Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Curr. Opt. Photon. 2023; 7(1): 97-103
Published online February 25, 2023 https://doi.org/10.3807/COPP.2023.7.1.97
Copyright © Optical Society of Korea.
Seojoo Lee^{1}, Ji-Hun Kang^{2,3,4}
Corresponding author: ^{*}jihunkang@kongju.ac.kr, ORCID 0000-0002-2201-1689
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we propose Babinet-principle-inspired metasurfaces for strong resonant enhancement of local magnetic fields. The metasurfaces are designed as complementary structures of original meta-surfaces supporting the local enhancement of electric fields. We show numerically that the complementary structures can support spoof magnetic surface plasmons that induce strong local magnetic fields without sacrificing the deep sub-wavelength-thick nature of the metasurface. By introducing a periodic array of metallic rods in the proximity of the metasurfaces, we demonstrate that a resonant enhancement of the local magnetic fields, more than 80 times the amplitude of an incident magnetic field, can emerge from a resonance of the spoof magnetic surface plasmons.
Keywords: Babinet's principle, Complementary structure, Magnetic resonance, Metamaterials, Metasurfaces
OCIS codes: (160.3918) Metamaterials; (240.6680) Surface plasmons; (260.5740) Resonance
Manipulations of electromagnetic (EM) waves by using structured media require a deep understanding of light interaction with the media and consequent EM field distributions in both near and far fields [1–7]. A prime example is the designing of optical metamaterials and their two-dimensional equivalent, metasurfaces. Engineering of far-field transmission and reflection coefficients using a metasurface allows us to acquire unprecedented effective electric permittivities and magnetic permeabilities [8–10], while control of the diffracted EM waves in the proximity of a metasurface has enabled metamaterial-based sub-wavelength optical resonators [3, 11].
Although the near and far fields are connected only in terms of the effective description (
Here, we demonstrate numerically that Babinet’s principle can be an alternate way to design metasurfaces for the strong local magnetic resonance without sacrificing the deep sub-wavelength-thick property. Our metasurfaces are conceived as Babinet’s complementary structures of their counterparts, plasmonic metasurfaces with negative effective permittivity. We show that the complementary structures can support SMSPs that induce strong local magnetic fields. By introducing a periodic array of metallic rods in the proximity of the complementary metasurfaces, we demonstrate that a resonant enhancement of the local magnetic fields can emerge from a resonance of the SMSPs.
Babinet’s principle states that the diffraction patterns from the original diffracting structure made of PEC are the same as those emerging from the Babinet-inverted complementary structure with exchanged polarizations of the incident electric and magnetic fields [21]. It should be noted that a rigorous statement of Babinet’s principle requires the diffractive structure to be infinitesimally thin. However, it has been demonstrated that the spirit of Babinet’s principle is also valid for a structure with sub-wavelength but finite thickness to predict qualitatively, not quantitatively, the diffraction patterns from the counterpart structure [22].
In terms of Babinet inversion, metasurfaces are one of the most suitable structures. As shown in Fig. 1, it is not clear whether Babinet’s principle can be applied in the case of excitation of surface plasmons in real metal with negative permittivity. However, a plasmonic metasurface with negative effective permittivity, operating in a terahertz or microwave spectral regime where most metals can be considered a PEC, is fully applicable to Babinet’s principle. Here, our main idea comes from the fact that SSPs supported by the plasmonic metasurface are a phenomenological description of surface-bound waves excited by the diffraction of incident EM waves. Therefore, if Babinet’s principle can be applied to the plasmonic metasurface, SSPs would appear in the form of SMSPs.
For negative effective permittivity, let us first consider an exemplary metasurface consisting of rectangular metallic ring resonators as shown in Fig. 2(a). Because Babinet inversion will be applied later, we designed the metasurface to operate in the microwave spectral regime. In our previous study, it was shown that this structure can exhibit negative effective permittivity as a result of a competition between two light channels in the metasurface, and that the effective permittivity in the
when the unit resonators are tightly coupled to each other [14, 23]. Here,
Now, one can readily apply Babinet inversion to the metasurface. For 0 ≤
With the Babinet-inverted metasurfaces, we numerically calculated the near-field spectra of the
We have seen that the Babinet-inverted metasurface itself already allows local enhancement of the magnetic field without introducing surface-bound waves like SMSPs. In order to incorporate the SMSPs into the magnetic field enhancement, we located PEC rods in front of the metasurface as shown in Fig. 4(a). The rods are infinitely long in the
To see more details of the resonant behavior, we increased the periodicity of the PEC rods to five times the lattice of the metasurface (5
A direct way to confirm this model based on the cavity mode of SMSPs is to see how the cavity modes, corresponding to the spectral peaks, form the near-field. Shown in Figs. 6(a) and 6(b) are numerically calculated x-y maps of near-field profiles of |
It should be noted that the cavity should be able to support higher modes, in principle. However, as we have discussed previously, the finite surface resolution of the metasurface limits the excitation of SMSPs with a shorter wavelength, so that what we see in Figs. 4 and 6 is only a single cavity mode. In this sense, we have assumed that the additional sharp spectral peak in Fig. 5(b) at 3.090 GHz could be the higher cavity mode, and this is confirmed by Fig. 7. Shown in Figs. 7(a) and 7(b) are near-field maps of |
We have applied Babinet’s principle to a plasmonic metasurface of effective negative permittivity supporting SSPs, and have successfully demonstrated the excitation of SMSPs in the Babinet-inverted metamaterial systems. We note that the excitation of the SMSPs by the spirit of Babinet’s principle is a phenomenological interpretation of light diffraction by metasurfaces in a near field, and is not strictly related to the effective medium description of the metasurfaces. Specifically, a Babinet inversion of a metasurface with negative effective permittivity does not mean that the complementary metasurface must possess negative permeability. A prime example of this can be found in [10], demonstrating that a Babinet inversion of a plasmonic structure with negative effective permittivity can result in a complementary structure with a positive effective permittivity with a high effective index of refraction.
In this paper, we have demonstrated a Babinet-principle-inspired metasurface for resonant enhancement of magnetic fields. By applying Babinet’s principle to a plasmonic metasurface supporting SSPs in the form of surface-bound waves, we have shown that the complementary structures can support SMSPs that induce strong local magnetic fields. For excitation of the spoof magnetic plasmons and resonant enhancement of the magnetic fields, we introduced a periodic array of diffractive rods in the proximity of the metasurface. The resonant enhancement of the local magnetic fields has been shown to emerge from the resonance of the SMSPs inside a cavity defined by the periodically located rods. We believe that our scheme provides an intuitive way to realize magnetic resonance in an ultrathin structure, and that the proposed metasurface system could play important roles in various disciplines where strongly enhanced magnetic fields are required.
The authors declare no conflicts of interests.
Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.
Research grant from Kongju National University in 2020; National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (Grant No. NRF-2021R1A2C2012617, NRF-2020R1C1C1012138).
Curr. Opt. Photon. 2023; 7(1): 97-103
Published online February 25, 2023 https://doi.org/10.3807/COPP.2023.7.1.97
Copyright © Optical Society of Korea.
Seojoo Lee^{1}, Ji-Hun Kang^{2,3,4}
^{1}School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA
^{2}Department of Optical Engineering, Kongju National University, Cheonan 31080, Korea
^{3}Department of Future Convergence Engineering, Kongju National University, Cheonan 31080, Korea
^{4}Institute of Application and Fusion for Light, Kongju National University, Cheonan 31080, Korea
Correspondence to:^{*}jihunkang@kongju.ac.kr, ORCID 0000-0002-2201-1689
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we propose Babinet-principle-inspired metasurfaces for strong resonant enhancement of local magnetic fields. The metasurfaces are designed as complementary structures of original meta-surfaces supporting the local enhancement of electric fields. We show numerically that the complementary structures can support spoof magnetic surface plasmons that induce strong local magnetic fields without sacrificing the deep sub-wavelength-thick nature of the metasurface. By introducing a periodic array of metallic rods in the proximity of the metasurfaces, we demonstrate that a resonant enhancement of the local magnetic fields, more than 80 times the amplitude of an incident magnetic field, can emerge from a resonance of the spoof magnetic surface plasmons.
Keywords: Babinet's principle, Complementary structure, Magnetic resonance, Metamaterials, Metasurfaces
Manipulations of electromagnetic (EM) waves by using structured media require a deep understanding of light interaction with the media and consequent EM field distributions in both near and far fields [1–7]. A prime example is the designing of optical metamaterials and their two-dimensional equivalent, metasurfaces. Engineering of far-field transmission and reflection coefficients using a metasurface allows us to acquire unprecedented effective electric permittivities and magnetic permeabilities [8–10], while control of the diffracted EM waves in the proximity of a metasurface has enabled metamaterial-based sub-wavelength optical resonators [3, 11].
Although the near and far fields are connected only in terms of the effective description (
Here, we demonstrate numerically that Babinet’s principle can be an alternate way to design metasurfaces for the strong local magnetic resonance without sacrificing the deep sub-wavelength-thick property. Our metasurfaces are conceived as Babinet’s complementary structures of their counterparts, plasmonic metasurfaces with negative effective permittivity. We show that the complementary structures can support SMSPs that induce strong local magnetic fields. By introducing a periodic array of metallic rods in the proximity of the complementary metasurfaces, we demonstrate that a resonant enhancement of the local magnetic fields can emerge from a resonance of the SMSPs.
Babinet’s principle states that the diffraction patterns from the original diffracting structure made of PEC are the same as those emerging from the Babinet-inverted complementary structure with exchanged polarizations of the incident electric and magnetic fields [21]. It should be noted that a rigorous statement of Babinet’s principle requires the diffractive structure to be infinitesimally thin. However, it has been demonstrated that the spirit of Babinet’s principle is also valid for a structure with sub-wavelength but finite thickness to predict qualitatively, not quantitatively, the diffraction patterns from the counterpart structure [22].
In terms of Babinet inversion, metasurfaces are one of the most suitable structures. As shown in Fig. 1, it is not clear whether Babinet’s principle can be applied in the case of excitation of surface plasmons in real metal with negative permittivity. However, a plasmonic metasurface with negative effective permittivity, operating in a terahertz or microwave spectral regime where most metals can be considered a PEC, is fully applicable to Babinet’s principle. Here, our main idea comes from the fact that SSPs supported by the plasmonic metasurface are a phenomenological description of surface-bound waves excited by the diffraction of incident EM waves. Therefore, if Babinet’s principle can be applied to the plasmonic metasurface, SSPs would appear in the form of SMSPs.
For negative effective permittivity, let us first consider an exemplary metasurface consisting of rectangular metallic ring resonators as shown in Fig. 2(a). Because Babinet inversion will be applied later, we designed the metasurface to operate in the microwave spectral regime. In our previous study, it was shown that this structure can exhibit negative effective permittivity as a result of a competition between two light channels in the metasurface, and that the effective permittivity in the
when the unit resonators are tightly coupled to each other [14, 23]. Here,
Now, one can readily apply Babinet inversion to the metasurface. For 0 ≤
With the Babinet-inverted metasurfaces, we numerically calculated the near-field spectra of the
We have seen that the Babinet-inverted metasurface itself already allows local enhancement of the magnetic field without introducing surface-bound waves like SMSPs. In order to incorporate the SMSPs into the magnetic field enhancement, we located PEC rods in front of the metasurface as shown in Fig. 4(a). The rods are infinitely long in the
To see more details of the resonant behavior, we increased the periodicity of the PEC rods to five times the lattice of the metasurface (5
A direct way to confirm this model based on the cavity mode of SMSPs is to see how the cavity modes, corresponding to the spectral peaks, form the near-field. Shown in Figs. 6(a) and 6(b) are numerically calculated x-y maps of near-field profiles of |
It should be noted that the cavity should be able to support higher modes, in principle. However, as we have discussed previously, the finite surface resolution of the metasurface limits the excitation of SMSPs with a shorter wavelength, so that what we see in Figs. 4 and 6 is only a single cavity mode. In this sense, we have assumed that the additional sharp spectral peak in Fig. 5(b) at 3.090 GHz could be the higher cavity mode, and this is confirmed by Fig. 7. Shown in Figs. 7(a) and 7(b) are near-field maps of |
We have applied Babinet’s principle to a plasmonic metasurface of effective negative permittivity supporting SSPs, and have successfully demonstrated the excitation of SMSPs in the Babinet-inverted metamaterial systems. We note that the excitation of the SMSPs by the spirit of Babinet’s principle is a phenomenological interpretation of light diffraction by metasurfaces in a near field, and is not strictly related to the effective medium description of the metasurfaces. Specifically, a Babinet inversion of a metasurface with negative effective permittivity does not mean that the complementary metasurface must possess negative permeability. A prime example of this can be found in [10], demonstrating that a Babinet inversion of a plasmonic structure with negative effective permittivity can result in a complementary structure with a positive effective permittivity with a high effective index of refraction.
In this paper, we have demonstrated a Babinet-principle-inspired metasurface for resonant enhancement of magnetic fields. By applying Babinet’s principle to a plasmonic metasurface supporting SSPs in the form of surface-bound waves, we have shown that the complementary structures can support SMSPs that induce strong local magnetic fields. For excitation of the spoof magnetic plasmons and resonant enhancement of the magnetic fields, we introduced a periodic array of diffractive rods in the proximity of the metasurface. The resonant enhancement of the local magnetic fields has been shown to emerge from the resonance of the SMSPs inside a cavity defined by the periodically located rods. We believe that our scheme provides an intuitive way to realize magnetic resonance in an ultrathin structure, and that the proposed metasurface system could play important roles in various disciplines where strongly enhanced magnetic fields are required.
The authors declare no conflicts of interests.
Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.
Research grant from Kongju National University in 2020; National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (Grant No. NRF-2021R1A2C2012617, NRF-2020R1C1C1012138).