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Abstract
Zero refractive index materials behave electromagnetically as single points despite the finite dimensions because a propagating electromagnetic wave passes with an infinite phase velocity. However, the composition of naturally occurring materials cannot produce a zero refractive index material because any effect of both of the dielectric and magnetic properties would have to vanish (be near zero). In this report, we demonstrate a zero refractive index metasurface with a refractive index of 0.16 + j0.09, the reflectance of 0.7%, and transmittance of 97.3% at 0.505 THz. The measured relative permittivity and relative permeability are 0.18 − j0.10 and 0.004 + j0.16 at 0.505 THz, respectively. Both the relative permittivity and relative permeability simultaneously approach zero at the same frequency, and the dielectric and magnetic properties appear to be absent (vanish) in the artificial material. The zero refractive index metasurface can offer a material platform for terahertz applications with unprecedented functionalities for 6G (beyond 5G) wireless communications, imaging, and security.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The on-demand control of light propagation is one of the ultimate goals in optics, and naturally occurring materials with fundamental phenomena such as refraction, reflection, and transmission provide an accessible platform for conventional optical components. The control of high-frequency electric and magnetic fields can artificially provide a design for unprecedented phenomena of electromagnetic waves in a two-dimensional material consisting of smartly engineered sub-wavelength structures [1–3]. The sub-wavelength structures are termed meta-atoms, and the two-dimensional artificial material is called a metasurface. Artificial materials consisting of sub-wavelength building blocks are metamaterials, and metamaterials have made it possible to produce extraordinary phenomena including negative refraction, a milestone in artificial material development [4]. The control of electromagnetic waves based on a metasurface is called flat optics [5], and conventional bulky optical components can be replaced with optically thin planar components. Planar optical components in the terahertz waveband are desired for cutting-edge applications such as in 6G (beyond 5G) [6] wireless communications [7,8], imaging [9,10], and security [11]. Terahertz continuous-wave (CW) sources with the oscillation of a single frequency with narrow bandwidths at room temperature such as quantum cascade lasers (QCLs) [12–16] and resonant-tunneling diodes (RTDs) [17,18] have been powerful and useful tools among terahertz applications. However, most terahertz optical components are bulky compared with terahertz CW sources because there are not many naturally occurring materials for applications to the terahertz waveband [19–21]. The development of materials in the terahertz waveband remains a significant problem, and metasurfaces can offer a platform for artificial materials enabling a compact integration of planer terahertz components with terahertz CW sources. The metasurfaces allow arbitrary design of material properties due to the direct control of electric and magnetic fields in the artificial material. A refractive index is described as the root of the product of the relative permittivity and relative permeability ($n = \sqrt {{\varepsilon _\textrm{r}}{\mu _\textrm{r}}} $), and Fresnel reflection is related to the relative wave impedance, the root of the relative permeability over the relative permittivity (${Z_\textrm{r}} = \sqrt {{\mu _\textrm{r}}/{\varepsilon _\textrm{r}}} $).
A wide range of refractive indices from high [22–24] to negative [25–27] values are presented in the terahertz waveband by the design approach of metamaterials due to the direct control of relative permittivity and relative permeability. Material properties with high and negative refractive indices produce slow and fast wave effects, respectively. Phase manipulation based on metasurfaces is applied to terahertz flat optic as meta lenses [28–30]. The control of the relative permeability in naturally occurring materials is commonly difficult to achieve at high frequencies [31]. Conventional metasurfaces face the problem of high Fresnel reflectance because it is not straightforward to design both relative permittivity and relative permeability of similar values. The work in [32] and [33] has recently reported reflectionless terahertz metasurfaces with high and negative refractive indices, respectively, where the relative permeability is close to the relative permittivity enabled by engineered meta-atoms. However, it remains to be elucidated whether the relative permittivity and also the relative permeability simultaneously vanish in an optically thin metasurface. Epsilon-near-zero (ENZ) photonics [34], where the relative permittivity vanishes to approximately zero, is a useful platform for optical components. The work in [35–39] has recently reported ENZ structures for the phase manipulation of terahertz waves. Furthermore, ENZ structures can offer attractive wave properties such as stretching, supercoupling, and squeezing for the development of optical components [40]. Unfortunately, Fresnel reflections in ENZ structures are unavoidable because ENZ structures control only the relative permittivity, but not the relative permeability. Near-zero refractive index photonics [41], where both the relative permittivity and relative permeability simultaneously vanish to approximately zero, is a unique platform substituted for ENZ platforms. The work in [42] simulates that zero refractive index artificial materials electromagnetically behave as single points due to an infinite phase velocity and infinite wavelength despite the finite structures. The phase velocity in a material is described as the phase velocity in vacuum over a refractive index. The phase velocity and wavelength are infinite in a material with a refractive index of zero resulting in no spatial phase shift [43]. Measurements in the optical region have confirmed the existence of zero refractive index metamaterials consisting of sub-wavelength building blocks [44,45]. Measurements in the microwave band have also confirmed a zero refractive index metamaterial consisting of three-dimensional structures [46]. To the best of our knowledge, only the research in [47] has shown a zero refractive index metasurface enabled by the simultaneous control of the relative permittivity and permeability in the terahertz waveband achieved by simulations. The work in [48] has shown a periodic array of split-ring resonator holes with a refractive index of zero due to localized waveguide resonance. The work in [49] has shown a nanosphere dispersed liquid crystal in the mid-infrared region.
In this article, we experimentally demonstrate a reflectionless metasurface with a refractive index of zero where both the relative permittivity and the relative permeability vanish to reach zero in the terahertz waveband. The zero refractive index metasurface consists of 10,080 pairs (126 × 80) of meta-atoms, symmetrically aligned paired cut metal wires, on both the front and back of a dielectric substrate. Terahertz time-domain spectroscopy (THz-TDS) confirms a refractive index of 0.16 + j0.09, extremely low reflectance of 0.7%, and high transmittance of 97.3% at 0.505 THz. The measured relative permittivity and permeability are 0.18 − j0.10 and 0.004 + j0.16 at 0.505 THz, respectively. The reflectionless metasurface also has a low refractive index |n| of less than 1.0 and high transmittance characteristics above 80% from 0.49 to 0.545 THz resulting from both the permittivity and permeability exhibiting near-zero properties. The positive and negative signs for the frequency characteristics of the relative permittivity are very similar to those of the relative permeability, and electromagnetic waves propagate without attenuation in the metasurface. At 0.485 THz the metasurface has a refractive index of −1.21 + j0.28 and transmittance of 82.4%, and at 0.57 THz the metasurface has a refractive index of 1.29 + j0.04 and transmittance of 83.0%. Summing up, the metasurface has a transmittance above 80% from 0.485 to 0.57 THz. This zero refractive index metasurface would enable building a platform of artificial materials for planar terahertz components with unprecedented functionalities such as gradient-refractive-index (GRIN) metalenses. The CW sources such as QCLs [12–16] and RTDs [17,18] have extremely narrow bandwidths. Further, the laminated structure of the zero refractive index metasurface could be applied to a three-dimensional structure with a refractive index of zero.
2. Zero refractive index metasurface
Figure 1 shows the full model of the zero refractive index metasurface consisting of symmetrically aligned paired cut metal wires on both front and back of a dielectric substrate. The double-sided paired cut metal wires perform as meta-atoms in the metasurface and simultaneously control both the dielectric and magnetic properties. The dielectric property arises from the electric field of the propagating terahertz waves parallel to the cut metal wires. The relative permittivity describing the dielectric properties resonates and changes from negative to positive values around a resonance frequency. The relative permittivity is zero at the state between the negative permittivity and the positive permittivity. The magnetic property is caused by the magnetic field of propagating terahertz waves perpendicular to the cut metal wires on both the front and back of the dielectric substrate. The phenomenon is explained by Faraday’s law, and the double-sided paired cut metal wires perform as a microscale induction coil. The relative permeability describing the magnetic properties resonates and changes from negative to positive values around a resonance frequency. The relative permeability is zero between the negative and positive permeabilities. The relative permittivity of zero and the relative permeability of zero result in a refractive index of zero.
Fig. 1. Zero refractive index metasurface consisting of symmetrically aligned paired cut metal wires on both the front and back of a dielectric substrate.
An equivalent circuit adequately explains the dielectric and magnetic properties in the zero refractive index metasurface. Figures 2(a) and (b) show the equivalent circuits of symmetrically aligned paired cut metal wires with the dielectric and magnetic properties, respectively. The dielectric property in the metasurface is mainly determined by the inductance component of a cut wire and the capacitance component at a gap between cut wires along the y-axis as in a series circuit. The series circuit behaves as a resonance circuit with the inductance and capacitance components at a resonant frequency. The resonance of the series circuit represents the resonance of the dielectric property. The magnetic property in the metasurface is mainly determined by the inductance and capacitance components of the cut wires on the front and back substrate as in a parallel circuit. The parallel circuit behaves as a resonance circuit with the inductance and capacitance components at a resonant frequency. The resonance of the parallel circuit expresses the resonance of the magnetic properties.
Fig. 2. Equivalent circuits of the double-sided paired cut metal wires with (a) dielectric and (b) magnetic properties.
3. Design of zero refractive index metasurface
Figure 3 shows a single meta-atom extracted from the zero refractive index metasurface in Fig. 1. The one-unit cell model with periodic boundary conditions efficiently designs the properties of the zero refractive index metasurface because the large full model of Fig. 1 is periodic along the x- and y-axes. The simulation of a large full model compared with the wavelength is a very time-consuming process. The control of length l and gap g of the cut metal wires enables the control of both the relative permittivity and relative permeability and the design of a zero refractive index property. Figures 4(a)–(f) show simulated contour maps for the real and imaginary parts of refractive indices, the real parts of the relative permittivity and permeability, reflectance, and transmittance, respectively, with varied gap g and length l of the cut metal wires at 0.50 THz. Other parameters are set as s = 361 µm, w = 120 µm, d = 50 µm, and h = 0.5 µm. The metal of the cut wires is copper, with a conductivity σ = 5.8 × 107 S/m. The dielectric substrate is a cyclo-olefin polymer with a measured refractive index of 1.53 + j0.0012 at 0.5 THz and has low loss properties in the terahertz waveband. The simulations are performed by the frequency domain solver of a finite element method simulator: ANSYS HFSS. As the convergence criteria in HFSS, the maximum number of passes and the maximum Delta S per pass are set to 15 and 0.005, respectively. The simulations use Floquet ports on the incident plane and output plane. The scattering matrices S11 and S21 from the simulations of the one-unit cell model derive effective optical constants such as the refractive index, relative permittivity, and relative permeability, from the following equations [50],
Fig. 3. One-unit cell model of a single meta-atom extracted from a zero refractive index metasurface for the design of dielectric and magnetic properties.
Fig. 4. Contour maps of (a) the real and (b) imaginary parts of refractive indices, real parts of (c) relative permittivity and (d) relative permeability, (e) reflectance, and (f) transmittance at 0.50 THz.
Figure 4(a) shows that the refractive indices change from −0.98 to 0.26 with the gap g and length l. The reflectance and transmittance displayed in Figs. 4(e) and (f) are from 0 to 5.0% and from 90 to 100%, respectively, and the material properties in Fig. 4(e) and (f) show low reflectance and high transmittance. Figures 4(a), (e), and (f) show that controlling the gap g and length l enables the design of a reflectionless metasurface with a low refractive index |n| of less than 1.0 and with high transmittance. The material properties with low refractive indices |n| of less than 1.0, reflectionless, and high transmittance characteristics can be directly applied to a wide variety of applications in near-zero refractive index photonics [41]. The control of refractive indices |n| of less than 1.0 with reflectionless and high transmittance characteristics can also fill the gap between high [32] and negative [33] refractive indices and help build a platform for reflectionless artificial materials. Further, Figs. 4(a), (e), and (f) show the only area of meta-atoms where it is possible to control refractive indices when gap g and length l are changed and with the other parameters of s, d, w, and h fixed in the contour maps. The area of meta-atoms would be able to allow the design of a wide range of refractive indices from extremely high to negative values with reflectionless and high transmittance characteristics. A challenge as a yet unresolved problem is to solve the relationship between the area and material properties using formulas. The design concept of material properties with identical meta-atoms developed here could offer an unprecedented platform for reflectionless artificial materials with a full range of refractive indices from extremely high to negative values, including the zero refractive index.
Figures 5(a)–(f) show simulated contour maps for the real and imaginary parts of refractive indices, the real parts of the relative permittivity and permeability, reflectance, and transmittance, respectively, with varied width w and spacing s of the cut metal wires at 0.50 THz. Other parameters are set as g = 106 µm, l = 202 µm, d = 50 µm, and h = 0.5 µm. The design of the reflectionless zero refractive index metasurface also needs the control of the width w and the spacing s. Figure 5(a) shows that the control of the width w and spacing s designs the real parts of the refractive indices from −0.73 to 0.19. Figures 5(e) and (f) show that the reflectance changes from 0% to 50% and the transmittance changes from 50% to 100%, respectively. Figures 5(c) and (d) show that the change of relative permeability is more stable than the change of relative permittivity with varied width w and spacing s. Figure 5(c) shows that the relative permittivity changes from −4.0 to 1.0 with varied width w and spacing s. Figure 5(d) shows that the relative permeability changes from −0.16 to 0.04 with varied width w and spacing s. With w = 100 µm and s = 340 µm, the difference between a relative permittivity of −3.63 and a relative permeability of −0.15 is a local maximal value, resulting in a refractive index of −0.73 + j0.05, reflectance of 43.2%, and transmittance of 52.4% due to the impedance mismatching.
Fig. 5. Contour maps of (a) the real and (b) imaginary parts of refractive indices, real parts of (c) relative permittivity and (d) relative permeability, (e) reflectance, and (f) transmittance at 0.50 THz.
4. Measurements and discussion
Figure 6(a) shows a fabricated zero refractive index metasurface consisting of 10,080 pairs (126 × 80) of meta-atoms, symmetrically aligned paired cut metal wires. The fabricated metasurface is a square 4 cm on a side. The wavelength is 600 µm at 0.50 THz. The dimensions of the zero refractive index metasurface are large enough compared with the wavelength and can be simply applied to terahertz flat optics. Figure 6(b) shows a laser microscope image of the fabricated meta-atoms. A low-loss cyclo-olefin polymer film coated with copper layers on both front and back is etched for the fabrication of the zero refractive index metasurface. Additional layers to ensure adhesion are usually used to ensure adhesion between the dielectric substrate and metal, but layers ensuring adhesion (chrome and titanium) will increase conductor loss. The cyclo-olefin polymer is processed using reverse sputtering technique before the sputtering procedure to ensure adhesion between the dielectric substrate and metal. The cyclo-olefin polymer is directly coated with copper without the additional layers to reduce conductor loss, using sputtering technique. Metals with high conductivity such as copper, gold, and silver are acceptable to reduce conductor loss. Copper layers need to coat both the front and back of the thin cyclo-olefin polymer before the wet etching because the double-sided meta-atoms produce the material property of a zero refractive index. The meta-atoms on the front side are fabricated by the wet etching, and those on the back side are also fabricated by the wet etching. The parameters of the fabricated meta-atoms are l = 202 µm, g = 106 µm, s = 361 µm, and w = 120 µm. The thickness of the dielectric substrate is d = 50 µm. The thickness of the copper is h = 0.5 µm, sufficiently thick considering the skin depth of copper of approximately 0.1 µm.
Fig. 6. (a) Fabricated zero refractive index metasurface consisting of symmetrically aligned paired cut metal wires on both the front and back of the cyclo-olefin polymer film. (b) Laser microscope image of meta-atoms.
Figures 7(a)–(e) show the frequency characteristics of the optical constants for measurements and simulations. Experiments by THz-TDS TOPTICA with a frequency resolution of 0.005 THz were conducted to measure the transmittance and reflectance of the fabricated metasurface. In the transmittance measurements, pulsed terahertz waves radiated from a transmitting photoconductive antenna pass through the fabricated metasurface and arrive at a receiving photoconductive antenna. The terahertz waves in the transmittance measurements are collimated with a diameter of approximately 18 mm. In reflectance measurements, vertically incident terahertz waves are vertically reflected on the fabricated metasurface and arrive at a receiving photoconductive antenna. The terahertz waves in the reflectance measurements are focused at the fabricated metasurface, and the calculated focusing spot and focal depth are approximately 4.2 mm and 47 mm at 0.50 THz, respectively. Scattering matrices from the measurements by THz-TDS derive the effective optical constants from Eqs. (1), (2), and (3). Deflection of the fabricated metasurface is unavoidable in the measurements and is a cause of the difference in optical lengths between the fabricated metasurface and a reference mirror in the reflectance measurements. The reflectance measurements are compensated for on the condition that the measured phases of the reflectance S11 are the same as the simulated phases. The compensation predicts that the fabricated metasurface is concave with a depth of 112.5 µm along the incident terahertz waves. Figures 7(a) and (b) show that at 0.505 THz the measured refractive index ($n = \sqrt {{\varepsilon _\textrm{r}}{\mu _\textrm{r}}} $), reflectance, and transmittance are 0.16 + j0.09, 0.7%, and 97.3%, respectively. The measurements by THz-TDS demonstrate material properties with a refractive index of zero, reflectionless characteristics, and high transmittance. Figures 7(c) and (d) show the frequency characteristics of the measured relative permittivity and relative permeability, respectively. The measurements agree well with the relative permittivity of 0.18 − j0.10 and relative permeability of 0.004 + j0.16 at 0.505 THz. Both the relative permittivity and the relative permeability approach zero at 0.50 THz, and the dielectric and magnetic properties appear to vanish in the fabricated zero refractive index metasurface. Figure 7(e) shows the real and imaginary parts of the relative wave impedance (${Z_\textrm{r}} = \sqrt {{\mu _\textrm{r}}/{\varepsilon _\textrm{r}}} $). The measurements confirm a relative wave impedance Zr of 0.45 + j0.75 at 0.505 THz. The frequency characteristics of the relative permittivity are similar to those of the relative permeability. The high transmittance, above 80%, is obtained from 0.485 THz to 0.570 THz due to the impedance matching between the fabricated metasurface and free space.
Fig. 7. Measurements and simulations of the frequency characteristics for (a) the refractive index, (b) transmittance and reflectance, (c) relative permittivity, (d) relative permeability, and (e) relative wave impedance.
The power absorption in the zero refractive index metasurface is expressed by the following equation [51]
Fig. 8. Measurements and simulations of the frequency characteristics of (a) dielectric energy loss |µr|Im(εr) and magnetic energy loss |εr|Im(µr) and (b) the sum of dielectric energy loss |µr|Im(εr) and magnetic energy loss |εr|Im(µr).
5. Summary
We experimentally demonstrate a reflectionless zero refractive index metasurface in the terahertz waveband. The zero refractive index metasurface consists of 10,080 pairs (126 × 80) of double-sided meta-atoms on a dielectric substrate. Measurements by THz-TDS show a refractive index of 0.16 + j0.09, a reflectance of 0.7%, and a transmittance of 97.3% at 0.505 THz. The measurements also yield a relative permittivity of 0.18 − j0.10 and relative permeability of 0.004 + j0.16 at 0.505 THz, and show that the relative permittivity and relative permeability simultaneously approach zero at 0.50 THz. Both dielectric and magnetic properties effectively vanish in the zero refractive index metasurface while the dielectric and magnetic properties cannot vanish in naturally occurring materials. The control of both the relative permittivity and permeability with similar values enable the reflectionless properties, avoiding the high Fresnel reflectance in conventional metasurfaces. The sum of the dielectric and magnetic energy losses is positive in the zero refractive index metasurface, and the conservation of energy is satisfied. The reflectionless zero refractive index metasurface would open the doors to a variety of optically thin planar terahertz components with attractive functionalities such as focusing, collimating, wavefront control, and light vortexes. Further, the path-breaking metasurface helps build a platform of artificial materials for 6G (beyond 5G) wireless communications and terahertz imaging.
Funding
Japan Society for the Promotion of Science (18K04970); Precursory Research for Embryonic Science and Technology (JPMJPR1815); Inamori Foundation; TEPCO Memorial Foundation.
Acknowledgments
The authors wish to thank Tatsuya Kimura, Junichi Yasuda, and Tatsuya Sato in performing the simulations and measurements.
Disclosures
The authors declare no conflicts of interest.
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