Abstract

It has been hard to achieve simultaneous plasmonic enhancement of nanoscale light-matter interactions in terms of both electric and magnetic manners with easily reproducible fabrication method and systematic theoretical design rule. In this paper, a novel concept of a flat nanofocusing device is proposed for simultaneously squeezing both electric and magnetic fields in deep-subwavelength volume (~λ3/538) in a large area. Based on the funneled unit cell structures and surface plasmon-assisted coherent interactions between them, the array of rectangular nanocavity connected to a tapered nanoantenna, plasmonic metasurface cavity, is constructed by periodic arrangement of the unit cell. The average enhancement factors of electric and magnetic field intensities reach about 60 and 22 in nanocavities, respectively. The proposed outstanding performance of the device is verified numerically and experimentally. We expect that this work would expand methodologies involving optical near-field manipulations in large areas and related potential applications including nanophotonic sensors, nonlinear responses, and quantum interactions.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In the field of nanophotonics, harnessing light energy in nanoscale has been a significant issue with the rise of plasmonics [1–3]. Surface plasmons (SPs) excited on the metallic surface can confine light without cut-off phenomenon when they are guided into deep subwavelength volume while dielectric nanoresonators cannot reduce their mode volume beyond diffraction limit [1–3]. Many plasmonic nanofocusing applications including micro / nanoscopy [1], biosensors [4–6], harmonic generation enhancement [7–9], optical tweezing [10], nano-lithography [11], and spontaneous emission control [12–14] share a common goal, which is extreme enhancement of electromagnetic energy in ultracompact volume. There have been many studies suggesting extreme electric field enhancement with various tapered metallic tips [15–20] or metal-insulator-metal (MIM) type resonators [17,21–25] resulting in about 104-fold enhancement of electric field intensity [17]. On the other hand, less attention has been paid on boosting nanoscale magnetic field intensity [26–30] despite various potential applications in nanophotonics and quantum optics including magnetic micro / nanoscopy [31–34], magnetic nonlinearity [9,35,36], and quantum responses [37,38]. It is generally owing to intrinsically lower power of magnetic field compared to that of electric field due to impedance relation. Moreover, it has been hard to squeeze magnetic field into a point-like space owing to wavelength-dependence of magnetic resonance volume with circulating current unlike cases of electric field nanofocusing [39]. Hence, boosting both electric and magnetic light-matter interactions with simultaneously boosted electromagnetic fields is potentially fruitful for various fields of optics. There have been only few studies to achieve this goal with plasmonic nanoantennas containing MIM structure [40,41]. Metallic cap-connected bow-tie nanoantenna for simultaneous enhancement of optical electric and magnetic fields proposed by Roxworthy and Toussaint [40] lacks experimental verification and feasible suggestion of simple fabrication method. Similar work by Chen et al. [41] also shows simultaneously boosted electric and magnetic fields with circulating plasmonic surface current. However, their work is not easy to be reproduced for large area fabrication and mass production since ion beam milling technique for thin metallic bridges is crucial but highly sensitive to unstable beam conditions. Moreover, as working principle of the device is explained in phenomenological way rather than systematic and analytical manner, it seems to involve limits when expanded and applied to more complex and multifunctional systems.

Here, we propose a novel and robust mechanism working at the near-infrared wavelengths to enhance both nanoscale electric and magnetic interactions inspired from our previous work [42]. The simple and intuitive idea is proposed for novel electric dipolar nanofocusing in nanocavities in terms of both electric and toroidal parts. It is known that rigorous model of electric dipole radiation includes two parts, electric and toroidal parts [43–45]. In the proposed devices, electric dipolar nanofocusing of electric and toroidal parts contributions is engineered for simultaneous nanoscale squeezing of electric and magnetic fields. Incident light is squeezed with funneled plasmonic apertures via SPs for innovative boost of electric and magnetic interactions in tiny nanocavities. With clear physical principle, systematic design rule, and simply reproducible experimental demonstration, novel resonant electric dipolar nanofocusing in large area is proposed for simultaneously squeezed electric and magnetic fields in deep subwavelength volume (~λ3/538). The rest part of the paper is organized as follows. At first, working principle and design rule of the device are discussed. Then, experimental evidence is provided with measurement of far-field spectrum. Throughout the paper, we conduct numerical analysis using commercial finite element method tool (COMSOL Multiphysics 5.2). Dielectric constants of the gold and the silicon dioxide are quoted from the work done by Palik and Malitson [46,47].

2. Results and discussions

2.1 The unit cell funneled aperture cavity for electric and magnetic hotspots

To enhance both electric and magnetic fields, we propose a funneled aperture cavity as the unit cell for light trapping. As shown in Fig. 1(a), the funneled aperture cavity consists of a tapered antenna region for plasmon concentration and a nanocavity region for the designated location of plasmonic hotspot. In our previous work, concentration of electric and magnetic fields is studied theoretically and numerically in case of MIM waveguide structure [42]. Critical simultaneous nanofocusing of electric and magnetic fields can be achieved when symmetric Ey and anti-symmetric Hz fields are resonantly trapped in a nanocavity. The key idea is to locate plasmonic node of Hz field and anti-node of Ey field inside the rectangular nanocavity simultaneously. The tapering region is for concentrating more energy so that nanofocusing efficiency would increase.

 

Fig. 1 (a) Schematic illustration of the proposed funneled aperture cavity for novel electric dipolar nanofocusing (θ = 15°, d2 = 750 nm, w0 = 70 nm, d1 = 355 nm, and h = 100 nm) at the wavelength of 1120 nm. Spatial distributions of (b) induced x-directional electric current (Jx), (c) y-directional electric field (Ey), and (d) z-directional magnetic field (Hz) at the cross-section of metal in the middle, respectively.

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Hence, to enhance Ey and Hz in the designated nanocavity, we numerically optimized d1 and d2 parameters with w0 and θ set to be 70 nm and 15° considering the experimental fabrication and the efficient energy trapping. It is well known that smaller plasmonic gap can be more advantageous for better field enhancement [48]. However, as resolution of our e-beam negative tone resist is limited, it is hard to guarantee precise large area patterning of nanocavity parts without residue problem after lift-off. Hence, w0 is fixed as 70 nm for reducing fabrication error. When we choose value of θ, there was a criterion to consider as follows. If θ is too small and tapering is adiabatically formed, plasmonic energy would be trapped in the unit cell funneled aperture in nearly homogeneous manner so that effect of plasmonic focusing into the rectangular nanocavity can be weakened. On the other hand, if θ is too large, SPs can be hard to funnel into the rectangular nanocavity and most of plasmonic energy can be absorbed at the tapering region rather than the nanocavity region. Hence, we fixed θ as moderate value of 15° which is conventionally familiar value in near-field scanning optical microscopy [49,50].

It is important to determine the lengths of the nanocavity and tapered antenna, d1 and d2, since field intensity and patterns of the hotspots in the nanocavity are critically dependent on them. Hence, the optimization of d1 and d2 was conducted to nanofocus a large portion of electromagnetic energy into the nanocavity while symmetric Ey and anti-symmetric Hz are trapped, simultaneously.

When y-polarized light is normally incident to the substrate side at a wavelength of 1120 nm [Fig. 1(a)], the electric dipolar nanofocusing is achieved under the condition of d1 = 355 nm and d2 = 750 nm with the desired anti-symmetric current density loop Jx, central symmetric Ey, and anti-symmetric Hz along x-axis [Figs. 1(b)-1(d)]. By the resonant current density distribution, asymmetrically squeezed cavity mode is formed inside the aperture while Ey and Hz fields are trapped inside the nanocavity.

2.2 Plasmonic metasurface cavity and performance characterization

In this section, we propose a two-dimensional periodic array of the funneled aperture cavity, which is named as the plasmonic metasurface cavity, to improve enhancement performance of electric and magnetic fields in large area. In case of the single funneled aperture cavity, large amount of input energy is scattered to SPs. Hence, we exploit constructive interference of SPs in a periodic array of the optimized funneled aperture cavities for efficiency-improved nanofocusing of SPs into the nanocavities. The SP scattering by the single funneled aperture cavity occurs dominantly at the gold/glass interface with a butterfly-like radiation pattern [Figs. 2(a) and 2(c)] rather than a dipole-like radiation pattern at the air/gold interface [Figs. 2(b) and 2(c)]. The difference between the SP radiation patterns originates from the difference of the refractive indices on the interfaces. As SP wavelength at the gold/glass interface (~773 nm) is fairly shorter than that at the gold/air glass (~1110 nm), different charge distributions at the two sides of the funneled aperture cavity cause the totally different scattering patterns, as shown in Figs. 2(a) and 2(b). For the two main scattering lobes at the gold/glass interface, the SPs are directed along the angle of α = β ≈54° [See the blue contour in Fig. 2(c).]. Furthermore, the SP scattering intensity at the gold/glass interface is almost twice higher than that at the air/gold interface. Hence, we only consider the SP-assisted constructive interference at the gold/glass interface.

 

Fig. 2 Normalized Ez field distribution describing SP scattering (a) at gold/glass interface and (b) at air/gold interface (c) Angular SP radiation pattern for the unit cell at the interface of the gold/glass and air/gold interface

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For the plasmonic metasurface cavity design [Fig. 3(a)], we chose the approximated constructive interference conditions of Λx ≈2 λsp sinα ≈1200 nm and Λy ≈2 λsp cosα ≈890 nm (λsp = 773 nm at the wavelength of 1120 nm) since dominant SP scattering occurs at the gold/glass interface. Consequently, by virtue of the constructive interference, the enhancement factors of average electric field intensity and magnetic field intensity, which are investigated in the deep-subwavelength (w0 × d1 × h = λ3/538) sized rectangular nanocavities, markedly increase from 7 to 60 and from 5 to 22 at the same target wavelength of 1120 nm, respectively [Fig. 3(b)]. Meanwhile, in terms of the maximum field intensity enhancement, the enhancement factors of electric field intensity and magnetic field intensity markedly increase from 39 to 510 and from 19 to 108, respectively.

 

Fig. 3 (a) Schematic diagram describing the top view of the metasurface cavity with periodically arranged unit cells (Λx = 1200 nm and Λy = 890 nm). The black-dotted line and arrow denote the rectangular nanocavity region where hotspot is excited. (b) Intensity enhancement factors for the periodic metasurface cavity (lines) and the single unit cell (stars) at the near-infrared wavelengths. The electric and magnetic field intensity enhancement is averaged in the nanocavities. (c) Calculated scattering cross-sections of multipolar contributions in the nanocavities in log scale. Cscapand Cscamdenote scattering cross-sections of electric and magnetic dipoles, respectively.

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To verify the origin of simultaneous electric and magnetic hotspots in terms of multipole scatterings, the electric and magnetic dipolar contributions are calculated. Multipole calculation is conducted inside the rectangular nanocavity rather than the whole unit cell aperture cavity. As shown in Fig. 3(c), y-directional electric dipole plays dominant role in simultaneous nanofocusing of electric and magnetic fields when magnetic dipolar nanofocusing is suppressed. As shown in Eqs. (1), physical meanings of electric dipole containing both electric and toroidal parts and magnetic dipole are totally different [43–45].

pα=1iω{d3rJαωj0(kr)+k22d3r[3(rJω)rαr2Jαω]j2(kr)(kr)2},
mα=32d3r(r×Jω)αj1(kr)kr(α=x,y,z),
Cscatotal=Cscap+Cscam+CscaQe+CscaQm=k46πε02|Einc|2[α(|pα|2+|mα|2c2)+1120αβ(|kQαβ|2+|kQαβc|2)+],(α=x,y,z),
where J, r, k, and jn denote electric current density, position vector, wave number, and the first kind spherical Bessel function. Electric part, the first term in the parentheses in Eq. (1), describes scattering by current density oscillation which is parallel to electric dipole moment. On the other hand, toroidal part, the second term in the parentheses in Eq. (1), accounts for contribution of circulating magnetic field on the surface normal to the electric dipole moment which is induced from toroid-like circulation of current density. Rigorous expressions in Eqs. (2) and (3) of magnetic dipole moment and scattering cross-sections of electric, magnetic, and higher-order multipoles were adopted to investigate multipolar contributions for the enhanced simultaneous nanofocusing [43–45]. Contributions of electric and magnetic quadrupoles are excluded in the plot of Fig. 3(c) as the values are extremely low compared to other dominant terms.

In Fig. 3(b), there are three noticeable enhancement peaks at the wavelengths of 1120, 1188, and 1288 nm in the spectra of averaged electromagnetic field intensity enhancement. Those three peaks show different characteristics of enhancement as shown in Fig. 4. Firstly, we analyze differences of performances and field distributions between the peaks at 1120 and 1188 nm. The target peak at 1120 nm shows markedly higher enhancement of electric field and slightly lower magnetic field enhancement compared to the peak at 1188 nm. The better nanofocusing performance is synthetically achieved at the resonant peak of 1120 nm since the most fundamental contribution of general light-matter interaction is based on electric dipolar response of matter. Secondly, we consider characteristics of the third peak. Under the optimized period conditions, the unintended multipolar Fano-like resonance [Fig. 3(b)] appears at 1288 nm with suppression of 1st and −1st order diffractions along y-direction [51]. Even though average magnetic field intensity is maximally enhanced at 1288 nm, it is not good for electric field enhancement compared to the other peaks [Figs. 3(b) and 4].

 

Fig. 4 (a-c) Electric and (d-f) magnetic energy density profiles at the metal cross-section in the middle at the wavelength of 1120, 1188, and 1288 nm (we and wm are equally normalized in (a-c) and (d-f), respectively.)

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As shown in Fig. 4(c), critical delivery of electric energy into the elongated nanocavity fails at 1288 nm. Hence, this peak would be more appropriate for applications of magnetic field nanofocusing rather than simultaneous nanofocusing of electric and magnetic energy. As a result, at the original target wavelength of 1120 nm, the optimized metasurface cavity shows the best performance for our goal of simultaneous enhancement of electric and magnetic fields.

2.3 Experimental demonstration of the plasmonic metasurface cavity

For experimental verification, we measure transmission spectrum with a custom-built free-space near-infrared spectroscopy setup as shown in Fig. 5(a). Comparison between numerical and measured characteristics of transmission resonance at the target wavelength (1120 nm) is conducted for experimental verification of field enhancement in the metasurface cavity. The super-continuum light source (NKT Photonics, Super EXTREME EXR 15) is used for a broadband source and the transmitted signal is collected through an optical fiber and measured by optical spectrum analyzer (ANDO, AQ6317B).

 

Fig. 5 (a) Schematic illustration of the custom-built spectroscopy setup for near-infrared metamaterial measurements (b) Field enhanced scanning electron microscopy image of the fabricated meta-cavity and its magnified image (c) Normalized transmission spectrum results by experimental measurement and numerical calculation.

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The plasmonic metasurface cavity sample is fabricated using e-beam lithography processes with lift-off. The structures with size of 220 μm by 220 μm are defined using the negative tone resist (ALLRESIST, AR-N 7520.18) by standard electron-beam lithography (ELIONIX ELS-7800, 80 kV, and 50 pA).

As shown in Fig. 5(c), the measured transmission spectrum through the sample shows the strong similar peak at the wavelength of 1120 nm and it matches well with the peak that appears in the numerically calculated transmission spectrum. We used plano-convex lens (focal length of 150 mm) rather than objective lens to reduce angular spectrum spreading of incident source and increase depth of focus [52,53].

3. Conclusion

In this paper, a novel large-area nanofocusing device for large simultaneous enhancement of electric and magnetic fields is demonstrated. By nanofocusing electric dipole containing both electric and toroidal parts via constructive interference of SPs in the metasurface cavity, the electromagnetic field enhancement is achieved in large area where size of each hotspot has deep subwavelength volume (~λ3/538).

The proposed concept can be easily integrated with various emitters including quantum dots and rare-earth ions for boosting multipolar contributions of spontaneous emission or stimulated emission. Moreover, polarization dependent operation of the device can be applied to optically switchable hotspot generation. The presented mechanism would be also fruitful for other nanoscale light-matter interactions based on both electric and magnetic manners including near-field imaging and spectroscopy, multipolar nonlinear optics, bio-molecular sensing, and quantum optics.

Funding

National Research Foundation (NRF-21A20131612805, NRF-2017R1E1A1A03070501, CAMM-2014M3A6B3063708, NRF-2015R1A5A1037668); Ministry of Science and ICT (MSIT) of the Korean government (NRF-2016H1A2A1906519).

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References

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  1. N. C. Lindquist, J. Jose, S. Cherukulappurath, X. Chen, T. W. Johnson, and S. H. Oh, “Tip‐based plasmonics: squeezing light with metallic nanoprobes,” Laser Photonics Rev. 7(4), 453–477 (2013).
    [Crossref]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  3. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
    [Crossref] [PubMed]
  4. A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20(12), 4813–4815 (2004).
    [Crossref] [PubMed]
  5. S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(2), 1565–1588 (2011).
    [Crossref] [PubMed]
  6. Y. Lee, S.-J. Kim, H. Park, and B. Lee, “Metamaterials and metasurfaces for sensor applications,” Sensors (Basel) 17(8), 1726 (2017).
    [Crossref] [PubMed]
  7. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
    [Crossref]
  8. F. F. Lu, T. Li, X. P. Hu, Q. Q. Cheng, S. N. Zhu, and Y. Y. Zhu, “Efficient second-harmonic generation in nonlinear plasmonic waveguide,” Opt. Lett. 36(17), 3371–3373 (2011).
    [Crossref] [PubMed]
  9. M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
    [Crossref] [PubMed]
  10. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
    [Crossref]
  11. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
    [Crossref]
  12. K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
    [Crossref]
  13. G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
    [Crossref]
  14. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110(23), 237401 (2013).
    [Crossref] [PubMed]
  15. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
    [Crossref] [PubMed]
  16. E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express 16(1), 45–57 (2008).
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  17. H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
    [Crossref]
  18. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, “Gap-dependent optical coupling of single “Bowtie” nanoantennas resonant in the visible,” Nano Lett. 4(5), 957–961 (2004).
    [Crossref]
  19. K. Şendur and W. Challener, “Near-field radiation of bow-tie antennas and apertures at optical frequencies,” J. Microsc. 210(3), 279–283 (2003).
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  20. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
    [Crossref] [PubMed]
  21. P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Plasmon filters and resonators in metal-insulator-metal waveguides,” Opt. Express 20(4), 3408–3423 (2012).
    [Crossref] [PubMed]
  22. J. Yang, C. Sauvan, A. Jouanin, S. Collin, J.-L. Pelouard, and P. Lalanne, “Ultrasmall metal-insulator-metal nanoresonators: impact of slow-wave effects on the quality factor,” Opt. Express 20(15), 16880–16891 (2012).
    [Crossref]
  23. Z. Li, J. Kou, M. Kim, J. O. Lee, and H. Choo, “Highly efficient and tailorable on-chip metal-insulator-metal plasmonic nanofocusing cavity,” ACS Photonics 1(10), 944–953 (2014).
    [Crossref]
  24. C. Zhang, J. Fang, W. Yang, Q. Song, and S. Xiao, “Enhancing the magnetic resonance via strong coupling in optical metamaterials,” Adv. Opt. Mater. 5(20), 1700469 (2017).
    [Crossref]
  25. S. Dobmann, A. Kriesch, D. Ploss, and U. Peschel, “Near-field analysis of bright and dark modes on plasmonic metasurfaces showing extraordinary suppressed transmission,” Adv. Opt. Mater. 2(10), 990–999 (2014).
    [Crossref]
  26. T. J. Antosiewicz, P. Wróbel, and T. Szoplik, “Magnetic field concentrator for probing optical magnetic metamaterials,” Opt. Express 18(25), 25906–25911 (2010).
    [Crossref] [PubMed]
  27. T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
    [Crossref] [PubMed]
  28. Z. Gao, L. Shen, E. Li, L. Xu, and Z. Wang, “Cross-diabolo nanoantenna for localizing and enhancing magnetic field with arbitrary polarization,” J. Lightwave Technol. 30(6), 829–833 (2012).
    [Crossref]
  29. N. Zhou, E. C. Kinzel, and X. Xu, “Complementary bowtie aperture for localizing and enhancing optical magnetic field,” Opt. Lett. 36(15), 2764–2766 (2011).
    [Crossref] [PubMed]
  30. S.-J. Kim, S. Yoo, K. Lee, J. Kim, Y. Lee, and B. Lee, “Critical nanofocusing of magnetic dipole moment using a closed plasmonic tip,” Opt. Express 25(13), 14077–14088 (2017).
    [Crossref] [PubMed]
  31. D. Lee and D.-S. Kim, “Light scattering of rectangular slot antennas: parallel magnetic vector vs perpendicularr electric vector,” Sci. Rep. 6(1), 18935 (2016).
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  32. K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photonics 1(1), 53–56 (2007).
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  33. D. K. Singh, J. S. Ahn, S. Koo, T. Kang, J. Kim, S. Lee, N. Park, and D.-S. Kim, “Selective electric and magnetic sensitivity of aperture probes,” Opt. Express 23(16), 20820–20828 (2015).
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  34. M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
    [Crossref] [PubMed]
  35. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
    [Crossref] [PubMed]
  36. M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
    [Crossref] [PubMed]
  37. L. Aigouy, A. Cazé, P. Gredin, M. Mortier, and R. Carminati, “Mapping and quantifying electric and magnetic dipole luminescence at the nanoscale,” Phys. Rev. Lett. 113(7), 076101 (2014).
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  38. D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
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  39. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
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  41. Y. Chen, Y. Chen, J. Chu, and X. Xu, “Bridged bowtie aperture antenna for producing an electromagnetic hot spot,” ACS Photonics 4(3), 567–575 (2017).
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  42. S.-J. Kim, S.-E. Mun, Y. Lee, H. Park, J. Hong, and B. Lee, “Nanofocusing of toroidal dipole for simultaneously enhanced electric and magnetic fields using plasmonic waveguide,” J. Lightwave Technol. 36(10), 1882–1889 (2018).
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  43. I. Fernandez-Corbaton, S. Nanz, and C. Rockstuhl, “On the dynamic toroidal multipoles from localized electric current distributions,” Sci. Rep. 7(1), 7527 (2017).
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  44. I. Fernandez-Corbaton, S. Nanz, R. Alaee, and C. Rockstuhl, “Exact dipolar moments of a localized electric current distribution,” Opt. Express 23(26), 33044–33064 (2015).
    [Crossref] [PubMed]
  45. R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407(15), 17–21 (2018).
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  46. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
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  48. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
    [Crossref]
  49. N. A. Issa and R. Guckenberger, “Optical nanofocusing on tapered metallic waveguides,” Plasmonics 2(1), 31–37 (2007).
    [Crossref]
  50. D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmons by a tapered gap,” Phys. Rev. B 75(3), 035431 (2007).
    [Crossref]
  51. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [Crossref] [PubMed]
  52. S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7, 12323 (2016).
    [Crossref] [PubMed]
  53. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
    [Crossref] [PubMed]

2018 (2)

S.-J. Kim, S.-E. Mun, Y. Lee, H. Park, J. Hong, and B. Lee, “Nanofocusing of toroidal dipole for simultaneously enhanced electric and magnetic fields using plasmonic waveguide,” J. Lightwave Technol. 36(10), 1882–1889 (2018).
[Crossref]

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407(15), 17–21 (2018).
[Crossref]

2017 (6)

I. Fernandez-Corbaton, S. Nanz, and C. Rockstuhl, “On the dynamic toroidal multipoles from localized electric current distributions,” Sci. Rep. 7(1), 7527 (2017).
[Crossref] [PubMed]

Y. Chen, Y. Chen, J. Chu, and X. Xu, “Bridged bowtie aperture antenna for producing an electromagnetic hot spot,” ACS Photonics 4(3), 567–575 (2017).
[Crossref]

Y. Lee, S.-J. Kim, H. Park, and B. Lee, “Metamaterials and metasurfaces for sensor applications,” Sensors (Basel) 17(8), 1726 (2017).
[Crossref] [PubMed]

C. Zhang, J. Fang, W. Yang, Q. Song, and S. Xiao, “Enhancing the magnetic resonance via strong coupling in optical metamaterials,” Adv. Opt. Mater. 5(20), 1700469 (2017).
[Crossref]

S.-J. Kim, S. Yoo, K. Lee, J. Kim, Y. Lee, and B. Lee, “Critical nanofocusing of magnetic dipole moment using a closed plasmonic tip,” Opt. Express 25(13), 14077–14088 (2017).
[Crossref] [PubMed]

D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
[Crossref]

2016 (2)

D. Lee and D.-S. Kim, “Light scattering of rectangular slot antennas: parallel magnetic vector vs perpendicularr electric vector,” Sci. Rep. 6(1), 18935 (2016).
[Crossref] [PubMed]

S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7, 12323 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (7)

L. Aigouy, A. Cazé, P. Gredin, M. Mortier, and R. Carminati, “Mapping and quantifying electric and magnetic dipole luminescence at the nanoscale,” Phys. Rev. Lett. 113(7), 076101 (2014).
[Crossref] [PubMed]

S. Dobmann, A. Kriesch, D. Ploss, and U. Peschel, “Near-field analysis of bright and dark modes on plasmonic metasurfaces showing extraordinary suppressed transmission,” Adv. Opt. Mater. 2(10), 990–999 (2014).
[Crossref]

Z. Li, J. Kou, M. Kim, J. O. Lee, and H. Choo, “Highly efficient and tailorable on-chip metal-insulator-metal plasmonic nanofocusing cavity,” ACS Photonics 1(10), 944–953 (2014).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

B. J. Roxworthy and K. C. Toussaint., “Simultaneously tuning the electric and magnetic plasmonic response using capped bi-metallic nanoantennas,” Nanoscale 6(4), 2270–2274 (2014).
[Crossref] [PubMed]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
[Crossref] [PubMed]

2013 (2)

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110(23), 237401 (2013).
[Crossref] [PubMed]

N. C. Lindquist, J. Jose, S. Cherukulappurath, X. Chen, T. W. Johnson, and S. H. Oh, “Tip‐based plasmonics: squeezing light with metallic nanoprobes,” Laser Photonics Rev. 7(4), 453–477 (2013).
[Crossref]

2012 (6)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

K. J. Russell, T.-L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[Crossref]

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Z. Gao, L. Shen, E. Li, L. Xu, and Z. Wang, “Cross-diabolo nanoantenna for localizing and enhancing magnetic field with arbitrary polarization,” J. Lightwave Technol. 30(6), 829–833 (2012).
[Crossref]

P. Neutens, L. Lagae, G. Borghs, and P. Van Dorpe, “Plasmon filters and resonators in metal-insulator-metal waveguides,” Opt. Express 20(4), 3408–3423 (2012).
[Crossref] [PubMed]

J. Yang, C. Sauvan, A. Jouanin, S. Collin, J.-L. Pelouard, and P. Lalanne, “Ultrasmall metal-insulator-metal nanoresonators: impact of slow-wave effects on the quality factor,” Opt. Express 20(15), 16880–16891 (2012).
[Crossref]

2011 (5)

N. Zhou, E. C. Kinzel, and X. Xu, “Complementary bowtie aperture for localizing and enhancing optical magnetic field,” Opt. Lett. 36(15), 2764–2766 (2011).
[Crossref] [PubMed]

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[Crossref] [PubMed]

S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(2), 1565–1588 (2011).
[Crossref] [PubMed]

F. F. Lu, T. Li, X. P. Hu, Q. Q. Cheng, S. N. Zhu, and Y. Y. Zhu, “Efficient second-harmonic generation in nonlinear plasmonic waveguide,” Opt. Lett. 36(17), 3371–3373 (2011).
[Crossref] [PubMed]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[Crossref]

2010 (4)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[Crossref] [PubMed]

T. J. Antosiewicz, P. Wróbel, and T. Szoplik, “Magnetic field concentrator for probing optical magnetic metamaterials,” Opt. Express 18(25), 25906–25911 (2010).
[Crossref] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

2009 (1)

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science 326(5952), 550–553 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (4)

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photonics 1(1), 53–56 (2007).
[Crossref]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[Crossref] [PubMed]

N. A. Issa and R. Guckenberger, “Optical nanofocusing on tapered metallic waveguides,” Plasmonics 2(1), 31–37 (2007).
[Crossref]

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, and X. Zhang, “Local electric field enhancement during nanofocusing of plasmons by a tapered gap,” Phys. Rev. B 75(3), 035431 (2007).
[Crossref]

2006 (1)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[Crossref] [PubMed]

2005 (2)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94(1), 017402 (2005).
[Crossref] [PubMed]

2004 (4)

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, “Gap-dependent optical coupling of single “Bowtie” nanoantennas resonant in the visible,” Nano Lett. 4(5), 957–961 (2004).
[Crossref]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[Crossref] [PubMed]

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20(12), 4813–4815 (2004).
[Crossref] [PubMed]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[Crossref]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

K. Şendur and W. Challener, “Near-field radiation of bow-tie antennas and apertures at optical frequencies,” J. Microsc. 210(3), 279–283 (2003).
[Crossref] [PubMed]

1965 (1)

Ahn, J. S.

Aigouy, L.

L. Aigouy, A. Cazé, P. Gredin, M. Mortier, and R. Carminati, “Mapping and quantifying electric and magnetic dipole luminescence at the nanoscale,” Phys. Rev. Lett. 113(7), 076101 (2014).
[Crossref] [PubMed]

Akselrod, G. M.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Alaee, R.

R. Alaee, C. Rockstuhl, and I. Fernandez-Corbaton, “An electromagnetic multipole expansion beyond the long-wavelength approximation,” Opt. Commun. 407(15), 17–21 (2018).
[Crossref]

I. Fernandez-Corbaton, S. Nanz, R. Alaee, and C. Rockstuhl, “Exact dipolar moments of a localized electric current distribution,” Opt. Express 23(26), 33044–33064 (2015).
[Crossref] [PubMed]

Alù, A.

D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
[Crossref]

Antosiewicz, T. J.

Argyropoulos, C.

G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8(11), 835–840 (2014).
[Crossref]

Atwater, H. A.

S. Kim, M. S. Jang, V. W. Brar, Y. Tolstova, K. W. Mauser, and H. A. Atwater, “Electronically tunable extraordinary optical transmission in graphene plasmonic ribbons coupled to subwavelength metallic slit arrays,” Nat. Commun. 7, 12323 (2016).
[Crossref] [PubMed]

Baida, F. I.

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011).
[Crossref] [PubMed]

Baranov, D. G.

D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017).
[Crossref]

Barnard, E. S.

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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
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N. C. Lindquist, J. Jose, S. Cherukulappurath, X. Chen, T. W. Johnson, and S. H. Oh, “Tip‐based plasmonics: squeezing light with metallic nanoprobes,” Laser Photonics Rev. 7(4), 453–477 (2013).
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B. J. Roxworthy and K. C. Toussaint., “Simultaneously tuning the electric and magnetic plasmonic response using capped bi-metallic nanoantennas,” Nanoscale 6(4), 2270–2274 (2014).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic illustration of the proposed funneled aperture cavity for novel electric dipolar nanofocusing (θ = 15°, d2 = 750 nm, w0 = 70 nm, d1 = 355 nm, and h = 100 nm) at the wavelength of 1120 nm. Spatial distributions of (b) induced x-directional electric current (Jx), (c) y-directional electric field (Ey), and (d) z-directional magnetic field (Hz) at the cross-section of metal in the middle, respectively.
Fig. 2
Fig. 2 Normalized Ez field distribution describing SP scattering (a) at gold/glass interface and (b) at air/gold interface (c) Angular SP radiation pattern for the unit cell at the interface of the gold/glass and air/gold interface
Fig. 3
Fig. 3 (a) Schematic diagram describing the top view of the metasurface cavity with periodically arranged unit cells (Λx = 1200 nm and Λy = 890 nm). The black-dotted line and arrow denote the rectangular nanocavity region where hotspot is excited. (b) Intensity enhancement factors for the periodic metasurface cavity (lines) and the single unit cell (stars) at the near-infrared wavelengths. The electric and magnetic field intensity enhancement is averaged in the nanocavities. (c) Calculated scattering cross-sections of multipolar contributions in the nanocavities in log scale. C sca p and C sca m denote scattering cross-sections of electric and magnetic dipoles, respectively.
Fig. 4
Fig. 4 (a-c) Electric and (d-f) magnetic energy density profiles at the metal cross-section in the middle at the wavelength of 1120, 1188, and 1288 nm (we and wm are equally normalized in (a-c) and (d-f), respectively.)
Fig. 5
Fig. 5 (a) Schematic illustration of the custom-built spectroscopy setup for near-infrared metamaterial measurements (b) Field enhanced scanning electron microscopy image of the fabricated meta-cavity and its magnified image (c) Normalized transmission spectrum results by experimental measurement and numerical calculation.

Equations (3)

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p α = 1 iω { d 3 r J α ω j 0 ( kr )+ k 2 2 d 3 r [ 3( r J ω ) r α r 2 J α ω ] j 2 ( kr ) ( kr ) 2 },
m α = 3 2 d 3 r ( r× J ω ) α j 1 ( kr ) kr (α=x,y,z) ,
C sca total = C sca p + C sca m + C sca Q e + C sca Q m = k 4 6π ε 0 2 | E inc | 2 [ α ( | p α | 2 + | m α | 2 c 2 ) + 1 120 αβ ( | k Q αβ | 2 + | k Q αβ c | 2 ) + ], (α=x,y,z),

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