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Abstract
Optical wavefront transformation is essential for communication and power transfer applications across all electromagnetic spectra. In this work, we report directional multi-beam compact wavefront transformers which convert cylindrical wavefronts into finite-aperture directional beams based on near-zero refraction in 3-D metamaterial at terahertz frequencies. For this purpose, a near-zero-index metamaterial (NZIM) with three-dimensional functionality is realized, and its effective material parameters are retrieved. Near-zero refraction in NZIM is verified through the uniform phase maintenance inside the multiple stacked NZIM layers. By embedding a cylindrical wavefront source inside NZIM configurations, uni-, bi-, and quad-directional wavefront transformers are realized. The results were compared and verified against the ideal cases.
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1. Introduction
Electromagnetic wavefront engineering, such as wavefront conversion and transformation, is essential for communication, imaging, and light-matter interaction studies [1–3]. Especially the terahertz (THz) frequency range possesses many unexplored potential applications [4,5] such as wireless communications, non-destructive imaging, sensing, etc. However, THz waves encounter strong absorption while propagation in the atmosphere [6] as well as in dielectric materials [7], and also metals are not ideal conductors [8] in the THz range. Besides the challenges in realizing efficient THz devices, a vast majority of these applications rely on the availability of beam control methodologies which is defined as the capacity to manipulate the THz beams with the preferred shape along the desired direction. Moreover, the development of THz spectroscopic applications [9–11], such as medical diagnoses, pharmaceutical quality control, and security screening, rests on the availability of beam-controlling devices.
Multi-beam transformation and switched beam operations are some forms of beam control in which a given transformer can simultaneously access many distinct far-field directions finitely. For example, plane wavefronts are necessary for Fourier optics applications, and multi-beam steering is crucial for power channeling requirements. It is known that a light source placed at the focal point of a convex lens produces planewaves. However, the dimension of the lens system and the requirement of short focal lengths are the challenging factors for achieving miniaturized optical elements. Metamaterials (MTMs) are potential candidates for realizing miniaturized optical devices [12,13]. MTMs are electrically thin, have sub-wavelength dimensions, and possess exotic optical properties such as the negative index of refraction [14,15], zero-index [16], and unit absorption. Notably, the possibility of near-zero refractive index (NZRI) in MTMs allows one to tailor electromagnetic wavefronts unprecedently. For example, in an NZRI medium, electromagnetic wave maintains a uniform phase, and one can explore this property for wavefront shaping, collimation, and super coupling [16–18]. It has also been demonstrated numerically [19,20] and experimentally [21,22] that MTMs with NZRI can give rise to directive emission.
This work reports the realization of multi-beam wavefront transformers based on NZIM in the THz band. Previously, researchers had demonstrated the concept of multi-beam transformers based on transformation optics (TO). In the TO [1,23] approach, a coordinate transformation was employed to convert the cylindrical wavefronts into finite-aperture spatial beams. However, most of the TO-based approaches are challenging to realize practically owing to the unrealistic constitutive parameters of permittivity and permeability.
We also noticed that without the TO approach, one could realize wavefront transformers using photonic crystals (PhCs) [24]. The wave propagation in PhCs at near-bandgap frequencies gives rise to the modulated envelope function irrespective of the nature of the wavefronts. Hence, a cylindrical wavefront source placed in the PhC cavity results in directional multi-beams. As the lattice constant of PhCs is comparable in size with the wavelength (∼λ), the periodic array of PhCs required for planewave transformation [25–27] is greater than the wavelength (>λ). On the other hand, the MTM’s unit cell size is less than the operating wavelength, so that the required planewave conversion can be achieved with zero-index-based MTM stackings [28,29] having dimensions comparable to the working wavelength (∼λ). Hence, compared to PhCs, MTM unit cells with sub-wavelength dimensions are more compact for realizing wavefront transformers. Therefore, we attempt the wavefront transformation problem using MTMs in this work.
Generally, to attain NZRI in MTMs, at least one of the material parameters should be nearly equal to zero, relative permittivity ${\varepsilon ^{\prime}_r} \simeq 0$ or relative permeability ${\mu ^{\prime}_r} \simeq 0$, as the refractive index $n = \sqrt {{\varepsilon _r}{\mu _r}}$. When ${\varepsilon ^{\prime}_r} \simeq 0$, the medium is said to be epsilon-near-zero (ENZ) medium [30] and when ${\mu ^{\prime}_r} \simeq 0$, the medium is said to be mu-near-zero (MNZ) medium [31]. Though $n \simeq 0$ at ENZ and MNZ frequencies, the wave impedance of the medium is infinite and zero, respectively, and this impedance mismatch results in high reflection [16]. Hence, to get high transmission, an MTM with permittivity and permeability simultaneously equal to zero, which is often said to be an epsilon-mu-near-zero (EMNZ) medium, is preferred.
In this work, a three-dimensional NZIM is realized with simultaneous ${\varepsilon ^{\prime}_r}$ and ${\mu ^{\prime}_r}$ equal to zero by bringing its electric and magnetic plasma frequencies in a closed interval. By embedding the excitation source inside the proposed 3-D NZIM with specific exit planes, the emitted wavefronts are converted into directional multi-beams, and electromagnetic power allocations are effectively controlled. Hence in this report, (i) the realization of epsilon-mu-near-zero MTM, (ii) the verification of the existence of NZRI in MTM, (iii) the construction of uni-, bi-, and quad-wavefront transformers, and (iv) comparison of the results with ideal cases are presented. We choose the terahertz (THz) waveband to demonstrate this work due to the prospect of developing communication and beam steering elements at THz frequencies.
2. Unit cell structure and its characteristics
Figure 1 shows the proposed 3-D MTM for achieving the wavefront transformer. The unit cell (Fig. 1(a)) is comprised of metallic rings with capacitive gaps, supported by trapezium bars (Fig. 1(b)) oriented in three orthogonal directions with a common center. The metallic rings and trapezium bars are made of Gold (electrical conductivity $\sigma = 4.561 \times {10^7}\textrm{ S}{\textrm{m}^{\textrm{ - 1}}}$), and it is immersed in a polyimide dielectric cube with relative permittivity, ${\varepsilon _r} = 3.5$ and loss tangent, $\tan \delta = 0.0027$. Polyimide is one of the promising substrates for metallic structures in the THz band, as its dielectric permittivity is constant for frequencies below 2 THz. Also, it shows strong adhesion to metals and exhibits mechanical stability. The thickness for the metallic rings and bars is chosen to be $d = 4\mathrm{\ \mu m}\textrm{.}$ The width and inner radius of the metallic rings are $w = 8\mathrm{\ \mu m}$ and $r = 51\mathrm{\ \mu m}$, respectively. The other geometric dimensions of the unit cell are the lattice constant $a = 140\mathrm{\ \mu m}$, the capacitive gap $g = 8\mathrm{\ \mu m,}$ the base of the trapezium $s = 4\mathrm{\ \mu m}$, and the angle between consecutive trapezium bars $\alpha = 64.5^\circ$.
Full-wave electromagnetic simulations are performed to obtain the transmission properties of the proposed 3-D NZIM numerically using finite-integration method-based solver CST Studio Suite. Effective material parameters of the proposed MTM are extracted using the standard retrieval procedure [32] where the unit cells are employed with fictitious waveguide boundary conditions, i.e., for a normal incidence transverse electric (TE) wave, ${\pm} y$ and ${\pm} x$ planes are used with perfect electric $(\hat{n} \times \vec{E} = \vec{0})$ and perfect magnetic $(\hat{n} \times \vec{H} = \vec{0})$ boundaries, respectively, and ${\pm} z$ planes are assigned with input and output excitation ports along with perfectly matched layer (PML) boundaries. The PML boundaries are specifically used to terminate the open space along the z-direction.
Figures 2(a)–2(b) show the transmission (S21) and reflection (S11) coefficients of a 3-D NZIM. The effective material parameters of the proposed 3-D structure are extracted and plotted in Figs. 2(c)–2(e). It is observed that the real parts of the effective relative permittivity (Fig. 2(b)) and relative permeability (Fig. 2(c)) are nearly equal to zero, around 1.024 THz and 1.082 THz, respectively. The general condition for the zero index of refraction, in which both ${\varepsilon ^{\prime}_r} \simeq 0\textrm{ and }{\mu ^{\prime}_r} \simeq 0$ are satisfied in the frequency band between 1.024 THz to 1.082 THz, with an operational bandwidth of 58 GHz (5.51%). It is noted that, since the real part of relative permittivity is not equal to relative permeability, the relative wave impedance $({z_r} = \sqrt {{\mu _r}/{\varepsilon _r}} )$ falls between 0 and 0.1 (Here, one has to multiply the vacuum impedance 377 Ω to get the absolute value) in the working region as shown in Fig. 2(f). This impedance mismatch results in a considerable reflection at the air-MTM interface, and hence reduced transmission is observed at the NZRI regime.
Fig. 2. Transmission and reflection coefficients of the 3-D NZIM with (a) magnitude and (b) phase. Real and imaginary parts of (c) relative dielectric permittivity, (d) relative magnetic permeability, (e) refractive index, and (f) relative wave impedance of the 3-D NZIM. The ZI regime is shaded between 1.024 THz to 1.082 THz in the refractive index plot.
Moreover, the complex nature of the wave impedance indicates that the realized MTM is both reactive and resistive at the NZRI regime. The advantage of the proposed 3-D NZIM is that the retrieved parameters are the same along all three principal directions owing to its symmetry. It may be further noted that the effective material parameters of the proposed 3-D NZIM remain the same when the Drude model of Gold is used instead of the conductivity model. The same trend for both models is mainly due to the choice of the frequency regime, as the conductivity model may be sufficient for frequencies below 1.5 THz.
As discussed in the introduction section, bringing both ENZ/MNZ regimes close together allows one to get simultaneous zero values for both permittivity and permeability with matched impedance for specific frequencies. Mainly because, usually in an MTM, ENZ/MNZ regime occurs around the frequency where the transition from negative to positive relative permittivity/permeability takes place, respectively. In MTMs, the negative permittivity region occurs below its electric plasma frequency $({f_{ep}})$, and the negative permeability region occurs below its magnetic plasma frequency $({f_{mp}})$. Hence, if one realizes an MTM with its electric and magnetic plasma frequencies close together, it will be possible to obtain the NZRI regime.
The closer electric and magnetic plasma frequencies is achieved with the proposed 3-D design shown in Fig. 1. In the proposed geometry, the orthogonally oriented trapezium bars are responsible for electric resonance, and inductive split circular loops are responsible for magnetic resonance. If electric and magnetic resonances exist simultaneously in a material, such a medium may have its electric and magnetic plasma frequencies in a tight frequency band. From Figs. 2(c) and 2(d), it can be noted that the effective relative permittivity and relative permeability transitions occur at plasma frequencies ${f_{ep}} = 1.082\textrm{ THz}$ and ${f_{mp}} = 1.024\textrm{ THz}$, respectively. Since the unit cell possesses both transition plasma frequencies within a short frequency band, it exhibits a near-zero index of refraction in the frequency range ${f_{mp}} \le f \le {f_{ep}}$, as shown in Fig. 2(e). The effect of the angle subtended by the consecutive trapezium bars (α) and the inner radius of the metallic rings (r) are analyzed and shown in Tables 1 and 2, respectively. From the tables, it is evident that the values chosen $\alpha = 64.5^\circ$ and $r = 51\mathrm{\ \mu m}$ are optimized for high transmission. And also, it is essential to note that the designed 3-D NZIM is scalable to other frequency bands by choice of appropriate dimensions.
Table 1. Effect of angle subtended by the consecutive trapezium bars (α)
Table 2. Effect of inner radius of the metallic rings (r)
3. Uniform phase maintenance in 3-D NZIM
The degree of NZRI can be evaluated through the phase profile of the transmitted wave inside NZRI MTM because the electromagnetic wave's phase is uniform in zero index medium. To check the phase uniformity at NZRI regimes, full-wave simulations are carried out with 20 layers $(9.7{\lambda _o})$ MTM’s configuration for a normal incident transverse electric (TE) polarized wave at 1.04 THz.
It is useful to note that the effective refractive index of the 3-D NZIM, obtained from a single unit cell employed with fictitious waveguide boundary conditions, is $n ={-} 0.0104 - j0.1092$ at 1.04 THz. However, for an MTM slab with a finite number of layers (e.g., 20 layers), the n value may not be the same as that of a single unit cell, as the introduction of periodicity along the z direction influences the frequency response. At the same time, this choice of frequency (1.04 THz) may be sufficient to ensure the degree of zero-refraction, as the chosen frequency is still within the NZRI band. The electric field distribution inside the NZIM stackings and in free space are shown in Fig. 3. When the wave propagates in free space, its electric field components travel in sinusoidal form with distinctive half-wavelengths, as shown in Figs. 3(a-c). However, for an NZIM, uniform phase distribution is maintained over 13 layers $(6.4{\lambda _o})$ despite strong attenuation, as shown in Figs. 3(d-f).
Fig. 3. E-field distribution along y- plane, its y- component plot and side view for electromagnetic wave propagation corresponding to 1.04 THz in (a-c) free space, (d-f) NZIM stackings, respectively.
Thus, the uniform phase maintenance for long-distance reveals the existence and the degree of NZRI response of the proposed 3-D MTM, because it establishes a near-zero index value of 0.078 $({\lambda _o}/{\lambda _{\textrm{NZIM}}})$ around 1.04 THz, despite the effects due to multiple stackings. Hence, the 3-D MTM array is utilized to demonstrate the wavefront transforming applications.
4. Directive radiation characteristics of NZIM-assisted antenna
An NZRI medium can direct the incoming waves in a direction perpendicular to its surface due to uniform phase behavior [16]. If a planar NZIM slab is considered, then the emerging waves will be parallel and show coherent phase variation, resulting in finite-aperture wavefront emission (approximated as planewaves) outside the surface. Therefore, the proposed 3-D NZIM can be stacked into multiple lens profiles to realize multi-beam wavefront transformers. The NZIM lens profiles are excited with an y-oriented electric dipole antenna with each arm length ${L_d} \simeq 75\mathrm{\ \mu m}$, diameter ${D_d} = 2\mathrm{\ \mu m}$ and separation gap ${g_d} \simeq 1\mathrm{\ \mu m}$ which is fed with a feed line of $I = 1\textrm{ A}$ alternating current between the two arms.
For the proof of the proposed NZIM-based wavefront transformer, ideal models of similar configurations made of a homogeneous zero-index medium are also simulated. The results are compared between the realized and ideal designs. The ideal zero-index material used for comparison has an effective relative permittivity, ${\varepsilon _r} = 0.009 - j0.17$ and effective relative permeability, ${\mu _r} = 0.009 - j0.17$ at 1.04 THz.
4.1 3-D NZIM-based uni-directional antenna
To numerically demonstrate the directive radiation characteristics of the proposed 3-D NZIM, initially, a lens profile with an electromagnetic beam reflector is designed to achieve a uni-directional antenna (UDA) as shown in Figs. 4 (a) and (b). The lens profile is created with $5 \times 3 \times 2$ unit cells along x, y, and z-directions, respectively. To restrict the radiation along the z-direction and to suppress the back-lobe level, a metallic reflector made of a perfect electric conductor (PEC) is kept behind the lens at $100\mathrm{\ \mu m}$ distance. When the line source situated at $50\mathrm{\ \mu m}$ distance from the interface is excited, uniform finite-aperture plane wavefronts emanate outside the NZIM slab. The absolute value of the real part of electric field distribution (Fig. 4(c)) and far-field radiation pattern (Fig. 4(e)) corresponding to 1.04 THz along the xoz-plane in the NZIM slab show that, most of the emerging beams are directed along the z-direction. Also, the magnitude of the main lobe directivity is 8.95 dBi (Here dBi represents the isotropic directivity in which the directivity of the designed system is compared with an isotropic source that radiates electromagnetic waves in the space uniformly). These aspects reveal the behavior of the proposed NZIM lens profile as a UDA. It is helpful to note that the obtained results are similar to that of the ideal model consisting of a homogeneous slab, as shown in Figs. 4(d) and (f). The far-field characteristics of the UDA, such as the directivity and side lobe level plots over a broad frequency range in the NZI regime are shown in Fig. 4(g). Hence, by employing an NZIM slab, one can transform an omni-directional electromagnetic source into a directive antenna.
Fig. 4. Uni-directional wavefront transformer with 3-D NZIM: (a) Design and (b) top view. The absolute value of real part of electric field distribution at 1.04 THz for (c) 3-D NZIM stacking case and (d) ideal case. Far-field plot at 1.04 THz along xoz-plane corresponding to (e) 3-D NZIM stacking case, and (f) ideal case, along with main lobe directivity (MLD) and side lobe levels (SLL). (g) Directivity and side-lobe levels correspond to the UDA wavefront transformer.
Mechanism: It is evident from Snell's law that the rays emerging from a near-zero index media will be refracted in a direction perpendicular to the interface, i.e., the angle of refraction measured from the normal will be nearly equal to zero. Thus, the angle of refraction will be lower when the refractive index is close to zero. Therefore, all the emerging rays will be refracted parallelly from the interface in almost the same direction. Hence, it can be noted that the zero refraction at the emerging plane is responsible for generating the finite-aperture plane wavefronts. This aspect leads to the realization of multi-beam wavefront transformers, where the radiation characteristics mainly depend on the various symmetrical stackings of the NZIM. Hence one can design and derive tri-, quad-, and hexa-beam transformers using ${C_{3v}}$ $(120^\circ$ rotational symmetry), ${C_{4v}}$ ($90^\circ$ rotational symmetry), and ${C_{6v}}$ ($60^\circ$ rotational symmetry) point-group symmetric geometries.
4.2 3-D NZIM-based quad-directional antenna
For instance, a ${C_{4v}}$ symmetric square-shaped NZIM lens profile is excited by a line source placed at its center to realize a directional uniform radiation pattern along four orthogonal directions. A quad-directional antenna (QDA) profile is achieved by removing three vertical unit cells at the center of cuboidal stacking with $5 \times 3 \times 5$ unit cells along x, y, and z-directions, respectively, as shown in Figs. 5(a) and (b).
Fig. 5. Quad-directional Antenna with 3-D NZIM: (a) Design and (b) top view. The absolute value of real part of the electric field distribution in QDA at 1.04 THz for (c) 3-D NZIM stacking case, and (d) ideal case. Far-field plot at 1.04 THz along xoz-plane corresponding to (e) 3-D NZIM stacking case, and (f) ideal case, along with main lobe directivity (MLD) and side lobe levels (SLL). (g) Directivity and Side-lobe levels correspond to QDA.
When the line source is excited, the QDA profile emits uniform finite-aperture parallel wavefronts along four directions $90^\circ$ apart from its adjacent main lobes. The absolute value of the real part of electric field distribution and the far-field radiation pattern corresponding to 1.04 THz along xoz-plane in the QDA profile are shown in Figs. 5(c) and (e), respectively. It is found that the obtained results agree with its ideal model, as shown in Figs. 5(d) and (f). It is important to note that the far-field directivity plot is symmetric about the transversal axis, and all four main-lobes are equal in magnitude (6.11 dBi). Though a slight scattering is observed at the corners of the square QDA profile, the reduced side lobe level (-17.2 dB) shows that those leaky waves decay significantly without affecting its far-field components. The directivity amplitude and side-lobe level plots over the working regime of the QDA configuration are shown in Fig. 5(g).
As all the points in the boundary of an NZIM will be in phase, the amount of radiation will be proportional to the surface area, i.e., the more the surface area, the more significant number of points that will act as a coherent source. Hence, the radiation emerging from the surface of NZIM mainly depends on its cross-sectional area as it consists of many domains acting as individual sources, which enhances the beam transfer with high power. This aspect of the NZIM profiles leads to control of the multi-beam radiation pattern via altering its surface's extents.
4.3 3-D NZIM-based bi-directional antenna
A lens profile with a rectangular central cavity is designed to analyze how the role of dimensions of the NZIM slabs control the radiation patterns. In this case, a bi-directional antenna (BDA) profile is achieved by forming a cavity with the dimension $3 \times 3 \times 1$ unit cells at the center of cuboidal stacking with $7 \times 3 \times 5$ unit cells along x, y, and z-directions, respectively, as shown in Figs. 6(a) and (b). When the line source, situated at the centre, is excited at 1.04 THz, the BDA profile emits radiations with greater power from the longer face than the shorter one, as shown in the absolute value of the real part of the electric field distribution (Fig. 6(c)) and the far-field pattern (Fig. 6(e)). The obtained results are in good agreement with that of its ideal model as shown in Figs. 6(d) and (f). Also, the main lobe directivity magnitude in BDA is 6.51 dBi which is greater than that of QDA and it shows that the emergent surface area of the NZIM plays a major role in the amount of radiation emitted. The directivity and side lobe level plots shown in Fig. 6(g) reveal the far-field properties of the BDA over the working regime. Hence, an optimized transformer with larger aperture of the NZIM slabs can be utilized to get plane wavefronts for longer extents.
Fig. 6. Bi-directional antenna with 3-D NZIM: (a) Design and (b) top view. The absolute value of real part of electric field distribution in BDA at 1.04 THz for (c) 3-D NZIM stacking case, and (d) ideal case. Far-field plot at 1.04 THz along xoz-plane corresponding to (e) 3-D NZIM stacking case, and (f) ideal case, along with main lobe directivity (MLD) and side lobe levels (SLL). (g) Directivity and Side-lobe levels correspond to BDA.
Though scattering and interference losses exist in the proposed 3-D NZIM-based wavefront transformer profiles, which leads to leaky waves along the other directions, we achieved a high directivity along the main lobe directions in each case. Since those leaky scattering waves are not highly directed and weak in intensity, they will decay faster and won't contribute to the far-field components. It is evident from the far-field directivity and side lobe level plots. The main lobe directivity of uni-, bi-, and quad-directional wavefront transformers with 3-D NZIM at 1.04 THz, are 8.95 dBi, 6.51 dBi and 6.11 dBi, whereas MLDs of ideal NZIM slabs are, 1.43 dBi, 4.5 dBi and 3.01 dBi, respectively. The corresponding side-lobe levels are -10.91 dB, -9.7 dB and -17.2 dB for MTM cases and -1.6 dB, -8.7 dB and -14.3 dB for ideal cases. The performance of the 3-D NZIM-based wavefront transformers can be improved by (i) reducing the losses associated with the stackings, (ii) attaining the refractive index value very close to zero, (iii) increasing the input power using exciting multiple line sources inside the cavities, and (iv) controlling the radiations along undesirable directions using metal coatings or absorbers.
4.4 Enhancement of directivity of BDA with metal coatings
It can be noted from Figs. 6(c) and (d) that the BDA profile emits radiations through shorter faces also, i.e., along the transverse direction (±x), where the directivity is -3.38 dBi. To enhance the directivity of the proposed BDA along the main lobe direction, the transverse directions (±x) of BDA profiles are coated with PECs with 1 µm thickness, as shown in Fig. 7(a), so that other side lobes will be suppressed. When the line source, situated at the centre, is excited at 1.04 THz, the metal-coated BDA profile radiates mostly along the longer extents as shown in the absolute value of the real part of the electric field distribution (Fig. 7(b)) and the far-field pattern (Fig. 7(c)). The main lobe directivity (MLD) in metal-coated BDA is 7.67 dBi, more significant than that of BDA without metal coatings (6.51 dBi). The directivity along the transverse direction (±x) is reduced to -9.08 dBi and also, the side lobe levels are suppressed to -20.3 dB in metal-coated BDA profile at 1.04 THz.
Fig. 7. (a) Design of metal-coated bi-directional antenna with 3-D NZIM. (b) The absolute value of real part of electric field distribution and (c) far-field plot along xoz-plane in metal coated BDA at 1.04 THz, along with main lobe directivity (MLD) and side lobe levels (SLL).
Further, the compactness of the proposed multi-beam antenna profiles can be revealed from two critical aspects, i.e., (i) the minimal requisite distance between the source and the transforming structure and (ii) its size. In all the cases of wavefront transformers mentioned above, the distance of the exciting source from the NZIM geometries is in subwavelength dimensions $( < \lambda /4)$ only. However, for most conventional lensing systems, the minimum distance required for achieving planar wavefronts from any diverging source is its focal length, which is always multiples of working wavelengths ($\lambda$). The complete size of UDA, QDA and BDA transformers are $2.43\lambda \times 1.45\lambda \times 0.97\lambda$, $2.43\lambda \times 1.45\lambda \times 2.43\lambda$ and $3.40\lambda \times 1.45\lambda \times 2.43\lambda$, respectively. However, the thickness of NZIM slabs required for attaining the proposed multi-beam transformers is just twice the lattice constant (2a) along each propagation direction, nearly equal to the wavelength ($0.97\lambda$). The thickness of the NZIM slab is one of the shortest conveyance lengths required for achieving finite-aperture plane wavefront conversion. These aspects show the compactness of the proposed NZIM-based wavefront transformers.
Despite many suggestions and realizations of various types of 2-D and 3-D microscale MTMs, their utilization as real device applications remain a significant challenge due to fabrication difficulties. However, recent advances suggest that several micro/nanometer feature-sized optical metamaterials could be fabricated through mask-directed micro-3D printing [33], multiphoton microfabrication [34], direct laser writing (DLW) [35], focused ion beam – stress-induced deformation (FIB-SID) method [36] and nanoimprint lithography (NIL) [37]. Nevertheless, constraints such as complexity in pattern design, lack of design flexibility, long-range disorder, and uncontrollability still exist, leading to genuinely scalable nanofabrication methodologies to realize practical metamaterials. Thus, the challenges in fabricating 3-D micro/nanoscale MTMs [38] result in passing on the subtle MTM science to the engineering or technology stage. Besides this, we look into the fabrication of the proposed 3-D NZIM using FIB-SID and mask-directed micro-3-D printing methods.
5. Conclusion
In this work, a three-dimensional metamaterial with a near zero index of refraction is presented in the THz regime, and its application in designing multi-beam compact wavefront transformers is reported. The retrieval procedure shows that the proposed MTM has a near-zero index bandwidth of 58 GHz (5.51%) centered at 1.053 THz. The uniform phase maintenance in NZIM stacking is illustrated and compared with free space. Manipulation of directive electromagnetic radiation through different NZIM lens profiles for uni-, bi-, and quad-beam transformers are reported and validated with ideal models. Further, the directivity of the BDA transformer profile is enhanced by reducing the side lobes via using metal coatings. The significance of this work is that instead of a cumbersome transformation optics-based approach, all the results were demonstrated with a specific 3-D MTM. Thus, our work could unleash practical applications in wavefront engineering and tailoring antenna patterns at THz frequencies.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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