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Abstract
Terahertz flat optics is a design concept for replacing conventional three-dimensional bulky optical components with two-dimensional ultra-thin optical components. However, high refractive index materials suitable for flat optics are frequently subject to high Fresnel reflections due to the cumbersome control of the relative permeability it requires. Here we experimentally demonstrate a reflectionless metasurface with a high refractive index of 5.88 + j1.57, extremely low reflectance of 1.3%, high relative permittivity of 6.73 + j0.85, and the high relative permeability of 5.03 + j2.11 at 2.97 THz. The super-fine ink-jet printer using silver paste ink fabricates the metasurface consisting of 80,036 pairs of cut metal wires on both the front and back of a 5 μm-thick polyimide film. The findings also demonstrate that weak conductors as well as good conductors can be used in the design of reflectionless metasurfaces with a high refractive index in the terahertz waveband. The presented metasurface can offer an accessible platform for terahertz flat optics in 6G (beyond 5G) wireless communications and imaging.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz waveband is a promising candidate for wireless communications in the advanced generation 6G [1,2], imaging [3,4], tomography [5], and security [6]. Terahertz continuous-wave (CW) sources oscillating with a single frequency at room temperature have been developed from approximately 1.0 to 3.0 THz [7–10] to bridge the terahertz gap between the millimeter waveband and the infrared region with accessible CW sources. Optical components such as lenses, wave plates, polarizers, beam splitters, and prisms for the manipulation of terahertz waves radiated from CW sources are frequently made from naturally occurring materials such as cyclo-olefin polymer with a refractive index of 1.5 [11], magnesium oxide (MgO) 3.1 [12], and silicon (Si) 3.4 [13]. Conventional optical components in the terahertz waveband are designed based on naturally occurring materials with such fixed refractive indices. Metasurfaces consisting of numerous meta-atoms with subwavelength structures make arbitrary designs with a selected refractive index and reflectance possible by the control of permittivity and permeability inside the artificial materials forming the structure. Flat optics based on metasurfaces [14–18] is a design concept replacing conventional three-dimensional bulky optical components made from naturally occurring materials with two-dimensional flat optical components. However, artificial materials as well as naturally occurring materials with a high refractive index suitable for flat optics are subject to high Fresnel reflections due to the cumbersome control of the magnetic resonance required for the relative permeability.
Figure 1 gives an overview of metasurfaces with a high refractive index in the terahertz waveband as a platform for artificial materials in terahertz flat optics. The values in Fig. 1 are plotted as far as we know from reported work on metasurfaces with high refractive indices [19–26] and reflectionless metasurfaces with high refractive indices [27–32]. The asterisks denote that the values are read off from (analog) graphs in the reports. The plotted dots and boxes show the measured and simulated values, respectively. In 2011, the work in [19] reported a metasurface with a high refractive index of approximately 24 in the 0.5-THz band. However, the control of the relative permittivity without control of the relative permeability produces a high refractive index in the metasurface, and large differences between relative permittivity and permeability cause high Fresnel reflections, impedance mismatching in circuit theory. The reported metasurfaces with a high refractive index have suffered from the problem of high Fresnel reflectance [19–26]. In 2017, our work in [27] demonstrated a reflectionless metasurface with a high refractive index in the 0.3-THz band. The relative permeability is close to the relative permittivity at the same frequency because of the simultaneous control of both dielectric and magnetic resonances arising from meta-atoms on both the front and back of a dielectric substrate. The work in [28–32] has also reported reflectionless metasurfaces with a high refractive index with meta-atoms on both front and back of a dielectric substrate. In 2019, the work in [30] reported simulations with a metasurface for a refractive plate consisting of symmetrically aligned paired cut metal wires on both the front and back of a dielectric substrate. The simulated metasurface has reflectionless properties and phase shifts resulting in high and negative refractive indices at 0.83 THz. However, measurements do not demonstrate the reflectionless metasurface with high and negative refractive indices in [30]. In 2017, the work in [27,31] had already reported the reflectionless metasurface with high, zero, and negative refractive indices in the 0.3-THz band consisting of symmetrically aligned paired cut metal wires on both the front and back of a dielectric substrate by measurements. The reflectionless metasurfaces with high, zero, and negative refractive indices consisting of symmetrically aligned paired cut metal wires on both the front and back of a dielectric substrate are our original artificial materials suitable for optical components in terahertz flat optics. The metasurface in [32] has high Fresnel reflections together with high refractive indices over a wide frequency range. The metasurface in the work [32] could be used to design broadband properties with high refractive indices and high Fresnel reflections. In this present manuscript, we focus on the reflectionless properties with high refractive indices suitable for optical components in terahertz flat optics. Reflectionless metasurfaces are essential for terahertz flat optics and can be applied to two-dimensional flat optical components. Our original reflectionless metasurface with high and negative refractive indices in [27,31] has already been applied to collimating lenses [33,34], focusing lenses [35], and refractive plates [30]. However, Fig. 1 suggests the terahertz gap for artificial materials, where reflectionless metasurfaces with a high refractive index and metasurfaces with a high refractive index have not been reported in the terahertz waveband above 1.0 THz. Reflectionless metasurfaces with a high refractive index as well as metasurfaces with a high refractive index have been developed in the subterahertz waveband below 1.0 THz. The fabrication of meta-atoms forming a metasurface for frequencies above 1.0 THz, wavelengths shorter than 300 μm, are in the order of ten micrometers and cumbersome from the viewpoint of semiconductor lithography suitable for nanofabrication. The super-fine ink-jet printer [36] controlling droplets of a single femtoliter enables quick drawing of minute structures in the order of ten micrometers. Further, it remains to be shown whether a metasurface with a high refractive index can be designed with a metal other than good conductors. The conventional metasurfaces with a high refractive index in Fig. 1 have been fabricated with good conductors such as gold [19,21,23,24,30], copper [25–27,29,31], and aluminum [22,28,32]. A metasurface in [20] with a high refractive index only due to relative permittivity at 0.48 THz was designed with the conductivity of silver and fabricated with silver paste ink.
Fig. 1. Metasurfaces with a high refractive index in the terahertz waveband. Dots and cubes show the measurements and simulations, respectively. *Asterisks denote that the values are read from graphs in the work cited.
In this report we experimentally demonstrate a reflectionless metasurface with a high refractive index at 3.0 THz. The super-fine ink-jet printer fabricates a metasurface consisting of 80,036 units (428 × 187) of symmetrically aligned paired cut metal wires on both the front and back of a 5-μm thick polyimide film, this is achieved with silver paste ink different from the good conductors listed above. Measurements by terahertz time-domain spectroscopy (THz-TDS) confirms a refractive index of 5.88 + j1.57, extremely low reflectance of 1.3%, relative permittivity of 6.73 + j0.85, and the relative permeability of 5.03 + j2.11 at 2.97 THz. In the metasurface, the relative permeability is close to the relative permittivity at the same frequency, resulting in the material properties with both high refractive index and extremely low Fresnel reflection. We also show that a reflectionless metasurface with a high refractive index can be designed using a silver paste ink with the real part of the conductivity of 4.9 × 105 S/m two orders of magnitude lower than the good conductors where it is in the order of 107 for gold 3.4 × 107 S/m, for copper 4.9 × 107 S/m, and for aluminum 2.0 × 107 S/m. The control of the real and imaginary parts of the conductivity allows the design of a reflectionless metasurface with a high refractive index. The relative permeability can be close to the relative permittivity with high values for both at the same frequency with poor conductors as well as with good conductors, resulting in the material properties with both a high refractive index and an extremely low Fresnel reflection. The reflectionless metasurface with a high refractive index can be applied to flat optical components with attractive functionalities such as arbitrary wavefront shaping, beam forming, high numerical aperture, polarization control, and optical vortices. Further, two-dimensional flat optical components in terahertz flat optics based on reflectionless metasurfaces with a high refractive index can be directly integrated with a variety of terahertz CW sources.
2. Reflectionless metasurface with a high refractive index
Figure 2 illustrates a metasurface with a high refractive index and low reflectance at 3.0 THz. The metasurface with double-sided meta-atoms for the control of dielectric and magnetic properties cause the reduction in the reflectance, because the real parts of the relative permittivity are close to those of the permeability at the same frequency, avoiding an impedance mismatch between the metasurface and vacuum. The dielectric and magnetic properties of the metasurface are controlled by the gap g around the metal wires and length l of the metal wires to design an effective high refractive index [27]. The effective refractive index neff and relative impedance Zr, the impedance of the metasurface divided by that of vacuum, can be expressed as
Fig. 2. (a) Reflectionless metasurface with a high refractive index at 3.0 THz consisting of symmetrically aligned paired cut metal wires on both the front and back of an ultra-thin dielectric substrate. Equivalent circuits of the symmetrically aligned paired cut metal wires with (b) dielectric and (c) magnetic properties.
The metasurface with the double-sided meta-atoms for the control of the dielectric and magnetic properties cause the reduction in the reflectance, because the real parts of the relative permittivity are close to those of the permeability at the same frequency, avoiding an impedance mismatch between the metasurface and vacuum. Figures 2(b) and (c) illustrate equivalent circuits of the metasurface consisting of symmetrically aligned pairs of cut metal wires with an effective high refractive index and low reflectance. The equivalent circuits in Figs. 2(b) and (c) show the performance of the metasurface with the control of the dielectric and magnetic properties. The resonance frequency f can be expressed by the following equation:
where L is the inductance and C is the capacitance. The dielectric resonance is determined by the inductance component of the cut metal wires and the capacitance component at the gap along the y-direction between the cut metal wires. The magnetic resonance is determined by the inductance component of the cut metal wires on the front and back of the metasurface and the capacitance component between the cut metal wires on the front and back. The simultaneous control of the dielectric and magnetic properties allows an arbitrary design of both the refractive index and reflectance as in Eqs. (1) and (2).3. Design of reflectionless metasurface with a high refractive index
Figures 3(a)–(f) show simulated contour maps at 3.0 THz for the real parts of the refractive indices, reflectance, transmittance, power loss, and the real parts of the relative permittivity and relative permeability, respectively, with the various gap lengths g around the metal wires and the lengths l of the metal wires. Other parameters are set as the width of the metal wires w = 8.9 μm, the spacing s = 4.5 μm, the thickness of the metal t = 0.14 μm, and the thickness of the dielectric substrate d = 5 μm. The dielectric substrate is a polyimide film with a refractive index of 1.8 + j0.04 in the terahertz waveband [37]. The scattering matrices S11 and S21 obtained from simulations by a finite element method simulator ANSYS HFSS derive the effective refractive index, relative permittivity, and relative permeability [38]. The thickness of the metasurface is defined as d + 2t, and the thickness is 5.3 μm here. The plots with the dots on the countour maps in Fig. 3 show the fabricated parameters of g = 6.5 μm and l = 25.3 μm described in Section 4 below, and have a refractive index of 7.91 + j1.17, reflectance of 9.9%, transmittance of 56.7%, power loss of 33.4%, relative permittivity of 5.52 − j3.12, and relative permeability of 6.96 + j7.28. The designed metasurface has the high refractive index and low reflectance because the relative permeability is close the relative permittivity.
Fig. 3. Contour maps of (a) the real parts of refractive indices, (b) reflectance, (c) transmittance, (d) power loss, and the real parts of (e) relative permittivity and (f) relative permeability with varied gaps g and lengths l at 3.0 THz. The dots in the maps show the fabricated parameters of g = 6.5 μm and l = 25.3 μm described in Section 4.
The designed metasurface is fabricated by the super-fine ink-jet printer as described in Section 4, and the metal is a silver paste ink (Harima Chemicals Group NPS-J). The conductivity of the metal must be taken into consideration in the design of metasurfaces at high frequencies [39]. Figure 4 shows the frequency characteristics of complex conductivity for silver paste ink [40], gold, and copper with the Drude model. The material properties of the silver paste ink has a plasma frequency of 320 THz and relaxation time of 0.19 ps. The complex conductivity of the silver paste is 4.9 × 105 + j1.8 × 106 S/m at 3.0 THz with the Drude model. The conductivities of gold and copper are 3.4 × 107 + j1.6 × 107 S/m and 4.9 × 107 + j2.3 × 107 S/m at 3.0 THz, respectively. For the silver paste ink the real part of the conductivity of 4.9 × 105 S/m is approximately two orders of magnitude poorer than those of gold at 3.4 × 107 S/m and copper at 4.9 × 107 S/m. Figures 5(a)–(f) show the contour maps at 3.0 THz for the real parts of the refractive indices, reflectance, transmittance, power losses, and the real parts of the relative permittivity and relative permeability, respectively, with varied real and imaginary parts of the complex metal conductivity. The parameters of the meta-atoms are set as g = 6.5 μm, l = 25.3 μm, w = 8.9 μm, s = 4.5 μm, d = 5 μm, and t = 0.14 μm. The gray, orange, and yellow dots show the complex conductivity for the silver paste ink, gold, and copper, respectively. Figure 5(a) shows that the real part of the refractive index of the silver paste ink, gold, and copper are 7.91, 6.25, and 6.12, respectively. Figure 5(b) shows that the reflectance of the silver paste ink, gold, and copper are 9.9, 9.1, and 9.9%, respectively. Figures 5(a) and 5(b) verify that the metasurfaces have refractive indices higher than approximately 5.9 and reflectances lower than approximately 13% with the real parts of the conductivity Re(σ) higher than approximately 5.0 × 106 or the imaginary parts of conductivity Im(σ) higher than approximately 1.8 × 106. Overall, the data here show that metasurfaces consisting of meta-atoms with weak conductors as well as good conductors enable reflectionless properties with high refractive indices. Figure 5(c) shows that the transmittance for silver paste ink, gold, and copper are 56.7, 82.2, and 82.8%, respectively. Figure 5(d) shows that the power loss for silver paste ink, gold, and copper are 33.4, 8.6, and 7.3%, respectively. The power loss is not low in the metasurface with silver past ink while that is low in the metasurface with gold and copper. Figures 5(c) and (d) confirm that the transmittance with the silver paste ink is lower than that for gold and silver due to conductor losses. Reflectionless metasurfaces with high refractive indices consisting of meta-atoms with weak conductors have low transmittance while those with good conductors have higher transmittance. Figure 5(e) shows that the real part of relative permittivity for silver paste ink, gold, and copper are 5.52, 8.85, and 8.90, respectively. Figure 5(f) shows that the real part of the relative permeability in the metasurfaces designed with silver paste ink, gold, and copper are 6.96, 4.27, and 4.20, respectively. Figure 5(f) also shows that the refractive index has a local maximum value of 8.8 and the relative permeability has a local maximum value of 11.7 for weak conductors with the real part of the conductivity Re(σ) less than 5.0 × 106. Figures 5(e) and 5(f) confirm that the relative permeability is close to the relative permittivity with high values for silver paste ink, resulting in properties with high refractive indices and extremely low Fresnel reflections. The metasurfaces consisting of symmetrically aligned paired cut metal wires with weak conductors as well as those with good conductors on both the front and back of the ultra-thin dielectric substrate in Fig. 2 make it possible to design for a high relative permeability due to the magnetic resonance. Figures 5(a)–(f) provide the new insight that the real and imaginary parts of the metal conductivity as well as the dimensions of the cut wires make it possible to design metasurfaces with high refractive indices and extremely low Fresnel reflections.
Fig. 4. Real and imaginary parts of the complex conductivity for silver paste ink, gold, and copper with the Drude model.
Fig. 5. Contour maps of the (a) real parts of refractive indices, (b) reflectance, (c) transmittance, (d) power loss, and the real parts of (e) relative permittivity and (f) relative permeability with varied real and imaginary parts of complex conductivity at 3.0 THz.
4. Measurements and discussion
This section 4 presents measurements of a fabricated reflectionless metasurface with a high refractive index at 3.0 THz to demonstrate the details described in Sections 2 and 3. Figure 6(a) shows a photograph of the reflectionless metasurface with a high refractive index at 3.0 THz on the polyimide film. Figures 6(b) and (c) show laser microscope images of the metasurface and meta-atoms, respectively. The metasurface is fabricated by the super-fine ink-jet printer on both the front and back of a dielectric substrate. The gap of the meta-atoms g, length l, width w, and the spacing s are 6.5 μm, 25.3 μm, 8.9 μm, and 4.5 μm, respectively. The parameters are mode values that frequently appear in parameters determined by laser microscopic measurements. The thickness of the dielectric substrate and meta-atoms are 5 μm and approximately 0.14 μm, respectively. It is not straightforward to fabricate numerous minute structures on an ultra-thin flexible dielectric substrate, and it is also a complex process to fabricate the numerous meta-atoms on the front and back. Plasma processing modifies the surface of the polyimide film before tracing of the meta-atoms to improve adhesion between the film and silver paste ink. The 80,036 pairs of aligned paired cut metal wires are drawn on the front and back of the polyimide film within an area of approximately 6 × 6 mm2. The fabrication time is short, a few hours, while other fabrication methods such as semiconductor processing need to go through multiple processes and takes longer times. A cross shape is drawn (marked) on both the front and back of the polyimide film to maintain the alignment of the cut metal wires. Cut metal wires are drawn on the front of the polyimide film, and the polyimide film is desiccated on a 70 °C hot plate for 1 hour. Wet meta-atoms not subjected to the drying process are fragile and sensitive in the further steps during the drawing procedure of the back. When the fabrication here is complete, the top (front side) of the polyimide film is placed on the base of the super-fine ink-jet printer, and metal wires are then drawn, now on the back of the polyimide film. The polyimide film with silver cut metal wires on both the front and back is baked on a hot plate at 220 °C for 1 hour to improve the conductivity of the silver paste ink. Figure 6(c) shows that the aligned paired cut metal wires are fabricated on the ultra-thin polyimide film with a 5 μm thickness with the meta-atoms becoming somewhat uneven and deformed.
Fig. 6. (a) Photograph of the polyimide film with the metasurface fabricated by the super-fine ink-jet printer. Laser microscope image of (b) the reflectionless metasurface with a high refractive index at 3.0 THz and (c) meta-atoms.
Measurements of the fabricated metal wires are performed by terahertz time-domain spectroscopy (THz-TDS) TOPTICA TeraFlash with a frequency resolution of 0.005 THz. The calculated focused spot size and focal depth are approximately 0.4 mm and 2.0 mm at 3.0 THz, respectively, in the transmittance measurements. The calculated focused spot size and focal depth are approximately 0.7 mm and 7.9 mm at 3.0 THz, respectively, in the reflectance measurements. The transmittance measurements of the dynamic ranges at 2.0, 3.0, and 4.0 THz were 52.7 dB, 34.9 dB, and 22.9 dB, respectively. The reflectance measurements of the dynamic ranges at 2.0, 3.0, and 4.0 THz are 52.6 dB, 21.6 dB, and 20.8 dB, respectively. The incident wave propagating from the direction of 0 degrees perpendicular to the metasurface and the reflected wave returning to the direction of 0 degrees perpendicular to the metasurface are measured in the reflectance measurements.
Figures 7(a)–(d) show the measurements and simulations of the real and imaginary parts of the refractive index, the reflectance and transmittance, the real and imaginary parts of the relative permittivity, and the real and imaginary parts of the relative permeability, respectively. It is difficult to avoid bending the sample in the measurement process, and the measurements are compensated for on the condition that the reflectance phase of the measurements are ideally the same as those of the simulations [41,42]. The compensation values suggest that the sample is concave with a depth of 75 μm along an incident wave. The dots show the measurements by THz-TDS, and the solid lines show the simulations taking into consideration the frequency-dependent complex conductivities of the silver paste ink. The measurements confirm an effective refractive index of 5.88 + j1.57, reflectance of 1.3%, and transmittance of 35.7% at 2.97 THz, while the simulations predict an effective refractive index of 7.47 + j0.79, reflectance of 4.3%, and transmittance of 64.3% at 2.97 THz. The mode values of the fabricated metasurface were adopted as the parameters in the simulations. The impedance matching in circuit theory that the real parts of the relative permeability is close to that of the relative permittivity at 2.97 THz in Figs. 7(c) and (d) causes a low reflectance of 1.3% at 2.97 THz in Fig. 7(b). Figure 7(b) also shows that the measured transmittance resonance is weak while the simulated transmittance resonance occurs at approximately 3.0 THz. Figure 7(c) shows that the real part of the relative permittivity is high at approximately 10 for the 3.0 THz frequency. Figure 7(d) shows that magnetic resonance occurs at 3.0 THz due to the symmetrically aligned paired cut wires on both the front and back of the 5-μm thick polyimide film in Figs. 2 and 6. Figures 7(a)–(d) show that the resonance in the real part of the relative permeability are a cause of the material properties with a high refractive index of 5.88 and an extremely low reflectance of 1.3% at 3.0 THz. The complex conductivity of the silver paste ink in Fig. 4 is based on the measurements in [40]. Surface roughness reduces the real part of the conductivity of metals [43] and substantially increases the imaginary part of the conductivity of metals [44]. The roughness (irregularities) on the silver cut wires could be the cause of the differences between the measurements and simulations. Fabrication errors and other experimental errors in optical systems may also be causes of the differences between the measurements and simulations. Conservation of energy issues can also be considered as below.
Fig. 7. Measurements and simulations of (a) real and imaginary parts of effective refractive index neff, (b) reflectance and transmittance, (c) real and imaginary parts of relative permittivity, and (d) real and imaginary parts of relative permeability.
Figure 8(a) shows the frequency characteristics for the summation of the dielectric energy |μr|Im(εr) and magnetic energy losses |εr|Im(μr) by the measurements and simulations. The conservation of energy is approximately satisfied even though not fully satisfied in a part of the measurements. Figure 8(b) shows the frequency characteristics for the power loss when the reflectance and transmittance are subtracted from the total power involved (100%). A power loss with a positive value means that the conservation of energy is satisfied. The power loss of the measurements and simulations are 63.1% and 31.4% at 2.97 THz, respectively.
Fig. 8. Frequency characteristics of (a) the summation of the dielectric energy loss and magnetic energy loss and (b) the power loss obtained from measurements and simulations.
5. Summary
We experimentally demonstrate a reflectionless metasurface with a high refractive index at 3.0 THz. The metasurface consisting of 80,036 (428 × 187) units of symmetrically aligned paired cut wires on both the front and back of a 5-μm thick polyimide film was fabricated by a super-fine ink-jet printer with silver paste ink. Measurements by THz-TDS confirm a refractive index of 5.88 + j1.57, reflectance of 1.3%, relative permittivity of 6.73 + j0.85, and relative permeability of 5.03 + j2.11 at 2.97 THz. The relative permeability is close to the relative permittivity with high values at the same frequencies, resulting in the property of a high refractive index and extremely low Fresnel reflection. Simulations with varied real and imaginary parts of the complex metal conductivity show that the relative permeability is close to the relative permittivity with high values at the same frequencies for the silver paste ink with the real part of the conductivity of 4.9 × 105 S/m two orders of magnitude lower than for the good conductors such as for gold at 3.4 × 107 S/m and copper at 4.9 × 107 S/m. Metasurfaces consisting of meta-atoms both with weak conductors such as silver paste ink as well as with good conductors such as gold and copper enable reflectionless properties with high refractive indices. The control of the complex conductivity for meta-atoms as well as the dimensions of meta-atoms effectively designed the metasurface properties. The reflectionless metasurfaces with a high refractive index made with weak conductors can be applied to flat optical components with attractive functionalities such as arbitrary wavefront shaping, beam forming, high numerical aperture, polarization control, and optical vortices. Further, the presented metasurface can offer an accessible platform for terahertz flat optics in 6G (beyond 5G) wireless communications and imaging.
Funding
Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C) (No.18K04970)); PRESTO from the Japan Science and Technology Agency (JST) (JPMJPR18I5); Inamori Foundation; Kato Foundation for Promotion of Science; Iketani Science and Technology Foundation; TEPCO Memorial Foundation; GMO Internet Foundation; The Noguchi Institute.
Acknowledgments
The authors wish to thank Dr. Kazuhiro Murata, Naoki Tashiro, and Junko Yoshino of SIJ Technology, Inc. for the fabrication by the super-fine ink-jet printer.
Disclosures
The authors declare no conflicts of interest.
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