Open Access
Add to BibSonomy
Abstract
The electromagnetic field concentration effect can greatly enhance light-matter interaction and is of practical interest in applications such as wireless power transfer and sensors. Zero-index media, unusual materials with near-zero relative permittivity (ɛ) and/or permeability (µ), play a key role in tailoring the properties of electromagnetic waves in unique ways. In this work, circuit-based isotropic µ-near-zero (MNZ) media were theoretically proposed and constructed based on two-dimensional transmission lines with lumped elements. Magnetic field concentration was experimentally demonstrated in this circuit-based system, which could be realized by using a small MNZ scatterer and the results agreed well with simulations. Moreover, the MNZ scatterer exhibited a robust enhancement of the magnetic field regardless of its position and number. By applying the magnetic field concentration effect of MNZ scatterers, we also study the flexible manipulation of the electromagnetic energy along different paths. These results not only provide a versatile platform to study abnormal scattering phenomena in metamaterials, but also offer a route to enhance the magnetic field in planar systems. Moreover, the manipulation of magnetic field under multiple MNZ scatterers may enable their use in new applications, such as in the robust energy transfer with properties of long-range and multiple receivers
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The control of electromagnetic (EM) waves at the subwavelength scale is of both fundamentally physical and practical significance. Recently, methods to control EM waves have been greatly expanded by the development of metamaterials with permittivity and permeability that can be flexibly designed [1–8]. As an important class of metamaterials, zero-index-metamaterials (ZIMs) have attracted marked research attention [3–7]. In ZIMs, the relative permittivity (ɛ) and/or permeability (µ) are zero. If only ɛ or only µ is near zero, the ZIM is also called an ɛ-near-zero (ENZ) or a µ-near-zero (MNZ) medium, respectively. To date, ZIMs have offered numerous unique ways to tailor the wave properties. Because of their small ɛ and/or µ, ZIMs have displayed enhanced light-matter interactions, such as enhanced EM fields [9,10], large optical nonlinearity [11–16], enhanced magneto-optical effects [17–19], strong optical activity [20], and energy transfer [21–23]. Furthermore, the wavelength can be increased to almost infinity in ZIMs and the phases of the EM waves are uniform in the material. Numerous novel applications of ZIMs for the propagation of EM waves have been demonstrated, including for directed emission [24,25], omnidirectional radiation [26], unidirectional transmission [27], squeezing [28–31], cloaking [32–35], the anomalous Doppler effect [36,37]. Importantly, focusing incident electromagnetic waves into an area of high concentration is of significant interest for various applications. Based on the unique refraction behavior at different boundaries, the field concentration have been studied theoretically in a flat device made of a hetero-junction of two rotated anisotropic ENZ medium [38]. In addition, subwavelength focusing and field concentration have been demonstrated experimentally in transmission line (TL) metamaterials associated with the very flat dispersion, which corresponds to an anisotropic MNZ medium [39].
Recently, scattering phenomena by subwavelength particles in ZIM background media have attracted significant interest as a research topic [40–50]. The optical properties of the ZIM medium can be significantly modified by the photonic doping via the addition of small particles; this includes control of the magnetic response by using doping with dielectric particles [48], and the realization of coherent perfect absorption beyond the traditional two channels [49]. In particular, Zhou et al., theoretically showed that a giant optical cross section can be realized by placing a resonator in a ZIM background medium [45]. In contrast to designing the spatial profile of the refractive index to control the propagation of light [51,52], in this photonic doping structure, the small resonator can cause the extreme concentration of light at the subwavelength nanoscale and has applications as an absorber and in solar cells [45,49]. This idea was further extended to the Weyl system to study energy concentration [53] and long-range dipole-dipole interaction [54] in artificial three-dimensional structures. While the ZIM background medium can flexibly control EM wave propagation, the background medium cannot always be easily changed, which may limit some applications, such as wireless power transfer (WPT) [55]. Based on the use of ZIM scatterers in place of a ZIM background medium, Luo et al., theoretically study the scattered waves in an anisotropic ENZ medium that were evanescent in the propagation direction and led to arbitrary control of the EM flux [56]. Recently, Song et al., theoretically demonstrated an alternate way to realize electric filed concentration effects with isotropic ENZ scattering [57]. The physical mechanism for this is based on the continuity condition of the electric displacement and the large contrast between the permittivity at the interfaces between the ENZ scatterers and the background medium [58]. Their work extended the scope of EM wave control using ZIMs. However, direct experimental demonstration of EM field concentration and its extension to an MNZ medium have not been reported to date.
In this work, by using two-dimensional (2D) TLs with lumped elements, a circuit-based MNZ scatterer was designed and fabricated, and it had the attributes of a subwavelength scale and planarization. Based on a near-field detection method, we demonstrated the magnetic field concentration effect in the circuit-based MNZ scatterer. Furthermore, the influence of the scattering positions on the magnetic field concentration effect was studied. It was found that the MNZ scatterers exhibited robust enhancement of the magnetic field regardless of its position and number. Moreover, by applying the magnetic field concentration effect of MNZ scatterers, the flexible manipulation of the electromagnetic energy along different paths is studied. These results provide a new platform for the construction of planar MNZ scatterers [58–60], which may be useful for integration in photonic devices, such as absorbers, detectors, and switches [61,62].
2. Near-field scattering properties of magnetic near-zero scatterers
In a background medium composed of normal materials (such as air), EM waves from an excitation source will be scattered by the MNZ scatterer inside the background structure, as shown in Fig. 1. For a transverse-electric (TE) polarized wave with an electric field along the y direction, impinging EM waves scatter along the x direction, and the z-component of the magnetic induction intensity ${B_z}$ is continuous according to the boundary conditions. As a result, the z-component of the magnetic field in the scatterer can be given by [57]:
where ${H_{zb}}$ is the magnetic field in the background. ${\mu _\textrm{b}}$ and ${\mu _s}$ denote the permeability of the background and the scatterer, respectively. From Eq. (1), it can be found that for a fixed background material, ${H_{zs}}$ increases with decreasing ${\mu _s}$. In particular, when ${\mu _s} < < {\mu _b}$, the magnetic field in the scatterer will be much larger than the background material ${H_{zs}} > > {H_{zb}}$. For the MNZ scatterer, there is a large difference between its magnetic field and that of the background material. As a result, a magnetic field concentration effect occurs in the MNZ scatterer because of the side scattering shadow [57], as shown in Fig. 1.Then, a circuit-based MNZ medium was constructed by loading lumped elements into the 2D TLs, as shown in Fig. 2(a). Here, the MNZ scatterer is marked by the blue line and the region outside is the circuit-based background medium. This structure is constructed on a commercial printed circuit board, F4B (relative permittivity ${\varepsilon _r} =$2.2 and loss tangent $\tan \delta =$0.0079) with a thickness h = 1.6 mm. The width of the microstrip is w = 2.8 mm and the length of a unit cell is p = 12 mm. In the designed structure, the effective MNZ scatterer was realized by simultaneously loading a series of lumped capacitors C = 5 pF in the x and z directions and no capacitors were loaded in the background medium. At the boundary of the background region, matching resistors with R = 71.4 Ω are loaded to avoid the influence of reflected waves. Magnified images of the lumped resistor and capacitor elements are shown in the inset of Fig. 2(a). The effective circuit models for the scatterer and the background medium are shown in Fig. 2(b). The structural factor of the TL is defined as $g = {Z_0}/{\eta _{eff}}$, where ${Z_0}$ and ${\eta _{eff}}$ are the characteristic impedance and the effective wave impedance of the TL, respectively [63–65]. The structure factor in this work is $g \approx 0.255$ [64,65]. Because the unit size in the TL system is much smaller than the wavelength, the effective permittivity of the 2D TLs for a quasi-static TE polarized solution can be written as [64,65]:
Fig. 2. (a) Prototype of the 2D TL with $15 \times 11$ unit cells, where the scatterer is a $3 \times 2$ TL with lumped capacitors. The lumped capacitors representing the scatterer are connected in series along the x and z directions to the TL system. The background part is a normal TL. The source was placed near to the center of the sample. Inset show the amplified capacitor C = 5 pF and resistor R = 71.4 Ω, respectively. The length of the unit size and the width of the microstrip are p = 12 mm and w = 2.8 mm, respectively. The perfect matching boundary is marked by the green dashed line. (b) The 2D circuit models of the MIZ and the background medium. (c) The effective EM parameters based on the TLs. (d) The 3D dispersion relationships of the TL-based metamaterials, with the loaded series lumped capacitors. The reference frequency ${f_c} = 1.14$ GHz is marked by a mesh surface.
In this work, the MNZ medium was focused on (frequency ∼1.14 GHz). First, the case where the whole structure was loaded with capacitors was considered to verify the effectiveness of the designed circuit-based MNZ medium. In the simulation, using the commercial software package (CST Microwave Studio), the circuit-based metamaterial was excited using a current source close to the center of the structure. From Fig. 3(a), it can be clearly seen that the simulated field intensity distribution is relatively uniform and Fig. 3(b) shows the corresponding phase distribution. The relative consistency of the phase in the structure further confirms the reliability of the designed MNZ medium.
Fig. 3. The simulated distributions of the electric field Ey (a) and phase $\varphi$ (b) distributions of the TL-based effective MNZ medium excited by one source. The perfect matching boundary is marked by the white dashed line.
Then, the case of the MNZ scatterer embedded in a background material is considered, as shown in Fig. 2(a). The background medium realized using a circuit-based structure is an isotropic medium (${\varepsilon _b} \approx$3.63, ${\mu _b} \approx$1), with an IFC that corresponds to a closed large circle [65]. In the designed structure, the difference in the permeability between the scatterer and the background medium is large enough (${\mu _b} > > {\mu _s}$) to study the magnetic field concentration effects of the MNZ scatterer. In order to evaluate the working bandwidth of the field concentration effect in circuit-based MNZ media, the response of the system is probed in the vicinity of the structure surface. Specially, the simulated magnetic field |H| spectrum is probed at the center of the scatterer and then it is plotted as a function of the frequency in Fig. 4. For the chosen parameters, the reference frequency is ${f_c} =$1.14 GHz, with a quality factor Q ${\approx}$ 34.6, estimated from the linewidth of the spectrum peak [66]. Specially, we take the magnetic field strength greater than 7 A/m as an example. At this time, the effective bandwidth of the magnetic field concentration effect is about 0.032 GHz. To show clearly, this region is shaded in red in Fig. 4.
Fig. 4. Simulated |H| spectra for the magnetic field concentration effect in circuit-based MNZ scatterer. Bandwidth with magnetic field strength greater than 7 A/m is marked.
The simulation field distributions of |Hx|, |Hz|, and |H| 1 mm above the structure surface are presented in Figs. 5(a)–5(c). In the circuit-based system, the field is mainly localized at the microstrips, while the field is weak at the hollowed-out position without microstrips [64,65]. From the simulated distributions of the fields |Hx| and |Hz| at ${f_c} =$1.14 GHz, we see that the magnetic field |Hx| in Fig. 5(a) is weaker than the magnetic field |Hz| in Fig. 5(b). Furthermore, the field concentration effect of the MMZ scatterer can be seen in Figs. 5(b) and 5(c), where the magnetic field can be flexibly controlled by the subwavelength MNZ scatterer.
Fig. 5. (a)–(c) The simulated field distributions of |Hx|, |Hz|, and |H| 1 mm above the structure surface at 1.14 GHz. The MNZ scatterer is marked by the white dashed rectangle. (d)–(f) Similar to (a)–(c), but for the measured field distributions at 1.073 GHz.
At the end of this section, experiments were carried out to demonstrate the subwavelength magnetic field control. For the experimental process, signals were generated from a vector network analyzer (Agilent PNA Network Analyzer N5222A). A vertical monopole source was placed near the center of the sample to excite the circuit-based prototype. A small homemade loop antenna was employed to measure the out-of-plane magnetic fields |Hx| and |Hz| along the x and z directions at a fixed height of 1 mm from the planar microstrip. The sample was placed on an automatic translation device with scanning steps of 1 mm, which makes it feasible to accurately to probe the field distribution using a near-field scanning measurement. The measured results in Figs. 5(d)–5(f) agree well with the simulated results in Figs. 5(a)–5(c). To quantitatively demonstrate subwavelength magnetic field control with the MNZ scatterer, the measured values of the |H| were extracted at two lines (marked by the pink dashed lines in Fig. 5(f)) in Fig. 6. From the measured |H| in the two lines with and without the MNZ scatterer, the magnetic concentration effect of the MNZ scatterer can be demonstrated in the circuit-based system. In fact, the scatterer is subwavelength, and the magnetic field is mainly localized inside the scatterer, so the spatial localization is very strong. In order to show this feature clearly, the width of the localization is given by the full width half maximum (FWHM) of the |H| distribution [34]. The FWHM value of the field concentration is 0.024$\lambda$, as marked in Fig. 6. Specially, there are two side lobes near the concentration peak. This is because the magnetic field intensity in the z direction of the system is large, and it is mainly distributed on the microstrip in x direction [8]. As a result, the magnetic field intensity of the microstrip along the x direction near the scatterer is greater than that along the z direction, which leads to two side lobes near the concentration peak.
Fig. 6. The measured values of |H| in the z direction at the two lines marked by the pink dashed lines in Fig. 5(f). The FWHM value of the concentration peak is marked.
3. Manipulating electromagnetic energy based on the magnetic field concentration effect
While the above structure mentioned has an MNZ scatterer placed in the center of the structure, it should be emphasized that the magnetic concentration effect of the MNZ scatterer can occur at any position in the structure in Figs. 7(a)–7(f). From the |H| distribution (Fig. 7(a)) and the corresponding vector graphic of the energy flux (Fig. 7(d)) at the structure surface, we can see that the EM wave can propagate in all directions without the MNZ scatterer at 1.14 GHz. However, after the small MNZ scatterer was embedded, magnetic field concentration effects appeared. Moreover, the MNZ scatterer exhibited a robust enhancement of the magnetic field regardless of its position and number in Figs. 7(b) and 7(c). Figures 7(e) and 7(f) indicate the corresponding vector graphic of the energy flux of Figs. 7(b) and 7(c), respectively. The flux control and redistribution are clearly observed in Figs. 7(e) and 7(f). In addition, we also study the influence of the distance between scatterers on the localized field peaks. We find that shortening the distance between scatterers will not destroy the field concentration. Therefore, the field concentration effect can be further extended to the cases where the distance between two scatterers is smaller. Specially, this manipulation of flux may be used for the design of new WPT devices with multiple receivers.
Fig. 7. (a)–(c) When the frequency is 1.14 GHz, the simulated magnetic field |H| distribution in the structures without the MNZ scatterer, with one shifting MNZ scatterer, and with two MNZ scatterers, respectively. (d)–(f) The corresponding vector graphic of the energy flux.
Furthermore, by applying the magnetic field concentration effect of MNZ scatterers, we study the flexible manipulation of the EM energy along different paths. Two examples are shown in Figs. 8(a)–8(d). When two scatterers are placed along the horizontal direction, we find that the EM wave will be confined along such a path, as shown in the magnetic field distribution (Fig. 8(a)) and the corresponding energy flux distribution (Fig. 8(b)). After shifting two scatterers along an oblique direction, the propagating path of EM energy will change along this oblique direction in Figs. 8(c) and 8(d). Specially, even if the distance between scatterers decreases along the horizontal direction, the field concentration effect remains almost unchanged. To emphasize the role of the MNZ medium, a systematic comparison of a system that shows the magnetic field concentration effect with a system without this effect was carried out. Circuit-based systems can be used to realize an isotropic MNG medium (${\varepsilon _s} \approx$3.63, ${\mu _s} \approx$-31.9) at a frequency of 0.2 GHz. Comparing the results in Figs. 8(e)–8(h), we demonstrate that the circuit-based system can be observed in a working system only with the MNZ medium. In addition, when the frequency above 1.14 GHz, the circuit-based system realizes isotropic DPS media. Different from the magnetic field concentration of MNZ scatterer ($f = {f_c}$) and the strong scattering of MNG scatterer ($f < {f_c}$), DPS scatterer ($f > {f_c}$) has little effect on the transmission of EM waves. Therefore, the magnetic field concentration effect with MNZ scatterer provides an efficient way to manipulate the EM energy, which may have practical application in the WPT devices with the properties of long-range and multiple receivers in the subwavelength scale.
Fig. 8. (a) When the frequency is 1.14 GHz, the simulated magnetic field |H| distribution in the structures with two MNZ scatterers along the horizontal direction. (b) The corresponding vector graphic of the energy flux. (c) (d) Similar to (a) (b) but for the case that two scatterers along an oblique direction. (e)-(h) Similar to (a)–(d) but for the effective MNG medium with a frequency of 0.2 GHz. To see clearly, the red arrows and blue arrows denote the energy flux vectors at the frequency is 1.14 GHz and 0.2 GHz, respectively.
At present, metamaterials have been demonstrated to be powerful tools to improve the functionalities and to obtain new performance of WPT systems [67]. Although it is a fundamental challenge for traditional materials to manipulate EM waves on the subwavelength scale, metamaterials can flexibly control the near-field of the EM waves. For example, the coupling between the transmitter and the receiver in WPT systems can be enhanced with the aid of negative-index or MNG metamaterial insertion [67]. The underlying physical mechanism to improve the efficiency of WPT is based on the amplification of evanescent field. In addition, by adding metamaterials with high permeability to the receiving and the transmitting coils, the transmission efficiency can also be improved because the magnetic flux in the coil is increased [68]. However, there are still some problems to be solved in the practical applications of metamaterials in WPT system. First of all, it is difficult to realize miniaturization because of the large size of adding metamaterials slab. Secondly, it is difficult to extend it to multiple receivers and long-distance transmission. Finally, it is also very difficult to apply it to the application scenarios where the size of transmitting and receiving coils differs greatly [67,68]. With the help of the magnetic field concentration effect realized by MNZ scatterers, these problems can be solved well. Here, although the circuit-based MNZ scatterer is designed based on the TL system, it can also be constructed by the array of resonant structure and well extended to the WPT systems of magnetic induction and magnetic resonance [67,68]. We are looking forward to utilizing the magnetic field concentration effect of MNZ media in the future to realize the miniaturization, diversified and efficient WPT devices.
Moreover, with the development of on-chip miniaturized microwave photonic devices, the realization of subwavelength optical mode localization becomes a very important scientific problem. In this work, the experimental realization of field concentration on planar circuit-based MNZ scatterer offers great practical advantages in the technology treatment and potential microwave applications, such as the miniaturized narrowband filters [69] and imaging [70]. The proposed circuit-based MNZ scatterers give important potential to accelerate the development of highly integrated functional devices and circuits in microwave regime.
4. Conclusion
In summary, the observed magnetic field concentration effect in our experiments confirms the theoretical prediction that EM waves can be flexibly controlled using ZIM scatterers. This experimental work demonstrated that an MNZ scatterer could realize magnetic field concentration and that this phenomenon is independent of the position and number of the scatterers. Furthermore, we study this field concentration effect can be used to realize the robust long-range energy transfer with almost arbitrary route. Importantly, our results provide a good scheme for the construction of new WPT devices with the long-range and multiple receivers properties. In addition, this magnetic field concentration effect has other promising applications, including for absorbers, sensors, and switches.
Funding
National Key Research and Development Program of China (2016YFA0301101); National Natural Science Foundation of China (11474220, 11774261, 61621001); China Postdoctoral Science Foundation (2019M661605, 2019TQ0232); Shanghai Super Postdoctoral Incentive Program; Natural Science Foundation of Shanghai (17ZR1443800, 18JC1410900).
Disclosures
The authors declare no conflicts of interest.
References
1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef]
2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef]
3. X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011). [CrossRef]
4. P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013). [CrossRef]
5. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017). [CrossRef]
6. X. X. Niu, X. Y. Hu, S. S. Chu, and Q. H. Gong, “Epsilon-near-zero photonics: A new platform for integrated devices,” Adv. Opt. Mater. 6(10), 1701292 (2018). [CrossRef]
7. N. Kinsey, C. DeVault, A. Boltasseva, and V. M. Shalaev, “Near-zero-index materials for photonics,” Nat. Rev. Mater. 4(12), 742–760 (2019). [CrossRef]
8. Z. W. Guo, H. T. Jiang, and H. Chen, “Hyperbolic metamaterials: From dispersion manipulation to applications,” J. Appl. Phys. 127(7), 071101 (2020). [CrossRef]
9. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: Electromagnetic enhancement at zero-index transition,” Opt. Lett. 33(20), 2350–2352 (2008). [CrossRef]
10. S. Campione, D. D. Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in ɛ-near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87(3), 035120 (2013). [CrossRef]
11. H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. B. Yin, and X. Zhang, “Phase mismatch–free nonlinear propagation in optical zero-index materials,” Science 342(6163), 1223–1226 (2013). [CrossRef]
12. A. Capretti, Y. Wang, N. Engheta, and L. D. Negro, “Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers,” Opt. Lett. 40(7), 1500–1503 (2015). [CrossRef]
13. T. S. Luk, D. de Ceglia, S. Liu, G. A. Keeler, R. P. Prasankumar, M. A. Vincenti, M. Scalora, M. B. Sinclair, and S. Campione, “Enhanced third harmonic generation from the epsilon-near-zero modes of ultrathin films,” Appl. Phys. Lett. 106(15), 151103 (2015). [CrossRef]
14. M. Z. Alam, S. A. Schulz, J. Upham, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material,” Nat. Photonics 12(2), 79–83 (2018). [CrossRef]
15. S. Jahani, H. Zhao, and Z. Jacob, “Switching Purcell effect with nonlinear epsilon-near-zero media,” Appl. Phys. Lett. 113(2), 021103 (2018). [CrossRef]
16. O. Reshef, I. D. Leon, M. Z. Alam, and R. W. Boyd, “Nonlinear optical effects in epsilon-near-zero media,” Nat. Rev. Mater. 4(8), 535–551 (2019). [CrossRef]
17. Z. W. Guo, F. Wu, C. H. Xue, H. T. Jiang, Y. Sun, Y. H. Li, and H. Chen, “Significant enhancement of magneto-optical effect in one-dimensional photonic crystals with a magnetized epsilon-near-zero defect,” J. Appl. Phys. 124(10), 103104 (2018). [CrossRef]
18. X. Zhou, D. Leykam, U. Chattopadhyay, A. B. Khanikaev, and Y. D. Chong, “Realization of a magneto-optical near-zero index medium by an unpaired Dirac point,” Phys. Rev. B 98(20), 205115 (2018). [CrossRef]
19. A. Davoyan and N. Engheta, “Nonreciprocal emission in magnetized epsilon-near-zero metamaterials,” ACS Photonics 6(3), 581–586 (2019). [CrossRef]
20. C. Rizza, A. D. Falco, M. Scalora, and A. Ciattoni, “One-dimensional chirality: Strong optical activity in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 115(5), 057401 (2015). [CrossRef]
21. S.-A. Biehs, V. M. Menon, and G. S. Agarwal, “Long-range dipole-dipole interaction and anomalous Förster energy transfer across a hyperbolic metamaterial,” Phys. Rev. B 93(24), 245439 (2016). [CrossRef]
22. J. Kim, A. Dutta, G. V. Naik, A. J. Giles, F. J. Bezares, C. T. Ellis, J. G. Tischler, A. M. Mahmoud, H. Gaglayan, O. J. Glembocki, A. V. Kildishev, J. D. Caldwell, A. Boltasseva, and N. Engheta, “Role of epsilon-near-zero substrates in the optical response of plasmonic antennas,” Optica 3(3), 339–346 (2016). [CrossRef]
23. Y. Li, A. Nemilentsau, and C. Argyropoulos, “Resonance energy transfer and quantum entanglement mediated by epsilon-near-zero and other plasmonic waveguide systems,” Nanoscale 11(31), 14635–14647 (2019). [CrossRef]
24. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. A. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef]
25. X. T. He, Y. N. Zhong, Y. Zhou, Z. C. Zhong, and J. W. Dong, “Dirac directional emission in anisotropic zero refractive index photonic crystals,” Sci. Rep. 5(1), 13085 (2015). [CrossRef]
26. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. 108(21), 213903 (2012). [CrossRef]
27. Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014). [CrossRef]
28. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ɛ-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006). [CrossRef]
29. A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ɛ-near-zero–filled narrow channels,” Phys. Rev. E 78(1), 016604 (2008). [CrossRef]
30. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008). [CrossRef]
31. R. P. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008). [CrossRef]
32. J. M. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010). [CrossRef]
33. H. C. Chu, Q. Li, B. B. Li, J. Luo, S. L. Sun, Z. H. Hang, L. Zhou, and Y. Lai, “A hybrid invisibility cloak based on integration of transparent metasurfaces and zero-index materials,” Light: Sci. Appl. 7(1), 50 (2018). [CrossRef]
34. Z. W. Guo, H. T. Jiang, K. J. Zhu, Y. Sun, Y. H. Li, and H. Chen, “Focusing and super-resolution with partial cloaking based on linear-crossing metamaterials,” Phys. Rev. Appl. 10(6), 064048 (2018). [CrossRef]
35. Z. W. Guo, H. T. Jiang, and H. Chen, “Linear-crossing metamaterials mimicked by multi-layers with two kinds of single negative materials,” JPhys Photonics 2(1), 011001 (2020). [CrossRef]
36. J. Chen, Y. Wang, B. Jia, T. Geng, X. Li, L. Feng, W. Qian, B. Liang, X. Zhang, M. Gu, and S. Zhuang, “Observation of the inverse Doppler effect in negative-index materials at optical frequencies,” Nat. Photonics 5(4), 239–242 (2011). [CrossRef]
37. J. Ran, Y. W. Zhang, X. D. Chen, K. Fang, J. F. Zhao, and H. Chen, “Observation of the zero Doppler effect,” Sci. Rep. 6(1), 23973 (2016). [CrossRef]
38. M. Memarian and G. V. Eleftheriades, “Analysis of anisotropic epsilon-near-zero hetero-junction lens for concentration and beam splitting,” Opt. Lett. 40(6), 1010–1013 (2015). [CrossRef]
39. S. H. Sedighy, C. Guclu, S. Campione, M. M. Amirhosseini, and F. Capolino, “Wideband planar transmission line hyperbolic metamaterial for subwavelength focusing and resolution,” IEEE Trans. Microwave Theory Tech. 61(12), 4110–4117 (2013). [CrossRef]
40. M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75(7), 075119 (2007). [CrossRef]
41. V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010). [CrossRef]
42. A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87(15), 155130 (2013). [CrossRef]
43. W. R. Zhu, L. M. Si, and M. Premaratne, “Light focusing using epsilon-near-zero metamaterials,” AIP Adv. 3(11), 112124 (2013). [CrossRef]
44. A. M. Mahmoud and N. Engheta, “Wave–matter interactions in epsilon-and-mu-near-zero structures,” Nat. Commun. 5(1), 5638 (2014). [CrossRef]
45. M. Zhou, L. Shi, J. Zi, and Z. F. Yu, “Extraordinarily large optical cross section for localized single nanoresonator,” Phys. Rev. Lett. 115(2), 023903 (2015). [CrossRef]
46. Z. Wang, Z. Y. Wang, and Z. F. Yu, “Photon management with index-near-zero materials,” Appl. Phys. Lett. 109(5), 051101 (2016). [CrossRef]
47. I. Liberal, Y. Li, and N. Engheta, “Magnetic field concentration assisted by epsilon-near-zero media,” Philos. Trans. R. Soc., A 375(2090), 20160059 (2017). [CrossRef]
48. I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017). [CrossRef]
49. J. Luo, B. B. Liu, Z. H. Hang, and Y. Lai, “Coherent perfect absorption via photonic doping of zero-index media,” Laser Photonics Rev. 12(8), 1800001 (2018). [CrossRef]
50. Z. Zhou, Y. Li, H. Li, W. Sun, I. Liberal, and N. Engheta, “Substrate-integrated photonic doping for near-zero-index devices,” Nat. Commun. 10(1), 4132 (2019). [CrossRef]
51. C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7(11), 902–906 (2013). [CrossRef]
52. T. Zentgraf, Y. M. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011). [CrossRef]
53. M. Zhou, L. Yang, L. Lu, L. Shi, J. Zi, and Z. F. Yu, “Electromagnetic scattering laws in Weyl systems,” Nat. Commun. 8(1), 1388 (2017). [CrossRef]
54. L. Ying, M. Zhou, M. Mattei, B. Liu, P. Campagnola, R. H. Goldsmith, and Z. F. Yu, “Extended range of dipole-dipole interactions in periodically structured photonic media,” Phys. Rev. Lett. 123(17), 173901 (2019). [CrossRef]
55. A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless power transfer via strongly coupled magnetic resonances,” Science 317(5834), 83–86 (2007). [CrossRef]
56. J. Luo, W. X. Lu, Z. H. Hang, H. Y. Chen, B. Hou, Y. Lai, and C. T. Chan, “Arbitrary control of electromagnetic flux in inhomogeneous anisotropic media with near-zero index,” Phys. Rev. Lett. 112(7), 073903 (2014). [CrossRef]
57. J. W. Song, J. Luo, and Y. Lai, “Side scattering shadow and energy concentration effects of epsilon-near-zero media,” Opt. Lett. 43(8), 1738–1741 (2018). [CrossRef]
58. P. Ginzburg, F. J. Rodríguez Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21(12), 14907–14917 (2013). [CrossRef]
59. S. M. Zhong and S. L. He, “Ultrathin and lightweight microwave absorbers made of mu-near-zero metamaterials,” Sci. Rep. 3(1), 2083 (2013). [CrossRef]
60. Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015). [CrossRef]
61. P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018). [CrossRef]
62. Y. Wu, X. Y. Hu, F. F. Wang, J. H. Yang, C. C. Lu, Y. C. Liu, H. Yang, and Q. H. Gong, “Ultracompact and unidirectional on-chip light source based on epsilon-near-zero materials in an optical communication range,” Phys. Rev. Appl. 12(5), 054021 (2019). [CrossRef]
63. G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically LC loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50(12), 2702–2712 (2002). [CrossRef]
64. Z. W. Guo, H. T. Jiang, Y. Long, K. Yu, J. Ren, C. H. Xue, and H. Chen, “Photonic spin Hall effect in waveguides composed of two types of single-negative metamaterials,” Sci. Rep. 7(1), 7742 (2017). [CrossRef]
65. Z. W. Guo, H. T. Jiang, Y. H. Li, H. Chen, and G. S. Agarwal, “Enhancement of electromagnetically induced transparency in metamaterials using long range coupling mediated by a hyperbolic material,” Opt. Express 26(2), 627–641 (2018). [CrossRef]
66. Y. Q. Wang, Z. W. Guo, Y. Q. Chen, X. Chen, H. T. Jiang, and H. Chen, “Circuit-based magnetic hyperbolic cavities,” Phys. Rev. Appl. 13(4), 044024 (2020). [CrossRef]
67. M. Song, P. Belov, and P. Kapitanova, “Wireless power transfer inspired by the modern trends in electromagnetics,” Appl. Phys. Rev. 4(2), 021102 (2017). [CrossRef]
68. Q. Wu, Y. H. Li, N. Gao, F. Yang, Y. Q. Chen, K. Fang, Y. W. Zhang, and H. Chen, “Wireless power transfer based on magnetic metamaterials consisting of assembled ultra-subwavelength meta-atoms,” Europhys. Lett. 109(6), 68005 (2015). [CrossRef]
69. P. Jarry and J. Beneat, Design and Realizations of Miniaturized Fractal Microwave and RF Filters (John Wiley & Sons, New York, 2009).
70. A. P. Slobozhanyuk, A. N. Poddubny, A. J. E. Raaijmakers, C. A. T. van den Berg, A. V. Kozachenko, I. A. Dubrovina, I. V. Melchakova, Y. S. Kivshar, and P. A. Belov, “Enhancement of magnetic resonance imaging with metasurfaces,” Adv. Mater. 28(9), 1832–1838 (2016). [CrossRef]
