Subdiffraction focusing of total electric fields of terahertz wave

Optics Communications 458 (2020) 124764

Contents lists available at ScienceDirect

Optics Communications journal homepage: www.elsevier.com/locate/optcom

Subdiffraction focusing of total electric fields of terahertz wave Mengyu Yang a , Desheng Ruan a , Lianghui Du b , Chunyan Qin a , Zeyu Li c , Cuiping Lin a , Gang Chen a , Zhongquan Wen a ,∗ a

Key Lab of Optoelectronic Technology and Systems, Ministry of Education, Chongqing University, Chongqing, China Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, Sichuan 621900, China c Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang, Sichuan 621900, China b

ARTICLE

INFO

Keywords: Subdiffraction Subwavelength Terahertz

ABSTRACT Terahertz lens is an essential component in terahertz application. We propose a focusing of total electric fields planar lens based on super-oscillation. This planar lens is designed for a wavelength (𝜆) of 118.8 μm with a radius of 160𝜆, a focal length of 210 𝜆 and a numerical aperture of 0.606. Our experiment demonstrates a subdiffraction and subwavelength focusing of total electric fields. The full width at half-maximum of the focal spot is 0.67 𝜆, which is smaller than the diffraction limit of 0.825𝜆. The results shows that it has powerful application for terahertz imaging, especially in the fields of biomedical science.

1. Introduction Terahertz (THz) electromagnetic (EM) waves contain frequencies between 0.1 and 10 THz [1]. Some characteristics of the THz EM waves, such as their low photon energy, sensitivity to water molecules, and good permeability in dielectric and non-polar materials, make them extremely useful to a variety of applications in imaging [2– 5] and spectroscopy [6,7] and nondestructive detection [8]. Previous studies in visible light [9,10] have shown that focal spot reduction plays an important role in improving imaging resolution of the total electric fields. Unfortunately, traditional THz imaging is affected by the diffraction limit of the lens, with its resolution unable to meet the needs of high precision observation. The method of imaging is also a problem that needs attention. It is well known that the longitudinal component of electric field cannot be obtained by microscope [11]. Although the probe can detect the longitudinal electric field [12], its polarization selectivity makes it difficult to obtain the real electric field. Therefore, further decrease the size of the focal spot of total electric fields is particularly important for the implementation of super-resolution THz imaging technology. Although the near-field method can achieve subdiffraction and subwavelength focusing in THz [13,14], its application is limited by the short working distance and high precision experiment alignment. In the last few years, far field subdiffraction focusing lenses based on binary optical lenses [15,16], super-oscillation lenses [17–19] and super-critical lenses [20] have been studied in visible regime. However, the reported experiments showed that a subdiffraction and subwavelength focusing of the total electric fields in the THz range is difficult to achieve in far field [21,22]. Recently, due to the unique advantages

in controlling the optical field [23–26], metasurface and metamaterials are widely used in focusing in THz. For instance, super-oscillation, hyperbolic are applied to break the diffraction limit in THz. Metasurface lenses designed by hyperbolic phase can achieve subdiffraction focusing in THz and the focusing efficiency has been improved [27]. But due to the limitation of theory, the uniform and symmetrical focal spot cannot be achieved under the condition of uniform illumination, and the subdiffraction subwavelength can only be achieved in the 𝑥-axis direction. Our previous work showed a subdiffraction optical needle under the illumination of linearly polarized light, but hotspot is still larger than a wavelength [28]. Previously reported THz lenses are still affected by large focal spots or asymmetrical profiles, which limits their use in total electric fields imaging. To overcome these problems and achieve more detailed imaging, a subdiffraction subwavelength focusing of total electric fields is designed by using super-oscillation theory to obtain a smaller focal spot. We demonstrate a binary phase modulation lens with a focal length of 210𝜆 for subdiffraction subwavelength focusing in far field under illumination of a circularly polarized beam. Experimentally, the total electric fields on the focal plane is obtained, and an optical point of focus is delivered with a full width at half maximum (FWHM) of 0.67𝜆, below the diffraction limit 0.825𝜆. 2. Experimental design and model simulation An optical field pattern can be constructed by employing a binary phase modulation lens consisting of multiple concentric micro-rings made of Si, through the interference of transmitted diffraction beams.

∗ Corresponding author. E-mail address: [email protected] (Z. Wen).

https://doi.org/10.1016/j.optcom.2019.124764 Received 18 July 2019; Received in revised form 7 October 2019; Accepted 13 October 2019 Available online 16 October 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.

M. Yang, D. Ruan, L. Du et al.

Optics Communications 458 (2020) 124764

expressed as: ∞ ⎧ ⎪𝐸𝑝̂ (𝑟, 𝑧) = ∫ 𝐴0 (𝑙) 𝑒𝑥𝑝 [𝑗2𝜋𝑞 (𝑙) 𝑧] 𝐽0 (2𝜋𝑙𝑟) 2𝜋𝑙𝑑𝑙, 0 ⎪ ⎪ ′ ⎪𝐸𝑧 (𝑟, 𝜃, 𝑧) = −𝑗𝑐𝑜𝑠 𝜃𝐸𝑧 , ⎨ ∞ 1 ⎪𝐸 ′ = 𝐴 (𝑙) 𝑒𝑥𝑝 [𝑗2𝜋𝑞 (𝑙) 𝑧] 𝐽1 (2𝜋𝑙𝑟) 2𝜋𝑙𝑑𝑙, ⎪ 𝑧 ∫0 𝑞 (𝑙) 0 ⎪ ∞ ⎪𝐴 (𝑙) = 𝑡 (𝑟) 𝑔 (𝑟) 𝐽1 (2𝜋𝑙𝑟) 2𝜋𝑟𝑑𝑟. ⎩ ∫0

(3)

where 𝑝̂ represents the polarization direction of the incident light, t(r) is the transmittance function of the lens, and g(r) is the amplitude of the incident light. J0 and J1 are √ the zero- and first-order Bessel functions,

𝑞 (𝑙) = (1∕𝜆2 − 𝑙2 )1∕2 , 𝑙 = 𝑓𝑋2 + 𝑓𝑌2 , where 𝑓𝑥 and 𝑓𝑦 are spatial frequencies along the x and y directions, respectively. 𝜃 is the angular coordinate with respect to 𝑝. ̂ It can be seen from Eq. (3) that the optical distribution of the plane is related to the amplitudes of g(r) and t(r), the latter of which can be obtained by optimizing the phase. For a given incident light and some parameters, such as FWHM and side lobe, which represent the focusing characteristics on the focal plane, an optimum transmission function can be obtained that allows for subdiffraction focusing of total electric fields. Here, algorithm to optimize the design of the THz planar lens has been developed. Particle swarm optimization is used to find the optimal 𝑡(𝑟) = [𝑡1 , 𝑡2 , 𝑡3 ⋯ 𝑡𝑛 ], thereby obtaining the parameters necessary for the designed device. For a given design goal, multiple target parameters were converted into a single evaluation function value by weighting. The formula is as follows: [( ) ]2 Merit = 𝑤1 × 𝐹 𝑊 𝐻𝑀 − 𝐹 𝑊 𝐻𝑀𝑔 ∕𝐹 𝑊 𝐻𝑀𝑔 + 𝑤2 [( ) [( ]2 ) ]2 × 𝑆𝐿 − 𝑆𝐿𝑔 ∕𝑆𝐿𝑔 + 𝑤3 × 𝐼 − 𝐼𝑔 ∕𝐼𝑔 (4)

Fig. 1. (a) THz planar lens structure with concentric grooves. (b) Cross section of the lens.

Fig. 1 demonstrates the structure of the planar lens and the focusing of the plane wave by the lens. Fig. 1(b) depicts the cross section of the lens. The minimum width of the grooves was constrained to be a fixed value of T, or about a quarter of the wavelength. Since the device can be regarded as a grating, in order to suppress its high-order diffraction order, the selection period is T = 30 μm. The groove width, obtained by merging the adjacent grooves with the same phase, is an integer multiple of the minimum groove width. In order to make it possible to accomplish a binary modulation of the phase, the optimal groove depth H can be calculated from H = 𝜆∕(2(𝑛si − 1)), where the refractive index, 𝑛𝑠𝑖 of Si at a wavelength of 118.8 μm is 3.418, corresponding to a height difference between phase delay 0 and 𝜋 of 24.57 μm. The radius R of the lens was set to 160𝜆 with numerical aperture NA = 0.606, and 𝑅𝑖 was the radius of the ith ring. When the circularly polarized plane wave illuminates the substrate, a subdiffraction and subwavelength focal spot is produced at the position f = 210𝜆. Optical super-oscillation [29] is a phenomenon in which the oscillations of arbitrary band-limited functions are faster than their highest Fourier components, whereas typically, the oscillation velocity of the band limit function cannot exceed its highest Fourier component. The anomalous characteristics of the super-oscillations can be derived from the precise superposition of the spectral components of different amplitudes. The formation of the super-oscillating optical field can be derived as follows. The spatial light field distribution, 𝐸𝑟 , can be denoted by an amplitude distribution, 𝐴𝑟 , and a phase distribution, 𝜑(𝑟), as shown in the formula 𝐸 (𝑟) = 𝐴 (𝑟) 𝑒𝑥𝑝 [𝑖𝜑(𝑟)] . Additionally, 𝐴𝑟 and 𝜑 (𝑟) must meet the conditions such that { ( ) ∇2 𝜑 (𝑟) + ∇ ln 𝐴2 (𝑟) ⋅ ∇𝜑 (𝑟) = 0, [ ] ∇2 𝐴 (𝑟) + 𝑘2 − |∇𝜑 (𝑟)|2 𝐴 (𝑟) = 0.

where the 𝑤1 , 𝑤2 , 𝑤3 are the weights of each part, 𝐹 𝑊 𝐻𝑀 𝑔 , 𝑆𝐿𝑔 , 𝐼𝑔 are the required FWHM, side lobe and peak intensity, 𝐹 𝑊 𝐻𝑀, 𝑆𝐿, 𝐼 are FWHM, side lobe and peak intensity at the preset focal length that is actually optimized. The best fit and globally optimized solution for each particle was then saved after the evaluation. Finally, the position and speed of the updated particle were iterated again to calculate the degree of adaptation and evaluate the particle’s quality. This process was subsequently repeated until a convergent adaptation degree was found. 3. Results and discussion Fig. 2(a) shows the phase distribution corresponding to 𝑡 (𝑟) along the radius of the lens. The blue square corresponds to the distribution of concentric rings with phase 𝜋 and the rest of the component represents the distribution of concentric rings with phase 0. The width of the square represents the width of the ring and the radius of the ring corresponds to the position of the ring. From the distribution of the phase, the structure of the binary phase modulation of the lens can be extracted. The THz lens was simulated at 𝜆 = 118.8 μm. Fig. 2(b) depicts optical intensity distributions of the total electrical field on the focal plane at a distance of 210𝜆 (24.94 mm) from the surface of the lens. This clearly shows that the lens realizes a far field focusing of total electric fields with a focal length of 210𝜆. Fig. 2(c) shows the parameters involved in the focusing of the focal plane. The FWHM of the focal spot is 0.62𝜆 (73.7 μm, achieving subwavelength focusing) with a side lobe ratio (the ratio of maximum side lobe peak value to the main peak value) of 24.9%, demonstrating that the focal spot is already less than the diffraction limit of 0.825𝜆 (0.5𝜆/NA, 98 μm). Meanwhile through the analysis of its operation bandwidth, it is found that the variation of focusing intensity is less than 27% in the range of wavelength 110 μm–140 μm.

(1)

(2)

where the phase gradient, ∇𝜑(𝑟), is the local spatial frequency of the light field. When ∇𝜑(𝑟) is greater than the absolute value of the wave vector k = 2𝜋n0 ∕𝜆0 (n0 is the refractive index of the transmission medium and 𝜆0 is the wavelength in the vacuum), 𝐴𝑟 is attenuated in space. In particular, the localized light field sharply trends towards zero when |∇𝜑(𝑟)| ≫ 𝑘. When this scenario occurs, subdiffraction can be achieved. It can be shown that the phase of the super-oscillation function oscillates rapidly in the local domain [30], therefore, phase control is important in the construction of a super-oscillation [31]. With the vector angular spectrum, when a circularly polarized plane wave, such as a light source, illuminates the lens and propagates along the +Z direction (the position of the exit surface of the lens is taken as Z = 0), the diffraction total electric fields of the focal plane can be 2

M. Yang, D. Ruan, L. Du et al.

Optics Communications 458 (2020) 124764

A focal spot of total electric fields was found near the theoretical focal length by moving the THz imager along the THz beam propagation direction. Fig. 5(a) shows the intensity distribution of the total electric fields obtained at the position of z = 223.48𝜆 (26.55 mm), which is regarded as the actual focal length of the THz focusing lens. One can see that the intensity distribution of the side lobe collected on the focal plane of the lens is not uniform, and the size of the focal spot varies in multiple directions. This phenomenon is attributed to the nonuniformity of the intensity distribution of the incident light, which has been previously demonstrated. To acquire the FWHM of the focal spot, the results obtained from the experimental were fitted. At the same time, to minimize this effect, we took the maximum intensity value as the center point and rotated 180 degrees clockwise from the positive direction of 𝑋-axis at intervals of 18 degrees, in order to obtain the intensity distribution curve of the total electric fields as illustrated in Fig. 5(b). It is known from the analysis and calculation that the FWHM in all directions is less than the diffraction limit, which means that the total electric field can be subwavelength subdiffraction focusing. The intensity curve (blue line) in Fig. 5(c) was generated from the average of the intensity distributions. The normalized average intensity distributions (red line) of the total electric fields on the focal plane at the position of z = 210𝜆 is shown in Fig. 5(c) for comparison. Although there is a difference in the distance from the surface of the lens, good similarity was found for the intensity distributions. The FWHM of the focal spot obtained by our experiment is 0.67𝜆 (75.6 μm), close to the simulation result of 0.62𝜆 (73.7 μm). In addition, the experimental value of the FWHM is smaller than the diffraction limit 0.825𝜆, implying subdiffraction focusing was achieved, with a minimum focal spot size close to the super-oscillation criterion of 0.38𝜆/NA≈0.62𝜆. The non-conformity of the focal lengths between the simulated and the experimental ones is believed to be caused by manual measurement error during the course of the experiment. The side lobe ratio in the experiment is 34.24%, indicating that the intensity of the side lobe is relatively weak compared to that of the main lobe and has less influence on practical applications.

Fig. 2. Theoretical design results. (a) The optimized phase spatial distribution of the lens along the radius R. (b) Color maps of the total electrical field intensity distribution in the focal plane. (c) The FWHM and side lobe ratio distributions in the focal plane at z = 210𝜆.

4. Conclusion

Fig. 3. Photo of the fabricated lens with a diameter of 160𝜆 and a ring width of 30 μm.

We have demonstrated that super-oscillatory focusing of total electric fields can be achieved by optimizing the phase distribution. A binary phase THz lens based on vectorial angular spectrum theory and particle swarm optimization was proposed. Experimental results showed a subdiffraction and subwavelength focusing of total electric fields THz lens were achieved. The ultra-long focal length of the experiment was 223.48𝜆 (26.5 mm), and our experiment demonstrates that a subdiffraction and subwavelength focal spot of total electric fields can be formed when the lens is illuminated by THz waves with a wavelength of 118.8 μm. According to the intensity distribution of the total electric field captured by the THz imager on the focal plane, the FWHM of the focal spot is 0.67𝜆 (75.6 μm), which breaks the diffraction limit 0.825𝜆. Such a subdiffraction and subwavelength focusing of total electric fields makes it the potential to be used in a large number of applications, including imaging, security, radar, and communications technology.

Silicon was chosen as the material as the composition of the lens, due to its well-established processing technique and its high transmittance in the THz regime. Fig. 3(a) depicts the structure of the THz lens, with a magnified view of the center of the lens shown in Fig. 3(b). The maximum lateral dimensional deviation of grooves is +0.21um during the process. The depth error of grooves at the center and edge of the lens is −0.61um and +0.01um, respectively. Theoretically, there is no significant change in the intensity distribution of focal plane with the transverse error and depth error. Its main lobe strength is 0.024% lower than that of the designed. From this, it can be concluded that the machining error is in the extent permitted. The THz planar lens was measured with the experimental setup shown in Fig. 4. A FIRL100 laser (Edinburgh Instruments Ltd, UK) served as a linear polarized THz source with a wavelength of 118.8 μm. Although the optimal design of the lens was calculated for circularly polarized light, illumination of our fabricated THz planar lens can also be achieved with a linearly polarized wave. Linearly polarized light can be produced by a linear superposition of two orthogonal, circularly polarized light sources. Two off-axis parabolic mirrors were used to expand the beam to 2 inches in diameter. This beam vertically illuminated the surface of the THz lens and was focused on the focal plane. Then, a THz imager, IR/V-T083 (Nippon Electric Company Ltd, Japan), was mounted on a three axis electrical moving stage, with a resolution of 320 × 240. This imager was used to acquire the optical field distribution of total electric fields on the focal plane. As the THz frequency is invisible to sight, a red laser was combined with the THz beam by a beam-combination mirror along the optical axis, in order to guide the THz laser’s path.

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This study was supported by the National Key Basic Research and Development Program of China (2013CBA01700), National Natural Science Foundation of China (61575031, 61177093, 61474011), Program for New Century Excellent Talent in University (NCET-13-0629) and Fundamental Research Funds for the Central Universities (106112016CDJZR125503, 106112016CDJXZ238826), Natural Science Foundation of Chongqing, China (cstc2019jcyj-msxmX0315). 3

M. Yang, D. Ruan, L. Du et al.

Optics Communications 458 (2020) 124764

Fig. 4. Schematic diagram of the experimental setup.

Fig. 5. (a) Color map of the intensity distribution of the total electric fields at z = 223.48𝜆. (b) Curve of the intensity distribution in different directions on the focal plane.(c) Curve of the average intensity distribution at z = 223.48𝜆 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

References

[16] J. Wang, F. Qin, D.H. Zhang, D. Li, Y. Wang, X. Shen, T. Yu, J. Teng, Appl. Phys. Lett. 102 (2013) 3844. [17] G.H. Yuan, E.T. Rogers, N.I. Zheludev, Achromatic super-oscillatory lenses with sub-wavelength focusing, Light Sci. Appl. 6 (2017). [18] M. Li, W. Li, H. Li, Y. Zhu, Y. Yu, Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci, Sci. Rep. 7 (2017). [19] D. Ruan, G. Chen, G. Liang, H. Chen, H. Yuan, K. Zhang, L. Zhu, L. Du, L. Wang, L. Cao, All-dielectric metalens for terahertz wave imaging, Opt. Express 26 (2018) 14132. [20] F. Qin, K. Huang, J. Wu, J. Teng, C.W. Qiu, M. Hong, A supercritical lens optical label-free microscopy: Sub-diffraction resolution and ultra-long working distance, Adv. Mat. 29 (2016). [21] M. Takeda, S. Nakatani, Subwavelength focusing technique using a plasmonic lens, J. Appl. Phys. 51 (2012) 854–858. [22] A. Kannegulla, L.J. Cheng, Subwavelength focusing of terahertz waves in silicon hyperbolic metamaterials, Opt. Lett. 41 (2016) 3539–3542. [23] Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, D. Tang, Critical coupling with graphene-based hyperbolic metamaterials, Sci. Rep. 4 (2014) 5483. [24] T.T. Lv, Y.X. Li, H.F. Ma, Z. Zhu, Z.P. Li, C.Y. Guan, J.H. Shi, H. Zhang, T.J. Cui, Hybrid metamaterial switching for manipulating chirality based on VO2 phase transition, Sci. Rep. 6 (2016) 23186. [25] H.T. Yudistira, S. Liu, T.J. Cui, H. Zhang, Tailoring polarization and magnetization of absorbing terahertz metamaterials using a cut-wire sandwich structure, Beilstein J. Nanotechnol. 9 (2018) 1437–1447. [26] Shi, Z. Li, D.K. Sang, Y. Xiang, Z. Han, THZ photonics in two dimensional materials and metamaterials: Properties, devices and prospects, J. Mater. Chem. C 6 (2018) 1291. [27] H. Chen, Z. Wu, Z. Li, Z. Luo, X. Jiang, Z. Wen, L. Zhu, X. Zhou, H. Li, Z. Shang, Z. Zhang, K. Zhang, G. Liang, S. Jiang, L. Du, G. Chen, Sub-wavelength tightfocusing of terahertz waves by polarization-independent high-numerical-aperture dielectric metalens, Opt. Express 26 (2018) 29817–29825. [28] Ruan, Z. Li, L. Du, X. Zhou, L. Zhu, C. Lin, M. Yang, G. Chen, W. Yuan, G. Liang, Z. Wen, Realizing a terahertz far-field sub-diffraction optical needle with sub-wavelength concentric ring structure array, Appl. Opt. 57 (2018) 7905–7909. [29] M.R. Dennis, A.C. Hamilton, J. Courtial, Superoscillation in speckle patterns, Opt. Lett. 33 (2008) 2976. [30] F.M. Huang, Y. Chen, F.J.G.D. Abajo, N.I. Zheludev, Optical super-resolution through super-oscillations, J. Opt. A: Pure Appl. Opt. 9 (2008) S285. [31] N. Jin, Y. Rahmat-Samii, Advances in particle swarm optimization for antenna designs: Real-number, binary, single-objective and multiobjective implementations, IEEE Trans. Antennas Propag. 55 (2007) 556–567.

[1] J. Lloyd, K. Wang, A. Barkan, D.M. Mittleman, Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time-domain spectroscopy, Opt. Commun. 219 (2003) 289–294. [2] S.J. Oh, Y.M. Huh, J.S. Suh, J. Choi, S. Haam, J.H. Son, Cancer diagnosis by terahertz molecular imaging technique, J. Infrared Millim. Terahertz Waves 33 (2012) 74–81. [3] H. Fu, P. Wang, T. Koike-Akino, P.V. Orlik, Y. Chi, Terahertz imaging of binary reflectance with variational Bayesian inference, in: IEEE International Conference on Acoustics, Speech, and Signal Processing, 2018. [4] A. Wald, T. Schuster, Tomographic terahertz imaging using sequential subspace optimization, 2018. [5] F. Hu, Y. Fan, X. Zhang, W. Jiang, Y. Chen, P. Li, X. Yin, W. Zhang, Intensity modulation of a terahertz bandpass filter: utilizing image currents induced on MEMS reconfigurable metamaterials, Opt. Lett. 43 (2018) 17. [6] D.F. Plusquellic, K. Siegrist, E.J. Heilweil, O. Esenturk, Applications of terahertz spectroscopy in biosystems, Chem. Phys. Chem. 8 (2010) 2412–2431. [7] X.A. Chen, W.U. Xue, S. Zhang, L. Wang, Study of plant growth regulators detection technology based on terahertz spectroscopy, Spectrosc. Spect. Anal. (2018). [8] T. Lu, C. Wang, L. Ding, X. Liu, J. Zhang, L. Kong, Recent research in the continuous terahertz wave on nondestructive detection of carbon fibre composite, Nano-Micro Conf. 1 (2017) 01076. [9] L. Chen, Y. Zhou, M. Wu, M. Hong, Remote-mode microsphere nanoimaging: new boundaries for optical microscopes, Opto-Electronic Adv. 1 (2018) 170001-1. [10] A. Nemati, Q. Wang, M. Hong, J. Teng, Tunable and reconfigurable metasurfaces and metadevices, Opto-Electronic Adv. 1 (2018) 180009-1. [11] T. Grosjean, D. Courjon, Polarization filtering induced by imaging systems: effect on image structure, Phys. Rev. E 67 (2003) 046611. [12] J. Baumgartl, S. Kosmeier, M. Mazilu, E.T.F. Rogers, N.I. Zheludev, K. Dholakia, Far field subwavelength focusing using optical eigenmodes, Appl. Phys. Lett. 98 (2011) 1468. [13] K. Ishihara, T. Ikari, H. Minamide, J.I. Shikata, K. Ohashi, H. Yokoyama, H. Ito, Terahertz near-field imaging using enhanced transmission through a single subwavelength aperture, Japan. J. Appl. Phys. 44 (2005) L929–L931. [14] S. Mastel, M.B. Lundeberg, P. Alonsogonzález, Y. Gao, K. Watanabe, T. Taniguchi, J. Hone, F.H.L. Koppens, A.Y. Nikitin, R. Hillenbrand, Terahertz nanofocusing with cantilevered terahertz-resonant antenna tips, Nano Lett. (2017) 6526–6533. [15] J. Wang, F. Qin, D.H. Zhang, D. Li, Y. Wang, X. Shen, T. Yu, J. Teng, Subwavelength superfocusing with a dipole-wave-reciprocal binary zone plate, Opt. Precis. Eng. 102 (2003) 3844–3847. 4