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Abstract
Planar diffractive lenses, with metamaterial artificial structures and subwavelength thickness, provide unique and flexible platforms for optical design in the terahertz (THz) regime. Here, we present a metamaterial-based Rayleigh-Wood Fresnel-zone-plate (FZP) thin-film lens designed to focus a monochromatic THz beam at 1.0 THz with a high transmittance of 80%, short focal length of 24 mm, and subwavelength thickness of 48 µm. Specifically, the FZP lens is composed of 8 alternating concentric zones through a polymer film substrate, where odd zones are patterned with double-layer un-split ring resonators (USRRs) that provide a polarization-independent phase shift of π/2 compared to un-patterned even zones. Both simulation and experiment confirm that our FZP lens creates a focused beam at the designed frequency of 1.0 THz by constructive interference through alternating concentric metamaterial-patterned and un-patterned zones, producing a diffraction-limited resolution of 0.6 mm for imaging applications. In contrast to conventional approaches in which the uniform periodic array of metamaterial unit cells has been treated as an effective material, we newly find that double-layer USRRs can work as an independent meta-atom without degradation of its performances, which benefits the behavior of small arrays of double-layer USRRs located in the outer zones of the FZP lens. Such a planar thin-film lens would enable us to realize compact and lightweight THz systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The generation of tightly focused terahertz (THz) beams is important for various research fields, including high-resolution imaging applications [1–3] and high-field physics [4,5]. The conventional refractive lenses used in the THz regime are composed of bulky dielectrics such as polyethylene, Teflon, Tsurupica, and silicon, and the focal lengths of such refractive lenses are typically limited to longer than 50 mm. This limitation occurs because a shorter focal length requires a thicker lens substrate due to the larger radius of curvature, and the transmission loss consequently becomes quite high. For example, the commercially available, uncoated Teflon lens with a relatively high numerical aperture (NA) of ∼0.28 offers the power transmittance below 30% at 1.0 THz [6]. Although a metal-coated off-axis parabolic mirror is an alternative focusing element, it is useful only when the incident THz beam is assumed to be a plane wave.
One established approach for realizing short-focal-length lenses with reduced thickness is the utilization of planar diffractive optics. The planar diffractive optics have traditionally been used in the regions in which standard refractive optics is not available practically, such as the millimeter-wave [7], X-ray [8], and acoustic-sound [9] regions. For the THz regime, Fresnel-zone-plate (FZP) lenses have emerged as promising platforms because they provide flexible focusing performances [10,11]. FZP lenses are designed by choosing appropriate radii of multiple concentric zones to manipulate either the amplitude or phase of the incident waves such that constructive interference of the diffracted waves creates a focus. Already, both amplitude-type Soret and phase-type Rayleigh-Wood FZP lens structures for the THz regime have been fabricated on dielectric substrates using advanced microfabrication technologies, including material processing [12,13], 3D printing [14,15], and direct laser writing [16,17], yielding focal lengths shorter than 50 mm. However, most of these prior THz FZP lenses suffer from the relatively low power transmittance below 50% due to Fresnel reflection and absorption losses, as well as the Fabry-Pérot interference effect, because the total thickness is equivalent to or thicker than the designed wavelength.
In contrast to such natural dielectric materials, metamaterials composed of artificial metallic structures with thicknesses on the subwavelength scale have provided unique abilities to manipulate the amplitude, phase, or polarization of incident THz beams efficiently and flexibly [18–27]. Previously, we showed that a polarization-independent phase shift of π/2 at a designed THz frequency could be achieved with a high transmittance of 80% by a double-layer symmetric metamaterial structure of un-split ring resonators (USRRs) in a subwavelength-thick flexible polymer film [28]. This phase-shifter metamaterial could thus serve as the building blocks for the design of phase-type Rayleigh-Wood FZP lenses with desired focusing characteristics, such as high transmittance, short focal length, and subwavelength thickness.
In this paper, we propose and demonstrate a polarization-independent, metamaterial-based, Rayleigh-Wood FZP thin-film lens designed to focus a THz beam at 1.0 THz (λ = 300 µm). An important consequence of this FZP lens design is the simultaneous achievements of a high transmittance of 80%, short free-space focal length of f = 24 mm (80λ), and subwavelength thickness of 48 µm (0.16λ). The FZP lens was fabricated on a flexible polymer film substrate with an outermost zone radius of 7.68 mm, corresponding to an NA of ∼0.30. Both simulation and experimental results confirm that our FZP thin-film lens creates a focus by constructive interference of the incident 1.0-THz beam through alternating concentric metamaterial-patterned and un-patterned zones, providing a diffraction-limited spatial resolution of 0.6 mm (2λ) for imaging applications. Besides, unlike the previous study that the uniform periodic USRR array was treated as an effective material [28], we newly find that the double-layer USRRs can work as an independent meta-atom to provide the π/2 phase shift and 80% transmittance without degradation of its performance, which is a significant reason for the unprecedented performance of the FZP lens we demonstrate in the present work.
2. Design and fabrication
Figure 1 shows a schematic of our metamaterial-based FZP thin-film lens design. In principle, a phase-type Rayleigh-Wood FZP offers the focusing performance with higher transmittance than an amplitude-type Soret FZP, which consists of alternating transparent and opaque zones that block approximately half of the incident beam. According to the diffraction principle under paraxial approximation [29], the radius of each zone rN is given by
where N is the zone number, λ is the target wavelength, and f is the designed first-order focal length. In this study, we consider alternating concentric zones with up to N = 8 to achieve the diffraction-limited performance for focusing a 1.0-THz beam (λ = 300 µm) with a focal length of f = 24 mm, corresponding to an NA of ∼0.30. The odd zones of N = 1, 3, 5, and 7 are patterned with the metamaterial phase-shifter structure, while the even zones of N = 2, 4, 6, and 8 are left un-patterned. The metamaterial structure in the odd zones is based on our recent demonstration of a THz phase shifter consisting of symmetric double-layer USRRs with the same structure as those described in [28]. The metallic pattern of the symmetric double-layer USRRs was made of 200-nm-thick aluminum and composed of an inner square block (20 µm × 20 µm) and an outer square frame (56 µm × 56 µm). The inner and outer squares were connected symmetrically through four connection lines. The widths of the outer frame lines and connection lines were 4 µm. The distance between double-layer metallic patterns was 32 µm. With a subwavelength total film thickness of 48 µm, the THz phase shifter exhibited polarization independence, a high transmittance of over 80%, and phase retardation of π/2 compared to the blank polymer substrate of bisbenzocyclobutene (BCB) film at the designed THz frequency. In this study, we newly show that the double-layer USRRs can work as an independent meta-atom to produce the phase shift and high transmission required for the FZP lens as discussed hereinafter, in contrast to the previous study that we treated the uniform periodic USRRs array as an effective material [28]. Since the metamaterial unit cell has a subwavelength lattice size of 80 µm × 80 µm as shown in Fig. 1(c), the radius of each zone is digitalized by the unit cell size. The radii of all the zones and digitized pixel numbers, M, in this study are listed in Table 1.
Fig. 1. Schematic design of metamaterial-based Rayleigh-Wood FZP thin-film lens. (a) Top view, (b) side view, and (c) unit cell structure of alternating concentric zones. The double-layer USRR metallic patterns made of aluminum are shown in yellow. With a sub-wavelength film thickness of 48 µm, the odd zones are patterned with a double-layer symmetric metamaterial structure offering a polarization-independent phase shift of π/2 compared to the un-patterned even zones for a transmitted THz beam.
Table 1. Design parameters of FZP lens
The FZP thin-film lens was fabricated using a surface micromachining technique involving photolithography and wet patterning processes. The fabrication processes were the same as those described in [28]. Figure 2(a) shows a photograph of the fabricated FZP lens attached to an aluminum foil with a 20-mm aperture for the experimental characterization as described hereinafter. The visible camera image clearly shows the alternating concentric zone structures because the metamaterial-patterned and un-patterned zones have a color difference due to reflection and diffraction for the visible light. In addition, the magnified images obtained using a visible optical microscope in Figs. 2(b) and 2(c) show the alternating concentric zone structures digitized with an 80-µm metamaterial unit cell size. We note here that the outer area of the metamaterial-patterned zone (N = 7) remains as un-patterned polymer BCB substrate, and thus the part of this region within a radius of 7.68 mm serves as the outermost zone corresponding to N = 8.
Fig. 2. Pictures of the fabricated FZP lens. (a) Fabricated FZP lens is attached to aluminum foil with a 20-mm aperture and held with gloved fingers. The magnified pictures in (b) and (c) show alternating digitized concentric zones and the boundaries of the metamaterial-patterned and un-patterned zones, respectively.
3. Simulation and experiment
3.1 Scalar interference simulation
Firstly, we conducted a numerical simulation with a laboratory-made MATLAB program based on scalar interference to study the beam focusing properties of the designed FZP lens, as schematically shown in Fig. 3. In the simulation, we assumed that a collimated THz beam with Gaussian profile was irradiated onto the FZP lens at normal incidence. Following the Huygens principle, the diffracted waves at each pixel of the FZP lens functioned as new point sources, and the point sources in the metamaterial-patterned odd zones had a phase shift of π/2 compared to those in the un-patterned even zones. The waves from all the point sources interfered with each other, leading to visualization of the spatial intensity distribution of the THz beam transmitted through the FZP lens. Note here that the scalar interference simulation used in this study is kind of an analysis calculation, which is not a 3D full-wave numerical calculation. Because of the analysis calculation, there is no boundary conditions involved here.
Fig. 3. Schematic of the scalar interference simulation model. This model is polarization independence.
The pixel size of the FZP lens was simply chosen to correspond to the metamaterial unit size of 80 µm. We used (x, y, z) = (m, n, 0) to identify each pixel of the FZP lens, where the maximum values of integers, m and n, were both 250. The pixel size in the observation plane was also 80 µm, and these pixels were marked using (x, y, z) = (a, nmax/2, b) for the X-Z observation plane as shown by the shaded area in red in Fig. 3. We set the maximum values of integers, a and b, were 250 and 688, respectively. By calculating the distance, r, of each pixel from the FZP lens to the observation plane as
It should be mentioned that a plane wave with uniform intensity profile could also be used as the incident beam instead of a Gaussian-profile wave in the simulation without changing the resulting focal length. This characteristic can be understood by the interference mechanism of the FZP lens. However, the calculated light intensity before normalization at the focal spot would decrease, since a Gaussian wave has the maximum intensity at the center of the beam, while a plane wave has uniform intensity profile.
3.2 Experimental characterization
Secondly, we characterized the fabricated FZP thin-film lens experimentally. Figure 4 shows a schematic of the experimental setup for the measurement of the beam focusing properties. For a monochromatic frequency-tunable THz source, we used a sub-nanosecond-pumped, injection-seeded THz-wave parametric generator (is-TPG) based on a MgO-doped LiNbO3 crystal [30–32]. With the continuous tunability of the THz frequency, the frequency linewidth of 3.5 GHz [33] was sufficiently narrow to fit within the bandwidth of monochromatic operation of the FZP lens at 1 THz. The THz beam from the is-TPG source was collimated using a Tsurupica lens and then introduced to the FZP lens at normal incidence, with a Gaussian beam diameter of 13 mm at 1/e2, which was almost the same as the size of the FZP lens aperture. The spatial intensity distribution of the THz beam transmitted through the FZP lens was measured by three-axis scanning of a pyroelectric detector (PHLUXi, Inc., PYD-2 series). This pyroelectric detector had a small active area with a diameter of 1 mm that served as a spatial filter. The coordinate axes used in this study are shown in Figs. 3 and 4.
Fig. 4. Schematic experimental setup for characterization of the beam focusing properties of the FZP lens. is-TPG: injection-seeded THz-wave parametric generator.
4. Results
Prior to the characterization of the beam focusing properties, we first measured the transmittance spectra of the patterned and un-patterned zones of the fabricated FZP lens using the is-TPG source. Figure 5(a) presents the results of frequency-domain measurements of the power transmittance for the uniform metamaterial area located at the innermost zone and the blank polymer film substrate of the same device. For this power transmittance measurement, the THz beam from the is-TPG was focused by a Tsurupica convex lens and the THz frequency of the is-TPG source was swept from 0.8 to 1.2 THz. The simulated power transmittance of the metamaterial and the blank substrate are also shown in Fig. 5(a). Both cases exhibit a measured transmittance of 80% at the designed frequency of 1.0 THz and are in agreement with the simulation results, demonstrating the high-transmittance of the FZP lens. At the same frequency, the phase shift between the metamaterial and the blank substrate reaches π/2 as shown by the simulated result in Fig. 5(b), leading to efficient focusing for the 1.0-THz beam. The results in Figs. 5(a) and 5(b) are consistent with those of our previous study in which measurements were performed by THz time-domain spectroscopy [28].
Fig. 5. (a) Simulated and measured power transmittance for the uniform metamaterial and blank film substrate. (b) Simulated phase shift between the uniform metamaterial and blank film substrate that corresponds to the patterned and un-patterned zones, respectively, of our FZP lens.
Figures 6(a) and 6(b) show the simulated and measured intensity distributions of the THz beam focused by the FZP lens in the X-Z plane at Y = 0 mm, respectively. In both cases, the THz frequency was fixed at the designed frequency of 1.0 THz. The measured intensity distribution without the FZP lens is also shown in Fig. 6(c). Since the general profiles of the two distributions [Figs. 6(a) and 6(b)] are the same, these results indicate that the FZP lens created a focused THz beam by constructive interference though the alternating concentric zones. Although the focal point in the simulation was observed at Z = 24 mm in line with the design, the focal point obtained experimentally was located slightly farther away, at Z = 27 mm. This discrepancy between the simulation and experiment may be due to imperfect collimation of the incident THz beam in the experiment or the fact that the scalar interference method used in the simulation did not include the polarization difference between waves at the observation position, causing the focal length to be artificially shorter than the actual focal length. Further, the scalar interference method did not include the physical diffraction that occurred at the edge of each zone due to the digitalized 80-µm pixel, which would have affected the focal length as well.
Fig. 6. [(a) and (d)] Simulated and [(b) and (e)] measured spatial intensity distributions with FZP lens at 1.0 THz in the X-Z plane at Y = 0 and in the X-Y plane at the focal position, respectively. [(c) and (f)] Measured spatial intensity distributions without the FZP lens. (g) Measured intensity line profile in the X direction at Y = 0 and Z = 27 mm with and without FZP lens.
The simulated and measured intensity distributions in the X-Y plane at each focal position are shown in Figs. 6(d) and 6(e), respectively. The focused beam size in the experiment is larger than that in the simulation, which is mainly due to the experimental limitation of the spatial resolution caused by the finite 1-mm-diameter aperture of the pyroelectric detector. Another possible reason could be the artificial effect in the simulation mentioned in the previous paragraph. The measured intensity distribution in the X-Y plane at Z = 27 mm without the FZP lens is also shown in Fig. 6(f). The detected THz-wave signal intensity at the focus position of the FZP lens was enhanced by factor of 4.2 compared to that without the FZP lens, as shown by the intensity line profile in Fig. 6(g).
To characterize the focused beam diameter precisely, we used a conventional knife-edge method. For this measurement, the diverging THz beam after the focal point was collected by another Tsurupica lens and then detected by a pyroelectric detector. At the focal plane, a metallic plate was scanned independently in the X- and Y-directions. Figures 7(a) and 7(b) show the results for the respective directions at the experimentally observed focal position of Z = 27 mm. The first derivative was calculated numerically from the measured knife-edge profile. As a result of Gaussian fitting for the first derivative, focused THz beam diameters at full widths at half-maximum (FWHMs) were derived to be 0.57 and 0.68 mm for the X- and Y-directions, respectively, corresponding to the theoretical diffraction-limited performance of 0.6 mm (2λ) for our FZP lens. Furthermore, the measured beam diameters as a function of beam propagation distance are shown in Fig. 7(c). From this measurement, the depth of focus (DOF) of this FZP lens was estimated to be 6 and 8 mm for the X- and Y-directions, respectively. These results indicate that the relatively long DOF of the short-focal-length FZP lens would enable the realization of an alignment-insensitive THz imaging configuration with the diffraction-limited resolution.
Fig. 7. Knife-edge measurements of focused beam diameter for (a) X-direction and (b) Y-direction both at Z = 27 mm. The solid lines are the Gaussian best fit curves for the first derivative of the measured data. (c) Measured FWHM focused beam diameters as a function of beam propagation distance.
Using the focused THz beam created by the FZP lens, we performed THz transmission imaging. The sample to be imaged was a USAF 1951 test target printed using metal ink on paper, as shown in the visible image in Fig. 8(a). This test target was placed at the experimentally observed focal plane of the FZP lens. Then, the elements of 1, 2, and 3 with the line width (w) of 1.0, 0.89, and 0.79 mm, respectively, in group number of −1 were measured by raster scanning an area of 20 mm × 20 mm, as indicated by the dashed square in Fig. 8(a). Figure 8(b) shows the result of 1.0-THz transmission imaging. The metallic patterns for all the elements of 1, 2, and 3 in group number of −1 were resolved as shown by the line intensity profile in Fig. 8(c), indicating that the spatial resolution of better than 0.79 mm (2.6λ) in this 1.0-THz transmission imaging is consistent with the diffraction-limited performance of 0.6 mm (2λ) as shown in Figs. 7(a) and 7(b). This imaging result demonstrates that the fabricated FZP lens is promising as planar focusing optics which can be integrated into compact THz imaging systems.
Fig. 8. THz transmission imaging using the FZP lens. (a) Visible image and (b) 1.0-THz transmission imaging result of the USAF 1951 test target. The dashed square in (a) shows the area imaged by the focused THz beam created by the FZP lens. (c) Line intensity profile of the dashed line in (b). The metallic patterns for the elements of 1, 2, and 3 in group number of −1 were resolved.
5. Discussion
The phase difference between neighboring zones of the phase-type FZP lens was π/2 in this work. It should be noted that, while the fabricated FZP lens showed focusing performances superior to those of conventional refractive lenses and other prior THz FZP lenses, the focusing efficiency could be improved further. It is known from the Huygens principle that the efficiency of a phase-type FZP lens is maximized when the phase difference between the neighboring zones is π [29]. This behavior was confirmed by the simulation result that, by optimizing the phase retardation of the metamaterial phase shifter from π/2 to π, the beam intensity at the focal plane could be improved by a factor of 2. The simulation results for different phase shifts between the neighboring zones are shown in Fig. 9(a). By changing the phase difference, φ, from 0 to π, we monitored the intensity distribution of the observation plane (Y-Z plane at X = 0) and recorded the maximum intensity as the focus strength. In this calculation, we defined the relative focus efficiency by normalizing each focus strength to the focus strength in the φ = π case. The curve shows a sine waveform, which is in accordance with the mathematical expression for electromagnetic wave interferences and thus it is reasonable. It should be mentioned that for the φ = 0° case, the relative focus efficiency is close to zero, as the beam does not exhibit focusing in the observation plane, but the beam is still propagating in space.
Fig. 9. Simulation results of (a) relative focus efficiency dependence with phase difference between neighboring zones and (b) focal length dependence on working frequency.
Furthermore, the FZP lens can be used to focus THz beams at frequencies other than 1 THz, although the focal length is dependent on the frequency [29]. We investigated the focal length dependence on the working frequency by the simulation. The FZP lens was set the same in this work with a phase difference of π/2 between neighboring zones, but the working frequency was swept from 0.9 to 1.1 THz. The calculated focal length of our FZP lens as a function of the THz frequency is shown in Fig. 9(b). The focal length shows a linear dependence on the working frequency in the range of 0.9–1.1 THz, with shorter focal lengths at lower frequencies and longer focal lengths at higher frequencies. This frequency-dependent beam focusing property suggests that the FZP lens may be useful for the frequency-selective depth-resolved imaging with frequency-tunable THz sources. It should be mentioned that the focal length dependence on the working frequency can also be calculated by using Eq. (1). The zone number and the corresponding radius of the zone were set the same as in the FZP lens design in this work. By sweeping the working frequency, the corresponding focal lengths were obtained with a slightly larger value of 0.8 mm than those of the simulation.
The FZP lens in this study employs metamaterial structures in its patterned zones. According to the zone design described in Table 1, except in the innermost zone, there are only few metamaterial units to constitute the other odd zones. Meanwhile, the metamaterial is generally known to work as an array to control the incident electromagnetic wave and a small array will degrade its performance. Nonetheless, the characterization results in Figs. 6 and 7, as well as the THz imaging result in Fig. 8, demonstrate the unprecedented focusing performance of the metamaterial-based FZP lens. This performance originates from the metamaterial structure design of double-layer USRRs that solves the above-mentioned degradation issue from small metamaterial array.
According to our previous work on the metamaterial design [28], the anti-parallel dipole resonance of the double-layer USRRs resulted in a π/2 phase shift and 80% transmittance, where we treated the large array of uniform periodic USRRs as an effective material. In further recent studies, we have found that the anti-parallel dipole resonance of the double-layer USRRs is a localized resonance, indicating that the resonant frequency does not rely much on the metamaterial unit lattice size [34], but rather remains constant, as shown in Fig. 10. The dashed line in Fig. 10(a) presents the lattice-size dependence of the center frequencies of the anti-parallel dipole resonance that exhibits the high transmission. Although in the small lattice sizes around 70 µm the resonant frequencies have an obvious change due to the interaction of the neighboring metamaterial units, the larger lattices above 80 µm show a small change in the resonant frequencies, which proves the localized resonance. For the FZP in this study, we used the lattice size of 80 µm for the metamaterial patterns in the odd zones, which follows the localized resonance. The π/2 phase shift associated with the anti-parallel dipole resonance expresses similar localized resonance characteristics, as indicated by the dashed line in Fig. 10(b). Thus, the double-layer USRRs can be treated as an independent meta-atom. In other words, even for a small array of this metamaterial design, the ability to control the incident THz beam does not degrade much. Hence, the outer odd zones (N = 3, 5, and 7) retain the π/2 phase shift compared to the neighboring even zones in this study.
Fig. 10. Simulated spectra performances of double-layer USRRs with metamaterial lattice size mapping for (a) transmittance and (b) phase shift. The dashed lines in (a) and (b) show the position of anti-parallel dipole resonances with phase shift of π/2, expressing a small change in the resonance frequency above the lattice size of 80 µm and indicating the localized resonance of double-layer USRRs.
Meanwhile, due to the property of the localized resonance, the meta-atoms located at the edge of each zone still work within the metamaterial array to provide a sharp phase discontinuous between the metamaterial-patterned and un-patterned zones, which satisfies the requirements of diffraction for the FZP design. Besides, the independent USRRs lattice property of the localized resonance enables robust tolerance during the device fabrication process. This is a benefit for practical application. Therefore, by the several merits from the localized resonance on double-layer USRRs discussed above, the demonstrated FZP shows superior focusing performances.
The power transmittance of the FZP lens was demonstrated to be 80% in both the patterned and un-patterned zones. This performance is already quite high, but it could be improved further. The primary factor that could be addressed to increase the transmittance further lies in the material loss in both the metamaterial-patterned and un-patterned zones. Thus, the solution could be to search for new low-loss materials for THz-wave devices.
6. Conclusion
We demonstrated a phase-type Rayleigh-Wood FZP lens consisting of alternating concentric metamaterial-patterned and un-patterned zones fabricated on a flexible polymer thin-film substrate. We have confirmed by both simulation and experiment that our FZP lens can focus a monochromatic THz beam at the designed frequency of 1.0 THz (λ = 300 µm) with advantageous characteristics of high transmittance of 80%, short free-space focal lengths of f = 24 mm (80λ, simulation) and f = 27 mm (90λ, experiment), and subwavelength thickness of 48 µm (0.16λ). With the developed FZP lens, we achieved the diffraction-limited resolution of 0.6 mm (2λ) for THz-wave imaging applications. This THz lens, therefore, is a promising planar optics component that could be integrated into compact and lightweight THz systems with monochromatic THz sources such as laser-driven parametric sources, quantum cascade lasers, resonant tunneling diodes, and photomixers.
Funding
Japan Society for the Promotion of Science (JP17H01282, JP17K18368, JP19K05286).
Acknowledgments
We thank Prof. H. Ito, Prof. M. Kumano, Dr. T. Notake, Dr. Y. Tokizane, and Dr. K. Nawata for fruitful discussions. Fabrication work was carried out in the Microsystem Integration Center (µSIC) of Tohoku University. This work was supported in part by JSPS KAKENHI (JP17K18368, JP17H01282, and JP19K05286), FY2021 RIKEN-Tohoku University Science and Technology Hub Collaborative Research Program, and Innovative Science and Technology Initiative for Security Grant Number JPJ004596, ATLA, Japan.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. D. M. Mittleman, “Twenty years of terahertz imaging [Invited],” Opt. Express 26(8), 9417–9431 (2018). [CrossRef]
2. G. Valušis, A. Lisauskas, H. Yuan, W. Knap, and H. G. Roskos, “Roadmap of terahertz imaging 2021,” Sensors 21(12), 4092 (2021). [CrossRef]
3. E. Castro-Camus, M. Koch, and D. M. Mittleman, “Recent advances in terahertz imaging: 1999 to 2021,” Appl. Phys. B 128(1), 12 (2022). [CrossRef]
4. T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over mater and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013). [CrossRef]
5. C. Ouyang, S. Li, J. Ma, B. Zhang, X. Wu, W. Ren, X. Wang, D. Wang, Z. Ma, T. Wang, T. Hong, P. Yang, Z. Cheng, Y. Zhang, K. Jin, and Y. Li, “Terahertz strong-field physics in light-emitting diodes for terahertz detection and imaging,” Commun. Phys. 4(1), 5 (2021). [CrossRef]
6. Thorlabs, Inc., “PTFE Plano-Convex Lenses,” https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=1627
7. H. D. Hristov and M. H. A. J. Herben, “Millimeter-wave Fresnel-zone plate lens and antenna,” IEEE Trans. Microwave Theory Tech. 43(12), 2779–2785 (1995). [CrossRef]
8. W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based on soft X-ray microscopy,” Opt. Express 17(20), 17669–17677 (2009). [CrossRef]
9. D. C. Calvo, A. L. Thangawing, M. Nicholas, and C. N. Layman, “Thin Fresnel zone plate lenses for focusing underwater sound,” Appl. Phys. Lett. 107(1), 014103 (2015). [CrossRef]
10. D. Headland, Y. Monnai, D. Abbott, C. Fumeaux, and W. Withayachumnankul, “Tutorial: Terahertz beamforming, from concepts to realizations,” APL Photonics 3(5), 051101 (2018). [CrossRef]
11. A. Siemion, “Terahertz diffractive optics – smart control over radiation,” J Infrared Milli Terahz Waves 40(5), 477–499 (2019). [CrossRef]
12. S. Wang, T. Yuan, E. D. Walsby, R. J. Blaikie, S. M. Durbin, D. R. S. Cumming, J. Xu, and X.-C. Zhang, “Characterization of T-ray binary lenses,” Opt. Lett. 27(13), 1183–1185 (2002). [CrossRef]
13. S. Tofani, D. C. Zografopoulos, M. Missori, R. Fastampa, and R. Beccherelli, “Terahertz focusing properties of polymeric zone plates characterized by a modified knife-edge technique,” J. Opt. Soc. Am. B 36(5), D88–D96 (2019). [CrossRef]
14. W. D. Furlan, V. Ferrando, J. A. Monsoriu, P. Zagrajek, E. Czerwińska, and M. Szustakowski, “3D printed diffractive terahertz lenses,” Opt. Lett. 41(8), 1748–1751 (2016). [CrossRef]
15. D. Headland, W. Withayachumnankul, M. Webb, H. Ebendorff-Heidepriem, A. Luiten, and D. Abbott, “Analysis of 3D-printed metal for rapid-prototyped reflective terahertz optics,” Opt. Express 24(15), 17384–17396 (2016). [CrossRef]
16. L. Minkevičius, S. Indrišiūnas, R. Šniaukas, B. Voisiat, V. Janonis, V. Tamošiūnas, I. Kašalynas, G. Račiukaitis, and G. Valušis, “Terahertz multilevel phase Fresnel lenses fabricated by laser patterning of silicon,” Opt. Lett. 42(10), 1875–1878 (2017). [CrossRef]
17. R. Ivaškevičiūtė-Povilauskienė, L. Minkevičius, D. Jokubauskis, A. Urbanowicz, S. Indrišiūnas, and G. Valušis, “Flexible materials for terahertz optics: advantages of graphite-based structures,” Opt. Mater. Express 9(11), 4438–4446 (2019). [CrossRef]
18. H. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef]
19. H. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef]
20. J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, “Metamaterial-based gradient index lens with strong focusing in the THz frequency range,” Opt. Express 18(26), 27748–27757 (2010). [CrossRef]
21. S. Zhang, J. Zhou, Y. Park, J. Rho, R. Singh, S. Nam, A. K. Azad, H. Chen, X. Yin, A. J. Taylor, and X. Zhang, “Photoinduced handedness switching in terahertz chiral metamolecules,” Nat. Commun. 3(1), 942 (2012). [CrossRef]
22. J. He, X. Wang, D. Hu, J. Ye, S. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21(17), 20230–20239 (2013). [CrossRef]
23. Z. Han, K. Kohno, H. Fujita, K. Hirakawa, and H. Toshiyoshi, “MEMS reconfigurable metamaterial for terahertz switchable filter and modulator,” Opt. Express 22(18), 21326–21339 (2014). [CrossRef]
24. Z. Han, K. Kohno, H. Fujita, K. Hirakawa, and H. Toshiyoshi, “Tunable terahertz filter and modulator based on electrostatic MEMS reconfigurable SRR array,” IEEE J. Sel. Top. Quantum Electron. 21(4), 114 (2015). [CrossRef]
25. R. Mendis, M. Nagai, Y. Wang, N. Karl, and D. M. Mittleman, “Terahertz artificial dielectric lens,” Sci. Rep. 6(1), 23023 (2016). [CrossRef]
26. S. Ohno, “Projection of phase singularities in moiré fringe onto a light field,” Appl. Phys. Lett. 108(25), 251104 (2016). [CrossRef]
27. Z. Han, S. Ohno, Y. Tokizane, K. Nawata, T. Notake, Y. Takida, and H. Minamide, “Off-resonance and in-resonance metamaterial design for a high-transmission terahertz-wave quarter-wave plate,” Opt. Lett. 43(12), 2977–2980 (2018). [CrossRef]
28. Z. Han, S. Ohno, Y. Tokizane, K. Nawata, T. Notake, Y. Takida, and H. Minamide, “Thin terahertz-wave phase shifter by flexible film metamaterial with high transmission,” Opt. Express 25(25), 31186–31196 (2017). [CrossRef]
29. D. Attwood, X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge, 1999).
30. S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4(1), 5045 (2015). [CrossRef]
31. S. Hayashi, K. Nawata, Y. Takida, Y. Tokizane, K. Kawase, and H. Minamide, “High-brightness continuously tunable narrowband subterahertz wave generation,” IEEE Trans. Terahertz Sci. Technol. 6(6), 858–861 (2016). [CrossRef]
32. Y. Takida and H. Minamide, “Frequency-domain spectroscopy using high-power tunable THz wave sources: towards THz sensing and detector sensitivity calibration,” Proc. SPIE 10210, 102100W (2017). [CrossRef]
33. Y. Takida, K. Nawata, T. Notake, T. Otsuji, and H. Minamide, “Optical up-conversion-based cross-correlationfor characterization of sub-nanosecond terahertz-wave pulses,” Opt. Express 30(7), 11217–11227 (2022). [CrossRef]
34. Z. Han, S. Ohno, and H. Minamide, “Spectral phase singularity in a transmission-type double-layer metamaterial,” Optica 7(12), 1721–1728 (2020). [CrossRef]
