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# Low cost and long-focal-depth metallic axicon for terahertz frequencies based on parallel-plate-waveguides

## Abstract

In this work we demonstrate a triangular surface lens (axicon) operating at frequencies between 350 and 450 GHz using parallel-plate-waveguide technology. The proposed axicon offers longer focal depth characteristics compared to conventional plastic lenses, surpassing common TPX lenses by one order of magnitude. Additionally, due to the triangular surface of the axicon, this device is able to focus THz radiation onto smaller areas than TPX lenses, enhancing the resolution characteristics of THz imaging systems. The frequency range of operation of the proposed axicon can be easily tuned by changing the space between plates, making this approach a very attractive candidate for low-cost, robust and easy to assemble solutions for the next generation of active THz devices.

## Design and fabrication

The PPWG-based lens presented in this work was fabricated from stainless steel sheets with 0.1 mm thickness and 20 mm width. The length of every plate varies in a linear fashion from 5 to 10 mm in steps of 1 mm. The spacing between plates is fixed at 0.55 mm. A schematic diagram and a photo of the axicon are shown in Fig. 1a,b.

Due to the geometry of the proposed axicon, the apex angle (θ) has a value of ≈ 56°. The apex angle has a direct impact on the performance of the axicon21,22,23. In Fig. 1a the dimensions of the plates are presented: d takes values from 5 to 10 mm in steps of 1 mm. The thickness of each plate was kept constant at 0.1 mm. Smaller thicknesses relative to the wavelength of operation are desirable in order to reduce scattering losses, however, the choice of 0.1 mm thick plates was made to keep an acceptable balance between mechanical robustness and scattering effects. The principle of operation of the axicon resides in the fact that an effective refractive index can be attributed to each pair of plates13. Then a difference in phase caused by the propagation of the light inside each pair of plates produces constructive interference at the exit face focusing the energy. The phase acquired in any pair of plates is given by13:

$$\varphi =kL\sqrt{1-\frac{{c}^{2}}{4{h}^{2}{f}^{2}}},$$
(1)

in which k is the wavenumber in a vacuum, L is the length of the plate, c is the speed of light in a vacuum, h the spacing between plates and f the frequency. Equation (1) remains valid when only the first transverse electric mode ($${TE}_{01}$$) is excited. Otherwise, extra calculations have to be carried out to take into account higher order modes. In this work, the frequency range of operation guarantees single mode operation26,27. Due to the dependency of the phase on the frequency, as is demonstrated in Eq. (1), it is expected that different frequencies focus at different positions after the axicon, i.e. chromatic aberration limiting the frequency range of operation of the device. Due the characteristics of PPWG devices this chromatic aberration is unavoidable. This is represented by the false color diagram in Fig. 1b.

## Experimental validation

To examine the performance of the proposed geometry, the fibre-coupled TeraSmart THz spectrometer from Menlo systems was used. The THz system is able to deliver broadband THz pulses of 1 ps temporal duration at a dynamic range of 90 dB covering the spectral range comprised between 0.1 THz and 5 THz. The THz spectrometer was arranged in a transmission configuration similar to the one shown in13. A schematic diagram of the setup is shown in Fig. 1c. To examine the depth of field (DOF) of the proposed geometry, the detection stage shown in Fig. 1c has been mounted on two motorized linear stages running along the y–z axis, raster scanning the y–z plane. The results are shown in Fig. 2. The propagation of the THz beam goes from left to right.

From the experimental results it is clear that the DOF of the axicon depends on the frequency of operation, with 450 GHz being the frequency which presents the longest DOF, extending for more than 30 mm. Beyond 500 GHz, the excitation of higher order modes degrades the quality of the focused beam. These results demonstrate the capability of this structure to effectively focus the THz radiation in a similar fashion to conventional lenses. In addition, the focusing efficiency is calculated by the ratio of the power inside a 3×FWHM region to the power inside the lens area28. The result of this calculation is shown in Fig. S1 in the supplementary section.

To quantify the DOF as a function of frequency and distance, a Gaussian curve was fitted along the vertical axis in Fig. 2 for every z position. From the fitting the Full-Width-Half-Maximum (FWHM) is retrieved and plotted. These results are presented in Fig. 3.

Additionally, the DOF of a conventional TPX lens is presented for comparison. The TPX lens has a diameter of 38.1 mm and focal length of 50 mm. The shaded regions in Fig. 3 represent the DOF region. The shaded regions start from the minimum point of the FWHM curve ($${FWHM}_{min}$$) for each frequency and continue to the point on the curve which reaches $$\sqrt{2}$$ times this minimum value ($$\sqrt{2}$$*$${FWHM}_{min}$$). The results clearly demonstrate the improved capabilities of the proposed technology compared to conventional TPX optics as the DOF of the metallic axicon is 16 times higher than that of the TPX lens. Furthermore, because Eq. 1 states that the refractive index of the lens depends on the separation between plates, the proposed approach can be tuned for the frequency range of interest by simply changing this distance, an enormous advantage compared to conventional optics.

In addition to the longitudinal measurements, in Fig. 4 transverse images taken at the focal distance are presented. These measurements were taken by mounting the detection stage in Fig. 1 on a pair of translational stages and raster scanning along the x–y plane at the focal point of each lens. In Fig. 4 three different frequencies are shown, 350 GHz, 400 GHz and 450 GHz. For comparison, the focal spot of the TPX lens at 400 GHz is also shown. Due to the fact that the variation of the focal spot of the TPX lens at these particular three frequencies is negligible, as demonstrated in Fig. 3, we only show the result at 400 GHz.

From the figure above it is clear that the PPWG based axicon achieves a smaller focal spot compared to the TPX optics, reducing the focal spot size by almost 25%. The elongated beam shown is a consequence of the 1-D geometry of the metallic axicon. Additionally, subtle side lobes are visible in Fig. 4a–c which are the result of the triangular shape of the axicon, generating a 1D Bessel beam along the y-direction. This is demonstrated in the supplementary section.

In order to prove the performance of the proposed technology for a practical application, a transverse image of a transparent sample was taken in transmission using the same setup shown in Fig. 1. The sample consists of the message “THz” cut out from a 1 mm thick cardboard card. This is shown in Fig. 5 on the left of panel (a). The THz image was taken by mounting the sample on a couple of translational stages moving along the x–y directions while the emitter and detections stage were kept fixed in transmission as shown in Fig. 1c. The sample was placed at the focal position of the PPWG axicon and the acquisition stage was moved in a transverse plane along the x–y axis. The results for the reconstruction of the sample at 350 GHz, 400 GHz and 450 GHz are shown in Fig. 5a–c, respectively. Afterwards, the sample was moved 30 mm beyond the focal point of the PPWG axicon and the same procedure was repeated. These results are presented in Fig. 5d–f for the same frequencies. In order to compare the performance of the proposed PPWG technology, the metallic axicon was removed and the sample was measured using the TPX lenses. Figure 5g–i present the reconstruction of the sample at the focal position of the plastic lens. Subsequently, the sample was moved 10 mm beyond the focal position and we raster scanned the sample again. The results are presented in Fig. 5j–l.

By comparing the panels of Fig. 5, the improved capabilities of the PPWG axicon are clear. The sample was reconstructed within a range of 3 cm beyond the focal position of the metallic axicon, while the TPX lens produces a very low contrast image even 1 cm away from its focal spot. These results were predicted from Fig. 3 in which a rapid increase in the FWHM of the TPX lens was found within a short distance (4 mm) while for the PPWG a slower increase of the FWHM was demonstrated. Additionally, Fig. 3 also successfully explains the blurred image of the sample at 350 GHz using the PPWG axicon; the DOF at 350 GHz is less than 30 mm, reducing the quality of the reconstruction of the image at that frequency. The panels of the results of the TPX scan were multiplied by a factor of 0.7 in order to match the color bar for the PPWG axicon results. The results presented in Fig. 5 unambiguously demonstrate the superior capabilities of the PPWG technology over conventional plastic lenses.

In conclusion, in this work we present a 1D metallic axicon based on PPWG technology. This axicon presents improved capabilities having a DOF ten times larger than the TPX lenses commonly used in THz systems. Additionally, due to the triangular surface, the axicon is capable of focusing the radiation in a smaller region than the TPX lens. Finally, the use of the proposed technology clearly demonstrates than, within a range of 3 cm, the axicon preserves its resolution capabilities for a range of frequencies between 350 to 450 GHz, creating potential uses for tomographic 3D reconstruction applications. The axicon was fabricated using stainless steel sheets, making it robust, easy to fabricate and additionally low cost. The operation of the proposed axicon at different frequencies is easily possible by changing the spacing between plates. Additionally, changing the space between plates makes it possible to increase/decrease the DOF and increase/decrease the spot size of the beam, adjusting the performance to the preferences of the operator. PPWG technology has proved useful in the manufacture of novel THz devices and we predict wide implementation of the proposed technology in the next generation of THz networks and THz imaging systems.

## Data availability

The data presented in this paper is available at: https://figshare.com/articles/dataset/Metallic_lens_paper/13066031.

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## Funding

We are grateful for partial financial support for this work from the Royal Society Wolfson Merit Award (EPM); and the Engineering and Physical Sciences Research Council (EP/s021442/1).

## Author information

Authors

### Contributions

A.I.H.S. conceived the study. A.I.H.S. fabricated the device and performed the experimental analysis. A.I.H.S and E.M.P. wrote the article. All authors discussed the results and contributed to the manuscript.

### Corresponding author

Correspondence to Emma Pickwell-MacPherson.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Hernandez-Serrano, A.I., Pickwell-MacPherson, E. Low cost and long-focal-depth metallic axicon for terahertz frequencies based on parallel-plate-waveguides. Sci Rep 11, 3005 (2021). https://doi.org/10.1038/s41598-021-82503-x

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