1. Introduction

Terahertz metamaterials [1] are artificial materials with subwavelength structures and can manipulate terahertz waves such as absorber [2], antireflection coating [3], and polarization conversion [4]. Metamaterials have evolved into metadevices [5] for active control of terahertz waves with various external modulations such as optical pump [6–8], electric field [9,10], temperature [11], and Micro Electro Mechanical Systems (MEMS) [12]. Metamaterials can provide unprecedented refractive indices such as negative refractive indices due to the direct control of the relative permittivity and permeability. A material with a negative refractive index would make possible a perfect lens [13] and superlenses [14] with resolutions beyond the diffraction limit in imaging. The work in [15,16] was the first to report a negative refractive index utilizing the meta-atoms of split ring resonators and metal wires in the microwave band. A steric structure consisting of metal rings and wires has demonstrated near perfect imaging beyond the diffraction limit in the microwave band [17]. A low-loss metamaterial with a negative refractive index would be essential, especially for high resolutions even though conductor and dielectric losses are in principle unavoidable. However, it is not straightforward to demonstrate an ideal metamaterial in the terahertz waveband because the dimensions of the meta-atoms are of the order of ten to a hundred microns, and this considerably limits the design flexibility of steric structures. Further, substrates are commonly required to be able to fabricate metamaterials, but there are few materials with low losses in the terahertz waveband. Two-dimensional metamaterials, meta-surfaces, have a high potential utility in the terahertz waveband as the application of a lamination structure would make bulky metamaterials with a three-dimensional structure possible. Some papers have reported measurements and simulations of meta-surfaces with a negative refractive index in the terahertz wave band which were composed of several meta-atoms, such as an I-shaped structure [18], a cross-shaped structure [19], and symmetrically aligned paired cut metal wires [20]. The simultaneous dielectric and magnetic resonances of two-dimensional meta-atoms here enable the achievement of negative refractive indices. A high figure of merit (FOM), the real part over the imaginary part in a complex refractive index, is a barometer of the utility in low-loss materials. Work on negative refractive indices has discussed FOMs able to obtain a desirable metamaterials with negative refractive indices and low losses: among these one [18] measures a FOM of 1.48 at 0.47 THz; and others [19,20] FOMs of 11 at 1.02 THz and 23 at 1.3 THz, which have been shown by simulations. Various structures of negative refractive index metamaterials have also been reported in the terahertz waveband such as short-slab pair and wires [21], bi-layer S-strings [22], close-ring pair [23], Mie resonance [24], and fishnet [25–27].

A terahertz metamaterial with a negative refractive index enables terahertz imaging beyond the diffraction limit due to the restoration of a terahertz evanescent wave. Terahertz imaging has the potential to evolve into game changing industrial applications because terahertz waves can be transmitted through objects that are opaque to visible light and enables visualization of inner structures. In [28] terahertz near-field imaging with a subwavelength resolution beyond the diffraction limit was reported with probe detection of terahertz evanescent waves. Terahertz imaging with a resonant tunneling diode (RTD) in [29] has utilized a propagating continuous wave (CW) without an evanescent wave at 0.30 THz and measured a spatial resolution of 1 mm, equal to the wavelength. A material with a negative refractive index can directly integrate various terahertz CW sources for terahertz near-field imaging. Semiconductor devices such as RTD are commonly planar structures, and the integration of a two-dimensional attached structure has been utilized to obtain high gains without a bulky Si lens [30]. Terahertz sources have also developed rapidly, and the oscillation frequency of RTD has reached 1.92 THz [31]. The manipulation of terahertz waves and the miniaturization of optical systems are challenges that have to be overcome, and an unprecedented material able to achieve this [32] would be a powerful tool for the exploration of game changing terahertz applications.

In this paper, we propose a metamaterial with a negative refractive index n of −4.2 + j0.17, the extremely high transmitted power of 81.5%, and extremely low reflected power of 4.3% at 0.42 THz. The refractive index n_eff and wave impedance Z_r of the material are respectively defined as $n=\sqrt{{\epsilon }_{\text{r}}}\sqrt{{\mu }_{\text{r}}}$ and $Z_{\text{r}}=\sqrt{{\mu }_{\text{r}}}/\sqrt{{\epsilon }_{\text{r}}}$, where ε_r is the relative permittivity, and μ_r is the relative permeability. The impedance matching between a material and free space due to the simultaneous control of the relative permittivity and relative permeability would enable the design of a material with high transmission power, low reflection power, and low loss. The thickness of the substrate is λ/14, where λ is the wavelength in free space at 0.42 THz. The FOM of 24.2 is 16.4 times that of the 1.48 obtained with a measured negative refractive index [18]. The other reported FOM [19,20] were simulated. The metamaterial with a negative refractive index in this paper consists of asymmetrically aligned paired cut metal wires on the front and back of a dielectric substrate. The low-loss performance suggests the potential for a three-dimensional bulky metamaterial with a negative refractive index in the terahertz waveband as well as in the microwave band. In other published work [33,34], there are reports on the performance of asymmetrically aligned paired cut metal wires as a meta-atom, and a detailed discussion of material properties related to the permittivity and permeability suggested there is necessary. A high FOM of 42 was reported in the microwave band, but the reflected power is approximately 15% and cannot be considered low [33]. The substrate thickness in [33] is λ/22 at a resonant frequency, and a thicker structure is needed considering the fabrication processes for the terahertz waveband as well as for the microwave band. In [34] a measured dispersion diagram rather than a negative refractive index is reported. The substrate thickness in [34] is λ/17 at a resonant frequency, and a direct normalization of the design is not straightforward for applications to terahertz metamaterials, considering fabrication processes.

2. Design Method

Figure 1(a) shows a full model of the metamaterial with negative refractive index consisting of the asymmetrically aligned paired cut metal wires on the front and back of a dielectric substrate. The metamaterial is a self-supporting structure and would be suitable as a three-dimensional laminated metamaterial. Figure 1(b) shows the design model of one meta-atom with its periodic boundary conditions. The design model is a one-unit cell model extracted from the full model assuming periodic boundary walls around the exterior. An incident terahertz wave propagates with an electric field parallel to the y-axis. The full model of the metamaterial is periodic along the x and y-axes. The cut metal wires on the front and back are aligned asymmetrically with a half periodicity along the y-axis. A low-loss dielectric and metal should be chosen for the metamaterial. Conductivity losses cannot be avoided as there are no perfect electric conductors that do not give rise to losses. Further, the performance of this metamaterial utilizes the resonant phenomenon of the currents on the cut metal wires. Dielectric resonance is caused by the current on the cut metal wires induced by the electric field of the terahertz waves. Magnetic resonance arises from the current on the cut metal wires and is induced by the magnetic field of the terahertz waves according to Faraday’s law of induction. The permittivity and permeability can be designed with the parameters of the cut metal wires. Scattering matrices of the design model derive the effective optical constants, such as the relative permittivity, relative permeability, refractive index, and wave impedance [35]. Table 1 shows the parameters of the cut metal wires. The dielectric substrate is a cyclo-olefin polymer with a complex refractive index n_dielectric of 1.53 + j0.0012 measured at 0.50 THz. The conductor is copper with a conductivity of 5.8 × 10⁷ S/m. Figure 2 shows contour maps for the real and imaginary parts of the refractive indices, the transmission power, and reflection power. The design frequency is 0.41 THz, and the gap g and length l of the cut metal wires are varied to derive optimized parameters for the negative refractive index, high transmission power, and low reflection power. The dielectric and magnetic properties resonate simultaneously at the optimized parameters. The “X” marks at a length l of 351 μm and gap g of 104 μm denote a negative refractive index n of −5.0 + j0.22, a transmitted power of 81%, a reflected power of 1.5%, and a high figure of merit of 22.6 at 0.41 THz. Terahertz CW imaging has been developed in the frequency band near 0.41 THz [29]. The length l of the cut metal wires is approximately 0.5λ, and the width w is sufficiently short when compared with a wavelength. The periodicities along the x and y-axes are approximately 0.3λ and 0.6λ, respectively. A high transmission power is obtained for impedance matching between the metamaterial and free space due to small variations in the permittivity and permeability.

 

Fig. 1 (a) The metamaterial with a negative refractive index, high transmission power, and low reflection power consisting of asymmetrically aligned paired cut metal wires. (b) Design model of one meta-atom with the periodic boundary conditions.

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Table 1. Parameters of the cut metal wires

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Fig. 2 Contour maps for (a) the real part of refractive indices, (b) the imaginary part of the refractive indices, (c) transmission power, and (d) reflection power.

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3. Operating Principle

The operating principle of a negative refractive index in the metamaterial is explained by the effective optical constants as well as the equivalent circuits. A negative refractive index is caused by both negative permittivity and permeability. Permittivity and permeability denote dielectric and magnetic properties, respectively. Permittivity and permeability have negative values around the resonant frequencies for a metamaterial consisting of paired cut metal wires. Figure 3 shows simulations of the refractive index, relative permittivity, and relative permeability for the metamaterial consisting of paired cut metal wires of l = 351 μm, g = 104 μm, w = 31 μm, p = 208 μm, h = 50 μm, and t = 0.5 μm (from Fig. 1(b)). Figures 3(a) and 3(b) show (respectively) the frequency characteristics of the refractive index, relative permittivity, and relative permeability for a symmetrical structure. Figures 3(c) and 3(d) show the frequency characteristics of the effective optical constants for an asymmetrical shifted structure with 1/6 shifted alignments. Figures 3(e) and 3(f) show the frequency characteristics of the effective optical constants for an asymmetrical shifted structure with 2/6 shifted alignments. Figure 3(g) and 3(h) show the frequency characteristics of the effective optical constants for an asymmetrical shifted structure with 3/6 shifted alignments. Figure 3(a) shows that the refractive index is positive for this metamaterial of symmetrically aligned paired cut metal wires. Figure 3(b) shows that the resonance frequency of the dielectric property is stronger than that of the magnetic property in this metamaterial. Figures 3(c)–3(h) directly show the overlap of the negative permittivity and negative permeability, which enables a negative refractive index. The dashed curves in Figs. 3(a), 3(c), 3(e), and 3(g) show the border between the metamaterial and Bragg regimes. The half-wavelength inside the metamaterial is smaller than the unit-cell thickness in the Bragg regime, and the effective optical constants cannot be expected to be accurate [36].

 

Fig. 3 Top row: Frequency characteristics of (a) refractive indices and (b) permittivity and permeability for the symmetrically aligned paired cut metal wires. Row two: Frequency characteristics of (c) refractive indices and (d) permittivity and permeability for asymmetrical structures with 1/6 shifted alignment. Row three: Frequency characteristics of (e) refractive indices and (f) permittivity and permeability for asymmetrical structures with 2/6 shifted alignment. Bottom row: Frequency characteristics of (g) refractive indices and (h) permittivity and permeability for asymmetrical structures with 3/6 shifted alignment.

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Figures 3(b), 3(d), 3(f), and 3(h) are the dielectric properties for a symmetrical structure and asymmetrical shifted structures with alignments shifted 1/6, 2/6, and 3/6 in the left axis, respectively. An approximate equivalent circuit can effectively explain the differences between asymmetrically and symmetrically aligned paired cut metal wires. The dielectric resonance properties for a symmetrical structure is determined by an inductance component L_d at a cut metal wire and a capacitance component C_d at a gap of the cut metal wires along the direction of the electric field. The resonance frequency $f_{\text{d}}^{\text{s}}$ of the dielectric property is expressed as $f_{\text{d}}^{\text{s}}=1/2\pi \sqrt{L_{\text{d}}{C}_{\text{d}}}$ for a symmetrical structure. The capacitance component for an asymmetrical structure increases due to the addition of a parallel capacitance $C_{\text{d}}^{\text{'}}$. The resonance frequency $f_{\text{d}}^{\text{a}}$ of the dielectric property is expressed as $f_{\text{d}}^{\text{a}}=1/2\pi \sqrt{L_{\text{d}}\left(C_{\text{d}}+C_{\text{d}}^{\text{'}}\right)}$ for an asymmetrical structure. The shifted distance of the cut metal wires controls the capacitance $C_{\text{d}}^{\text{'}}$. The resonant frequency $f_{\text{d}}^{\text{a}}$ is decreased with the value of the shift, and the region with a negative permittivity shifts to lower frequencies as suggested by Figs. 3(b), 3(d), 3(f), and 3(h).

Figures 3(b), 3(d), 3(f), and 3(h) are the magnetic properties for a symmetrical structure and asymmetrical structures with the alignments shifted 1/6, 2/6, and 3/6 in the right axis, respectively. Here, the magnetic resonance properties for a symmetrical structure is determined by an inductance component L_m at the cut metal wires on the front and back and a capacitance C_m at the cut metal wires on the front and back. The resonance frequency $f_{\text{m}}^{\text{s}}$ of the magnetic property is expressed as $f_{\text{m}}^{\text{s}}=1/2\pi \sqrt{L_{\text{m}}{C}_{\text{m}}}$ for a symmetrical structure. The inductance component $L_{\text{m}}^{\text{'}}$ and capacitance component $C_{\text{m}}^{\text{'}}$ decrease for an asymmetrical structure as the parallel circuit becomes shorter. The resonance frequency of the dielectric property is expressed as $f_{\text{m}}^{\text{a}}=1/2\pi \sqrt{\left(L_{\text{m}}-L_{\text{m}}^{\text{'}}\right)\left(C_{\text{m}}-C_{\text{m}}^{\text{'}}\right)}$ for an asymmetrical structure. The shifted distance of the cut metal wires control the inductance $L_{\text{m}}^{\text{'}}$ and the capacitance $C_{\text{m}}^{\text{'}}$. The resonant frequency $f_{\text{m}}^{\text{a}}$ increases with the shifted value, and the region with negative permeability shifts to higher frequencies as in Figs. 3(b), 3(d), 3(f), and 3(h).

4. Fabrication and Measurement

Figure 4 shows a fabricated metamaterial with a negative refractive index consisting of asymmetrically aligned paired cut metal wires with a 3/6 shifted alignment. The length l of the cut metal wires is 351 μm, the gap g is 104 μm, the width w is 31 μm, and the periodicity p is 208 μm. The dielectric substrate is a cyclo-olefin polymer which has a measured refractive index of 1.53 + j0.0012 at 0.5 THz and is a low loss material. A cyclo-olefin polymer film with copper layers on the front and back is etched for the fabrication of the metamaterial. The thickness of the film is 50 μm. The copper layer is 0.5 μm, 4.9 times the skin depth at 0.42 THz. Figure 5(a) shows the measurements and simulations of the refractive indices. The refractive index of the measurement at 0.42 THz is −4.2 + j0.17. Effective optical constants are derived from the transmission and reflection measured by THz-TDS TOPTICA TeraFlash. The terahertz path lengths in optical systems for the transmission and reflection measurements are approximately 400 mm and 700 mm, respectively. The terahertz wave radiated from a photoconductive antenna is focused at the sample and reference. The focused beam at the sample and reference has spot size of approximately 2.5 mm and focal depth of approximately 14 mm at 0.42 THz for the transmission measurement. The angle of reflection is 0 degrees for the reflection measurements. The focused beam at the sample and reference has spot size of approximately 3.9 mm and focal depth of approximately 33 mm at 0.42 THz for the reflection measurement. The deviations between the measurements and simulation could be caused by the accuracy of THz-TDS measurements [37]. The measurements also confirm the negative refractive indices from 0.38 to 0.52 THz, and agree well with the simulations. Figure 5(b) shows the measured values of the transmitted and reflected power. The transmitted and reflected power are 81.5% and 4.3% at 0.42 THz, respectively. The frequency difference between the measurements and simulations is small at 0.01 THz. Figure 5(c) shows the measurements of the relative permittivity. The relative permittivity of the measurement at 0.42 THz is −5.3 + j0.11. Figure 5(d) shows that the measurements of the relative permeability at 0.42 THz is −3.3 + j0.35. Figure 5(e) shows that the relative wave impedance, the wave impedance of the metamaterial is divided by a wave impedance in free space. The relative wave impedance at 0.42 THz is 0.79 - j0.049. The relative wave impedance denotes the reflection and transmission characteristics between the sample and free space. The metamaterial performs with high transmission power and low reflection power when the relative wave impedance approaches 1 due to the small changes in the permittivity and permeability.

 

Fig. 4 (a) Photograph of the fabricated metamaterial with a negative refractive index. (b) Microscope view of the asymmetrically aligned paired cut metal wires with the 3/6 shifted.

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Fig. 5 Measured (dots) and simulated (solid curves) values of the (a) Real and imaginary parts of the refractive index; (b) Transmitted power and reflected power; (c) Real and imaginary parts of the relative permittivity; (d) Real and imaginary parts of the relative permeability; (e) Relative wave impedance.

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Measurements of the reflection by THz-TDS need data of the sample and a reference position, and a silver mirror is used when the reference of the reflection is measured. Great care must be shown to avoid bending of a sample in the fabrication process, and measurements of the reflection should be compensated for, taking into consideration errors in the optical path caused by shifts in the relative positions of sample and mirror. Comparison between the measurements and simulations of the reflection phases predict a position error of 58 μm with a convex shape along an incident terahertz wave. Figure 6 shows the FOM. The FOM of the measurement is 24.2 at 0.42 THz, and that of the simulation is 22.6 at 0.41 THz. The deviations between the measurements and simulations of the FOM (|Re(n)/Im(n)|) are occurred. Experimental errors and misalignments in optical systems for transmission and reflection measurements could cause the deviations between the measurements and simulations of the refractive indices.

 

Fig. 6 Measured and simulated values of the figure of merit expressed as the real part over the imaginary part of a complex refractive index.

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The power absorption in a material is expressed as $Q=\left(\omega {\epsilon }_0{\left|E\right|}^2/2\left|{\mu }_{\text{r}}\right|\right)\left[\left|{\mu }_{\text{r}}\right|\mathrm{Im}\left({\epsilon }_{\text{r}}\right)+\left|{\epsilon }_{\text{r}}\right|\mathrm{Im}\left({\mu }_{\text{r}}\right)\right]$, where ω is the angular frequency, ε₀ is the permittivity in free space, and E is the complex amplitude of the electric field [38]. The dielectric energy and magnetic energy losses are expressed as |μ_r|Im(ε_r) and |ε_r|Im(μ_r), respectively. Figure 7(a) shows that the sum of the dielectric and magnetic energy losses is positive, and that power is lost in the metamaterial. Figure 7(b) shows the frequency characteristics of the dielectric energy and magnetic energy losses. Figure 7(c) shows the frequency characteristics of the power loss calculated from the transmission power and the reflection power by THz-TDS. The power loss is positive at all frequencies, and overall these results confirm that conservation of energy is satisfied in the metamaterial with the negative refractive index. The deviations between the measurements and simulations in Figs. 6, 7(a), 7(b), and 7(c) could be caused by various potential reasons such as the misalignments in optical systems and higher conductor losses in the measurements. The ripples of the reflected power occur from 0.25 to 0.38 THz in Fig. 7(c) while those of the transmitted power do not occur. The ripples are caused by misalignments in optical systems for reflection measurements.

 

Fig. 7 Measured and simulated values of the frequency characteristics of (a) the sum of the dielectric energy loss and magnetic energy loss, (b) the dielectric energy loss and magnetic energy loss, and (c) the power loss from measurements and simulations.

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5. Conclusions

In summary, a metamaterial consisting of asymmetrically aligned paired cut metal wires was designed with a negative refractive index of −5.0 + j0.22, the extremely high transmission power of 81%, extremely low reflection power of 1.5%, and the high FOM of 22.6 at 0.41 THz. The negative refractive index is designed by the simultaneous control of the dielectric and magnetic resonance frequencies in the terahertz waveband. The terahertz metamaterial with the negative refractive index was fabricated by the etching of a cyclo-olefin polymer film with copper layers on the front and back. Measurements by THz-TDS demonstrate a negative refractive index of −4.2 + j0.17, an extremely high transmitted power of 81.5%, extremely low reflected power of 4.3%, and the high FOM of 24.2 at 0.42 THz. The bandwidth of the material with negative refractive indices is approximately 0.1 THz, and the metamaterial can be applied to optical components for terahertz continuous waves. The bandwidth of the material with negative refractive indices is approximately 0.1 THz, and the metamaterial can be applied to optical components for terahertz continuous waves. Optical components with broadband characteristics are needed for terahertz pulse waves. Extreme-sensitivity terahertz polarizers consisting of a metamaterial with broadband negative permittivity have a broad bandwidth of approximately 2.0 THz [39,40] as examples of broadband terahertz components. It is challenging to obtain metamaterials with broadband negative permeability, and various ideas have been reported [41–43]. This material with a negative refractive index, high transmission power, low reflection power, and low loss offers an attractive material in the terahertz waveband and opens the door to a variety of attractive industrial terahertz applications.