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Abstract
Manipulation of electromagnetic waves from radio to visible wavelengths could lead to technology to investigate unexplored wavebands. However, flexible control of terahertz waves is difficult, because few naturally occurring, appropriate materials and sophisticated optical components exist. We propose a 2.28-µm (0.02λ) ultra-thin terahertz metasurface collimator with a high directivity of 4.6 times (6.6 dB) consisting of 339 pairs of meta-atoms compared with a single terahertz continuous-wave source. The metasurface exhibits an extremely high refractive index of 15.0 and a low reflectance of 15.5% at 3.0 THz, and with Fresnel reflections for naturally occurring dielectric materials with high refractive indices avoided. This metasurface collimator should facilitate ground-breaking applications such as arbitrary phase converters, solid immersion lenses, and cloaking.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Historically, since the propagation of electromagnetic waves was described by Maxwell’s equations, the manipulation and design of electromagnetic waves have commonly been applied in all frequency bands, such as, for lenses, waveplates, and beam splitters. The terahertz waveband lies between the microwave and visible light waveband regions. Terahertz waves are increasingly attracting interest with the creation of novel applications, such as, real-time imaging [1] and high-capacity wireless communication [2], as well as the discovery of novel physical phenomena, such as the Higgs mode in superconductors [3] and chirality via spin [4]. Terahertz technology has developed through the interactions between generation, detection, and application of terahertz waves, and optical components for manipulation are necessary to support these developments. Terahertz continuous-wave (CW) sources have rapidly been developed for the generation of terahertz waves. The oscillation frequency of the resonant-tunneling diode (RTD) at room temperature reached 1.86 THz [5] in 2015 and 1.92 THz [6] in 2016. Quantum cascade lasers (QCL) at room temperature have recently been reported with CW terahertz waves from approximately 1.0 to 5.0 THz [7–11]. Commercialized terahertz cameras [12] and a flexible camera using carbon nanotubes [13] have been reported for the detection of terahertz waves. The development of technology for the manipulation of terahertz waves provides a route towards terahertz technologies for the generation and detection of terahertz waves in applications [14]. However, the performance and dimensions of conventional optical components manipulating terahertz waves have not kept up with this rapid development. One reason is the lack of naturally occurring materials suitable for the terahertz waveband. Three-dimensional bulky lenses, such as, cyclo-olefin polymer lenses, silicon lenses [7,10,11], and chalcogenide glass lenses [8] are often used with terahertz CW sources for the enhancement of output power, for example via, collimation and focusing. Optical components with planar structures are convenient from the viewpoint of integration with radiationn sources, and a single patch structure integrated on an RTD has been reported [15]. To the best of our knowledge, only the research in [16] has reported a terahertz collimator utilizing a plasmonic groove structure for QCL at 3.0 THz while numerous terahertz focusing meta-lenses have been reported.
In this study, by applying an unprecedented metasurface with a high refractive index and zero reflectance, we propose an ultra-thin planar collimator in the 3.0-THz band with an extremely high directivity of 4.6 times (6.6 dB). Meta-atoms consisting of 339 pairs with different parameters are arranged to ensure that the refractive index concentrically increases from the periphery to the center of the collimator. Symmetrically aligned paired cut metal wires on the front and back of a thin dielectric substrate allow the flexible design of a wide range of refractive indices and reflectance values because of the control of both the permittivity and permeability. An optimized refractive index is designed at specific regions of the collimator, and the material at the center is designed with an extremely high refractive index of 15.0 and a low reflectance of 15.5%. The focusing length, for example, can be 1.0 mm. The finite element method simulator ANSYS HFSS is used to validate the performance of the collimator with a high directivity value of 4.6 times (6.6 dB). The collimator is a planar 2.28-µm ultra-thin structure, 0.02λ, where conventional collimating terahertz lenses would be three-dimensional structures of naturally occurring materials. The high-performance planar collimator can simply be integrated on and directly fabricated with a wide range of terahertz CW sources, detectors, and applications. The unprecedented material of the collimator with an extremely high refractive index and low reflectance can also be applied in alternative optical components of solid immersion lenses for high-resolution imaging [17]. Further, the simultaneous control of the dielectric and magnetic properties in this metasurface should help accelerate the development of a wide range of applications at higher frequencies, such as, for radiative cooling [18] and transparent reflectors [19] in the infrared region.
2. Design for a wide range of refractive indices at 3.0 THz
Figures 1(a) and (b) illustrate a terahertz metasurface ultra-thin collimator and the model of a single meta-atom, one of the symmetrically aligned paired cut metal wires extracted from the full structure assuming periodicity of the meta-atoms and periodic boundary conditions, respectively. Parameters for metasurfaces with a wide range of refractive indices and low reflectance are derived for the design of the collimator. Appropriate parameters are chosen from contour maps with varying lengths l of the cut metal wires and gaps g between the cut metal wires using the design model in Fig. 1. The other parameters of the cut metal wires, as defined in Fig. 1, are w = 6 µm, d = 2 µm, px = 12 µm, and t = 0.14 µm. The design frequency is 3.0 THz, and the dielectric and metal are respectively a cyclo-olefin polymer with a refractive index of 1.53 + j0.0012 in the terahertz waveband [20] and a silver substrate of high conductivity σ = 4.13×107 + j2.93×107 S/m. The imaginary part of the conductivity is negligible in the 0.3-THz band [21–24] because the real part is far larger than the imaginary part as shown in Fig. 2. The imaginary part of the conductivity is taken into consideration in the 3.0-THz band with the Drude model. The design procedure including the complex conductivity can be applied to a metasurface with a wide range of refractive indices and low reflectance in the regions of the middle infrared ray, near infrared ray, and the visible light as well as for the terahertz wave. A simulation of the design model is performed by the finite element method simulator ANSYS HFSS. The optical constants of a metasurface, such as the effective refractive index, permittivity, and permeability, can be derived from the scattering matrices obtained from the design model using the following equations [25]:
Fig. 1. (a) Terahertz metasurface ultra-thin collimator for power enhancement and (b) the design model of a single meta-atom extracted from the full structure assuming periodicity.
Fig. 3. Contour maps at 3.0 THz for the (a) real and (b) imaginary parts of the refractive indices, (c) reflectance, (d) transmission, and (e) the real part of the normalized wave impedance of a single meta-atom in Fig. 1(b).
Fig. 4. Frequency characteristics of the (a) real and imaginary parts of the refractive index, (b) reflectance and transmission, real and imaginary parts of the (c) permittivity, (d) permeability, and (e) the real and imaginary parts of the normalized wave impedance of a single meta-atom in Fig. 1(b).
Figures 5(a)–(e) present contour maps of an imperfect structure excluding the cut wire on the back from Fig. 1. Figures 6(a)–(e) present the frequency characteristics of the real and imaginary parts of the refractive index, the reflectance and transmission, real and imaginary parts of the relative permittivity and permeability, and the real and imaginary parts of the normalized wave impedance, respectively, for the 31-µm length cut metal wires with a 2-µm gap. The other parameters of the cut metal wires in Figs. 5 and 6 are the same to those in Figs. 3 and 4. The refractive index, reflectance, and transmission are 3.36 + j1.70, 82%, and 17% for the imperfect structure at 3.0 THz, respectively. The phenomena with the extremely high refractive indices and low reflectance in Figs. 3 and 4 are not present in Figs. 5 and 6. Both symmetrical and imperfect structures have the high real parts of relative permittivity in Fig. 4(c) and 6(c). The dielectric resonance in Fig. 4(c) is an antiresonance [26]. The symmetrical structure has the high relative permeability because of the magnetic resonance in Fig. 4(d) while the imperfect structure has the low real parts of relative permeability because of the absence of magnetic resonance in Fig. 6(d). The real parts of the relative permittivity are not close to those of the permeability at the same frequency in Figs. 6(c) and (d), and the phenomena with the extremely high refractive indices and low reflectance do not occur in the imperfect structure. Figures 4 and 6 show that the magnetic resonance in the symmetrical structure causes the phenomena. Figures 7(a)–(d) present the contour maps for the real part of the refractive indices, imaginary part of the refractive indices, reflectance, and transmission with varying misalignments along the x- and y-axes, respectively, for the 31-µm length cut metal wires with a 2-µm gap.
Fig. 5. Contour maps at 3.0 THz for the (a) real and (b) imaginary parts of the refractive indices, (c) reflectance, (d) transmission, and (e) the real part of the normalized wave impedance of an imperfect structure excluding the cut wire on the back from Fig. 1(b).
Fig. 6. Frequency characteristics of the (a) real and imaginary parts of the refractive index, (b) reflectance and transmission, real and imaginary parts of the (c) permittivity, (d) permeability, and (e) the real and imaginary parts of the normalized wave impedance of imperfect structure excluding the cut wire on the back from Fig. 1(b).
3. Design of the metasurface collimator
Figure 8(a) shows the top view of a terahertz metasurface ultra-thin collimator with an extremely high refractive index and low reflectance for power enhancement. The structure of the collimator is symmetric along the x- and y-axes and consists of 339 pairs of aligned paired cut metal wires on the front and back of a dielectric substrate. The aligned paired cut metal wires function as meta-atoms and produce an effective refractive index and reflectance suitable for the respective regions of the collimator. The refractive index increases from the periphery to the center of the collimator, arranging the meta-atoms with the parameters of the dots in Fig. 3. All optical path lengths from collimator to signal source are identical, and the condition of the collimator is expressed
Fig. 7. Contour maps at 3.0 THz for the (a) real and (b) imaginary parts of the refractive indices, (c) reflectance, and (d) transmission with varying misalignments along the x- and y-axes for the 31-µm length cut metal wires with a 2-µm gap.
Fig. 8. (a) Terahertz meta-surface ultra-thin collimator performing with an extremely high refractive index and low reflectance for power enhancement in the 3.0-THz band. Distribution maps of (b) refractive indices, (c) reflectance, (d) transmission, and (e) power loss in the collimator arising from the designed meta-atoms.
Figure 8(b) presents a distribution map of the refractive indices in the collimator arising from the designed meta-atoms. The radius r of a circle including all cut metal wires in the collimator is 256 µm. The focusing length is 1.0 mm. Figure 8(b) indicates that the effective refractive indices increase concentrically from the periphery to the center of the collimator, ensuring phase control of an incident terahertz wave. Metasurfaces with high refractive indices cover a large area of the collimator. The maximum refractive index of the meta-atom is 15.0, with 15.5% reflectance and 45.8% transmission. Figures 8(c), (d), and (e) present contour maps of the reflectance, transmission, and power loss in the collimator. The collimator has the characteristics of extremely low reflectance. The transmission loss is mainly caused by conductor losses that cannot be avoided in practice.
4. Performance of the collimator and discussion
An ANSYS HFSS simulator was used to validate the performance of the meta-surface ultra-thin collimator for power enhancement. Figure 9(a) presents a three-dimensional phase distribution of an incident terahertz wave to the collimator in the xy-plane at 3.0 THz. Figure 9(b) presents a three-dimensional phase distribution of a terahertz wave passing through an imperfect collimator excluding cut wires on the back from the collimator in the xy-plane at 3.0 THz. Figure 9(c) presents a three-dimensional phase distribution of a terahertz wave passing through the collimator consisting of the symmetrically aligned paired cut metal wires on the front and back in Fig. 1(a) in the xy-plane at 3.0 THz. The observation point is at 100 µm from the collimator in Figs. 9(a)–(c). Only one-quarter of the model is simulated using image theory [27] to reduce the size of the computation. Figure 9(a) visualizes that a terahertz wave is spherically propagating from a terahertz CW source. Figure 9(b) visualizes that the phase distribution in the xy-plane is imperfectly flat. The spherical wave is converted to a nearly plane wave even though the imperfect structure excluding cut wires on the back from the collimator does not completely perform as a collimator. Figure 9(c) visualizes that the phase distribution in the xy-plane is almost flat and the collimator converts a spherical wave to a plane wave.
Fig. 9. (a) Three-dimensional phase distribution of an incident terahertz wave in the xy-plane at 3.0 THz. (b) Three-dimensional phase distribution of a terahertz wave propagating through an imperfect collimator excluding cut wires on the back side from the collimator in the xy-plane at 3.0 THz. (c) Three-dimensional phase distribution of a terahertz wave propagating through the collimator consisting of the symmetrically aligned paired cut metal wires on the front and back sides in the xy-plane at 3.0 THz.
Figure 10(a) presents the one-dimensional phase distribution with and without the imperfect collimator in the yz- and xz-planes, respectively. The phase differences with the imperfect collimator are 54° and 63° from –256 to 256 µm in the yz- and xz-planes, respectively. The phase differences without the imperfect collimator are 110° and 104° from –256 to 256 µm in the yz- and xz-planes, respectively. Figure 10(b) presents the one-dimensional phase distribution with and without the collimator in the yz- and xz-planes, respectively. The phase differences with the collimator are 31° and 43° from –256 to 256 µm in the yz- and xz-planes, respectively. The observation point is at 100 µm from the collimator in Figs. 10(a) and (b). The spherical phase distribution for the terahertz CW source results in very low directivity at the far field. The imperfectly flat phase distribution for the imperfect collimator results in directivity at the far field. The flat phase distribution for the collimator results in high directivity at the far field. The alignment of the cut wires on both front and back achieve the effect of the collimator with the conversion from the spherical wave to the plane wave with high directivity.
Fig. 10. (a) One-dimensional distribution of phases at 100 µm from the imperfect collimator with and without the imperfect collimator in the yz- and xz-planes at 3.0 THz. (b) One-dimensional distribution of phases at 100 µm from the collimator with and without the collimator in the yz- and xz-planes at 3.0 THz.
Figure 11(a) shows the directivity of an imperfect plane wave passing through the imperfect collimator and that of a terahertz wave radiated from a terahertz CW source. The directivity of a collimator is defined as the ratio of the power in a given direction from the collimator to the power averaged over all directions [27,16]. The imperfect collimator converts a spherical wave to an imperfect plane wave with a directivity of 2.4 times (3.8 dB). Figure 11(b) shows the directivity of the collimator, and the 2.28-µm ultra-thin collimator converts a spherical wave to a collimated plane wave with a directivity of 4.6 times (6.6 dB). The collimator enhances the directivity to 1.9 times (2.8 dB) greater than the imperfect collimator. Symmetrically aligned paired cut metal wires on the front and back of a thin dielectric substrate make the conversion from a spherical wave to a collimated plane wave with a high directivity of 4.6 times (6.6 dB) possible. The source radiates an approximately ideal spherical wave here. An infinitesimal dipole [27] with the directivity of approximately 1.76 dB is chosen here from the perspective of the integration on RTD and QCL. The distribution of refractive indices in the collimator can be optimized for a practical terahertz CW source. The substrate and metal may be flexibly chosen to be suitable for a terahertz CW source integrated with the collimator. Further, a collimator with a stacked structure would extend the phase control and produce a higher directivity, because the optical path length increases inside the stacked collimator.
Fig. 11. (a) Directivity of the imperfect collimator at 3.0 THz. (b) Directivity of the terahertz meta-surface ultra-thin collimator with extremely high refractive indices and low reflectance for power enhancement at 3.0 THz.
The robustness of the collimator is also important for the integration on practical terahertz CW sources. Figure 12 shows the frequency characteristics of the collimator. The metasurface composing the collimator is relatively narrowbanded in Fig. 4 because the phenomenon of the effective refractive index is resonant. The directivity of the collimator is relatively widebanded contrary to the expectation based on Fig. 4. The collimator has a wide range of refractive indices from 2.59 to 15.0 in Fig. 8(b), and the resonant phenomenon may be saturated in Fig. 12. The directivity of the terahertz CW source integrated with the collimator is greater than that of the terahertz CW source over a range from 2.0 to 4.0 THz, and the bandwidth of the collimator with half power is 20.0% from 2.5 to 3.1 THz compared with the center frequency of 3.0 THz. The bandwidth of the collimator satisfies the requirements of the terahertz CW sources well because the bandwidths of terahertz CW sources such as RTD [5,6] and QCL [7–11] are extremely narrow. Figure 13 shows the directivity change with the position of the terahertz CW source on the z-axis. The directivity is high even though the position changes considerably, from −400 µm (4.0λ) to 400 µm (4.0λ). The wavelength is 100 µm at 3.0 THz, and the directivity of the collimator is robust for the position of the terahertz CW source on the z-axis. Figures 14(a) and (b) show the directivity robustness with the tilting angles α and β of the terahertz metasurface ultra-thin collimator in the xy- and xz-planes, respectively. The directivity is almost unchanged when the terahertz CW source is tilted from −10 to 10 degrees in the xy- and xz-planes. Figures 12, 13, and 14 suggest the robustness of the collimator for the frequency characteristics and the positions of the terahertz CW source from the future perspective of practical integrations.
Fig. 12. Frequency characteristics of the directivity for the terahertz meta-surface ultra-thin collimator.
Fig. 13. Directivity robustness of the terahertz meta-surface ultra-thin collimator with a position on the z-axis.
Fig. 14. Directivity robustness with the tilting angles α and β of the terahertz meta-surface ultra-thin collimator in the xy- and xz-planes.
5. Conclusions
We propose a terahertz ultra-thin metasurface collimator for power enhancement at 3.0 THz. The metasurface in the collimator produces a wide range of refractive indices with low reflectance because of the simultaneous control of the dielectric and magnetic properties. The metasurface consists of symmetrically aligned paired cut metal wires on the front and back of a thin dielectric substrate. The refractive index increases from the periphery to the center of the collimator, maintaining low reflectance. The maximum refractive index is 15.0 with 15.5% reflectance, at 3.0 THz. A full model simulation demonstrates that the collimator converts a spherical wave to a plane wave with a high directivity of 4.6 times (6.6 dB) at 3.0 THz. The proposed terahertz planar collimator can be integrated into various terahertz CW sources, detectors, and applications. A metasurface with a high refractive index and low reflectance would also make it possible to develop unprecedented optical components for the manipulation of terahertz waves, such as arbitrary phase converters, solid immersion lenses, and cloaking devices.
Funding
Japan Society for the Promotion of Science (18K04970); Precursory Research for Embryonic Science and Technology (JPMJPR1815); TEPCO Memorial Foundation; Inamori Foundation.
Acknowledgments
The authors wish to thank Mr. Takashi Kotera at ANSYS Japan for his valuable advice on simulation techniques.
Disclosures
The authors declare no conflicts of interest.
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