**4. Bundt plasmonic Optenna performance**

The Bundt Optenna performance is evaluated using three-dimensional FDTD. The thin-film layer is selected to be silicon nitride as an example, with a silicon substrate. **Figure 6** shows the normalized magnitudes of the electric (magnetic) fields of one unit cell. The wavelength is selected here to be 2.3 μm with TM linear polarization along the x-direction. **Figure 6a** shows a vertical cross-section of a unit-cell (X-Y plane) at Z = 0. As shown, the SPP electric-fields inside the concentric horn are concentrated around the post as it has a small apex angle. The highest electric-field intensity is found to be within the 50 nm wide annular waveguide. Inside the thin-film layer, the high-intensity field propagates and spreads with more SPP concentration around the wedge and Bundt base. This high-intensity field is absorbed and exponentially attenuated within the thin-film layer. It almost vanishes within the underneath silicon substrate. The back-reflected electric-field is very small. A supplementary Video 1 (https://bit.ly/3t8Bundt) illustrates the electric-field propagating at 2.3 μm wavelength inside the Bundt Optenna.

**Figure 6b**–**d** illustrate the electric-field at cross-sections X-Z at Bundt annular waveguide input and output, respectively. They show the TE11 squeezing down to 50 nm wide annular area at the thin-film layer. **Figure 6**–**b** shows the TE11 mode normalized electric-filed at concentric horn input. **Figure 6c** shows the squeezed TE11 plasmonic electric-field at the annular waveguide input. The maximum normalized electric-field is 8 at the annular waveguide. Which is almost eight times enhancement in the field strength (i.e. 18 dB). **Figure 6e** illustrates the squeezed magnetic TE11

#### **Figure 6.**

*The three-dimensional FDTD simulations fields (normalized) within a unit-cell of infrared detection device at a wavelength of 2.3 μm, and TM incident polarization. The normalized electric-field magnitude (E/Eo): (a) a vertical cross-section in a unit-cell, (b) a horizontal cross-section at the input of concentric horn, (c) a horizontal cross-section at the input of annular waveguide, (d) a horizontal cross-section just outside the annular waveguide (i.e. at the entrance of the thin-film layer. The normalized magnetic-field magnitude (H/Ho): (e) a horizontal cross-section at the input of the annular waveguide [25].*

plasmonic -field magnitude at the annular waveguide input. It has a maximum of 4, which indicates ffi12 dB improvement in the field strength. **Figure 6d** shows the nanofocused electric-field at the entrance of the thin-film layer, where the electric-field strength starts to attenuate by optical absorption.

**Figure 7** illustrates the coupling ratio (CR) of TM-polarization in each Bundt Optenna stage versus wavelength. Figures (a), (b), (c), and (d) correspond to designs "1", "2", "3", and "4", respectively. The CR is defined as the ratio of transmitted power at each stage to input power. The CR into stage "1" is considerably high for all designs. However, it does not reach zero dB due to small back-reflections into freespace. The back-reflections are estimated to be less than �7 dB. The CR within the third stage shows a high collection efficiency of the Optenna. The CR of the second and third stages is less than the first stage due to SPP ohmic power loss on gold surfaces. The 3 dB bandwidth (BW) of Bundt Optenna is measured at Optenna third stage because it is the transferred power by the optenna to thin-film layer. The small ripples on curves are due to the Fabry-Perot effect at different interfaces of Optenna stages. **Table 2** shows the bandwidth for each Bundt design together with its centerwavelength (λo) and calculated optical fractional bandwidth (O-FBW). The O-FBW is the ratio of bandwidth to center-wavelength (i.e. BW/λo). The table shows a broadband optical response with a high optical fractional bandwidth ffi 35% up to 42%.

It is worth noting the following issues regarding the Bundt Optenna performance. The field squeezing results in a dramatic reduction in its cross-section area, which

**Figure 7.**

*The coupling ratio estimated in decibels of TM-polarized infrared radiation at successive stages of Bundt Optenna: (a) design "1", (b) design "2", (c) design "3", (d) design "4" [25].*


#### **Table 2.**

*The wavelength range, bandwidth (BW), and center-wavelength (λo) of different Bundt designs, measured in micrometer (μm).*

means a high gain in optical intensity despite power attenuation by SPP ohmic losses. The intensity is defined as the optical power divided by area. The nano-focused fields' intensity increases the effective absorption cross-section area of material atoms, and thus the materials absorption coefficient. Therefore, the thin-film absorption efficiency is expected to increase because of Bundt's high intensity that reaches, for example, 12.4 dB at the wavelength of 3.3 μm. The average ohmic losses on gold surfaces due to SPP are found to be almost -3 dB, which is considered reasonable. The different Bundt designs are found to be polarization insensitive over different tested bands. That is due to the two-dimensional symmetry of the Bundt structure. Therefore, the Bundt optical response is always the same for all types of incident polarizations. That is advantageous as Optenna can collect most of the incident radiation power regardless of its polarization. Moreover, the Bundt field of view is measured by varying radiation incidence angles while monitoring the output intensity. For all the designs, the maximum incidence angle is found to be ffi40°, indicating a Bundt Optenna field-of-view ffi 2 � 40° ffi 80°.

**Figure 8** illustrates the absorption enhancement factor (EF) inside the thin-film layer. It is defined as the ratio between thin-film absorbed power in the case with and without Bundt Optenna. It is measured in linear scale and decibels as well. The absorption EF is high and reaches a maximum of ffi8.5, 29, 80, and 15 dB for designs "1", "2", "3", and "4", respectively. The smallest EF is ffi2 dB at the band edges. The high EF of designs "2" and "3" are because of the very small attenuation coefficients of a silicon nitride material. Thus, the power absorption EF becomes significant due to Optenna. It can reach as high as ffi80 dB at a wavelength of ffi2.2 μm. The ripples on some curves are because of the Fabry-Perot effect due to residual multiple reflections among Optenna different stages. The enhanced absorption efficiency of the thin film layer is mainly due to the improved material absorption coefficient as the incident optical field intensities become much higher.
