-film layer. Therefore, the third stage allows excited SPP to penetrate and spread deep inside the thin-film, thus increasing the overall absorption area of the absorbing layer.

The Bundt Optenna array was designed and simulated over different infrared bands. That includes near-infrared (NIR), short-wave infrared (SWIR), and mid-wave infrared (MWIR) wavelengths bands. The dimensions of different Bundt stages are optimized during numerical simulations to get the best optical impedance matching. That means minimizing back reflections and maximizing transmission to obtain an almost flat response. We obtain four designs of the Bundt Optenna. Each design has specific dimensions. **Table 1** summarizes the dimensions of each design. It is found that there are some rules which should be satisfied in all these designs. The coaxial horn length "E" should be greater than the maximum wavelength of each design range. That is to ensure having one electric-field cycle along the horn length. Also, the inner perimeter of the annular waveguide (i.e. π � B) should be greater or equal to the maximum wavelength of the corresponding range. That ensures the magnetic field one period around the waveguide perimeter is not smaller than the maximum wavelength of TE11 mode. To minimize ohmic loss of SPP, the "E" dimension and (π � B) are selected to be equal to the maximum wavelength. The dimension "A" is chosen to maintain a symmetric coaxial horn. The dimensions "C", "D", "G", and "L" are chosen by numerical iterations to minimize back-reflections. The largest Bundt unit-cell 3.25x3.25x6.8 μm3 is for the MWIR design. While the largest unit-cell aspect ratio 3.6:1 is for the NIR design. The Bundt has an overall compact size with a reasonable aspect ratio. The Optenna designs "1", "2", "3", and "4" are useful in applications such as solar cells, optical communications photodetectors, SWIR sensors/ cameras, and MWIR thermal detection/ imaging with microbolometers, respectively.


*The assigned dimensions' are already indicated in Figure 1, and they are measured in "μm". The dimensions H = 0.7 μm and F = 50 nm are fixed for all the designs [25].*

#### **Table 1.**

*The four designs of Bundt Optenna that can cover the three infrared bands.*
