Abstract

Magnetic polariton is a significant mode in tailoring thermal radiative properties with micro/nanostructures metamaterials and can be explained by equivalent inductor-capacitor circuit model. However, the equivalent inductor-capacitor circuit model is out of operation when the magnetic polariton resonance frequency is close to the surface plasmon polariton excitation frequency and cases of oblique incidence. In this work, we present a mutual inductor-inductor-capacitor circuit model to describe magnetic polariton resonance conditions. The mechanism of coupling between the surface plasmon polariton and magnetic polariton is explained from the perspective of equivalent circuits. The interaction between the surface plasmon polariton and magnetic polariton is studied and considered as a mutual inductance in the MLC circuit model. This model is still applicable in the case of oblique incidence. Slit arrays with different geometric parameters and incident angles are calculated to verify the rationality of the mutual inductor-inductor-capacitor circuit model. This study may allow us to predict features and parameters and achieve tailoring of the thermal radiative properties of the micro/nano-structures metamaterials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

Z. X. Jia, Y. Shuai, M. Li, Y. Guo, and H. P. Tan, “Enhancement radiative cooling performance of nanoparticle crystal via oxidation,” J. Quant. Spectrosc. Radiat. Transf. 207(1), 23–31 (2018).
[Crossref]

2017 (5)

J. Y. Chang, H. Wang, and L. Wang, “Tungsten nanowire metamaterials as selective solar thermal absorbers by excitation of magnetic polaritons,” J. Heat Transf. 139(5), 052401 (2017).
[Crossref]

Z. H. Zheng, X. L. Liu, A. Wang, and Y. M. Xuan, “Graphene-assisted near-field radiative thermal rectifier based on phase transition of vanadium dioxide (VO2),” Int. J. Heat Mass Transf. 109(1), 63–72 (2017).
[Crossref]

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Y. Zhao and C. J. Fu, “Design of multiband selective near-perfect metamaterial absorbers with SiO2 cylinder/rectangle shell horizontally embedded in opaque silver substrate,” Int. J. Heat Mass Transf. 113(1), 281–285 (2017).
[Crossref]

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

2016 (1)

Y. B. Liu, R. Jin, J. Qiu, and L. H. Liu, “Spectral radiative properties of a nickel porous microstructure and magnetic polariton resonance for light trapping,” Int. J. Heat Mass Transf. 98(1), 833–844 (2016).
[Crossref]

2015 (2)

H. Wang and L. Wang, “Tailoring thermal radiative properties with film-coupled concave grating metamaterials,” J. Quant. Spectrosc. Radiat. Transf. 158(1), 127–135 (2015).
[Crossref]

J. M. Zhao and Z. M. Zhang, “Electromagnetic energy storage and power dissipation in nanostructures,” J. Quant. Spectrosc. Radiat. Transf. 151(1), 49–57 (2015).
[Crossref]

2014 (4)

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 50–57 (2014).
[Crossref]

B. Jae Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. Jin Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transf. 136(7), 072702 (2014).
[Crossref]

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 81–89 (2014).
[Crossref]

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transf. 149(1), 33–40 (2014).
[Crossref]

2013 (5)

Y. B. Chen and C. J. Chen, “Interaction between the magnetic polariton and surface plasmon polariton,” Opt. Commun. 297(1), 169–175 (2013).
[Crossref]

X. L. Liu, B. Zhao, and Z. M. Zhang, “Wide-angle near infrared polarizer with extremely high extinction ratio,” Opt. Express 21(9), 10502–10510 (2013).
[Crossref] [PubMed]

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[Crossref] [PubMed]

Z. M. Zhang and L. P. Wang, “Measurements and modeling of the spectral and directional radiative properties of micro/nanostructured materials,” Int. J. Thermophys. 34(12), 2209–2242 (2013).
[Crossref]

B. Zhao, L. P. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transf. 67(1), 637–645 (2013).
[Crossref]

2011 (1)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

2010 (1)

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

2009 (2)

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

L. Wang and Z. Zhang, “Resonance transmission or absorption in deep gratings explained by magnetic polaritons,” Appl. Phys. Lett. 95(11), 111904 (2009).
[Crossref]

2008 (1)

2007 (3)

V. D. Lam, J. B. Kim, S. J. Lee, Y. P. Lee, and J. Y. Rhee, “Dependence of the magnetic-resonance frequency on the cut-wire width of cut-wire pair medium,” Opt. Express 15(25), 16651–16656 (2007).
[Crossref] [PubMed]

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269(2), 411–417 (2007).
[Crossref]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

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]

1999 (1)

J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

1998 (1)

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80(25), 5667–5670 (1998).
[Crossref]

Baxter, J.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Bhatt, G.

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

Bian, Z.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Buddhiraju, S.

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

Chang, J. Y.

J. Y. Chang, H. Wang, and L. Wang, “Tungsten nanowire metamaterials as selective solar thermal absorbers by excitation of magnetic polaritons,” J. Heat Transf. 139(5), 052401 (2017).
[Crossref]

Chen, C. J.

Y. B. Chen and C. J. Chen, “Interaction between the magnetic polariton and surface plasmon polariton,” Opt. Commun. 297(1), 169–175 (2013).
[Crossref]

Chen, G.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Chen, K.

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

Chen, Y. B.

Y. B. Chen and C. J. Chen, “Interaction between the magnetic polariton and surface plasmon polariton,” Opt. Commun. 297(1), 169–175 (2013).
[Crossref]

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269(2), 411–417 (2007).
[Crossref]

Chen, Y.-B.

B. Jae Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. Jin Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transf. 136(7), 072702 (2014).
[Crossref]

Chiu, F.-C.

B. Jae Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. Jin Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transf. 136(7), 072702 (2014).
[Crossref]

Danielson, D.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

David, S. N.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Dresselhaus, M. S.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Economon, E. N.

Economou, E. N.

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]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[Crossref] [PubMed]

Fan, S.

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
[Crossref] [PubMed]

Fedorov, A. G.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Fisher, T. S.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Fu, C. J.

Y. Zhao and C. J. Fu, “Design of multiband selective near-perfect metamaterial absorbers with SiO2 cylinder/rectangle shell horizontally embedded in opaque silver substrate,” Int. J. Heat Mass Transf. 113(1), 281–285 (2017).
[Crossref]

Garci’a-Vidal, F. J.

J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Guo, Y.

Z. X. Jia, Y. Shuai, M. Li, Y. Guo, and H. P. Tan, “Enhancement radiative cooling performance of nanoparticle crystal via oxidation,” J. Quant. Spectrosc. Radiat. Transf. 207(1), 23–31 (2018).
[Crossref]

Han, S.

B. Jae Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. Jin Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transf. 136(7), 072702 (2014).
[Crossref]

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Jae Lee, B.

B. Jae Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. Jin Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transf. 136(7), 072702 (2014).
[Crossref]

Jeon, K. S.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Jia, Z. X.

Z. X. Jia, Y. Shuai, M. Li, Y. Guo, and H. P. Tan, “Enhancement radiative cooling performance of nanoparticle crystal via oxidation,” J. Quant. Spectrosc. Radiat. Transf. 207(1), 23–31 (2018).
[Crossref]

Jin, R.

Y. B. Liu, R. Jin, J. Qiu, and L. H. Liu, “Spectral radiative properties of a nickel porous microstructure and magnetic polariton resonance for light trapping,” Int. J. Heat Mass Transf. 98(1), 833–844 (2016).
[Crossref]

Jin Lee, H.

B. Jae Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. Jin Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transf. 136(7), 072702 (2014).
[Crossref]

Jones, C. W.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Kafesaki, M.

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]

Kim, H. M.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Kim, J. B.

Kortshagen, U.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Koschny, T.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[Crossref] [PubMed]

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]

Lam, V. D.

Lee, B. J.

Lee, S. J.

Lee, Y. P.

Li, M.

Z. X. Jia, Y. Shuai, M. Li, Y. Guo, and H. P. Tan, “Enhancement radiative cooling performance of nanoparticle crystal via oxidation,” J. Quant. Spectrosc. Radiat. Transf. 207(1), 23–31 (2018).
[Crossref]

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Liang, Y.

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 50–57 (2014).
[Crossref]

Lim, D. K.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Lipson, M.

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

Liu, L. H.

Y. B. Liu, R. Jin, J. Qiu, and L. H. Liu, “Spectral radiative properties of a nickel porous microstructure and magnetic polariton resonance for light trapping,” Int. J. Heat Mass Transf. 98(1), 833–844 (2016).
[Crossref]

Liu, X. L.

Z. H. Zheng, X. L. Liu, A. Wang, and Y. M. Xuan, “Graphene-assisted near-field radiative thermal rectifier based on phase transition of vanadium dioxide (VO2),” Int. J. Heat Mass Transf. 109(1), 63–72 (2017).
[Crossref]

X. L. Liu, B. Zhao, and Z. M. Zhang, “Wide-angle near infrared polarizer with extremely high extinction ratio,” Opt. Express 21(9), 10502–10510 (2013).
[Crossref] [PubMed]

Liu, Y. B.

Y. B. Liu, R. Jin, J. Qiu, and L. H. Liu, “Spectral radiative properties of a nickel porous microstructure and magnetic polariton resonance for light trapping,” Int. J. Heat Mass Transf. 98(1), 833–844 (2016).
[Crossref]

Lou, R.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Ma, Y.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Maginn, E.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Manthiram, A.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
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Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Nozik, A.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Pendry, J. B.

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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J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
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Porto, J. A.

J. A. Porto, F. J. Garcı’a-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
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Preist, T. W.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80(25), 5667–5670 (1998).
[Crossref]

Qiu, J.

Y. B. Liu, R. Jin, J. Qiu, and L. H. Liu, “Spectral radiative properties of a nickel porous microstructure and magnetic polariton resonance for light trapping,” Int. J. Heat Mass Transf. 98(1), 833–844 (2016).
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E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
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E. Rephaeli, A. Raman, and S. Fan, “Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling,” Nano Lett. 13(4), 1457–1461 (2013).
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Rolison, D. R.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Sakurai, A.

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transf. 149(1), 33–40 (2014).
[Crossref]

Sambles, J. R.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80(25), 5667–5670 (1998).
[Crossref]

Sands, T.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Shamonina, E.

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Shi, L.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Sholl, D.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Shuai, Y.

Z. X. Jia, Y. Shuai, M. Li, Y. Guo, and H. P. Tan, “Enhancement radiative cooling performance of nanoparticle crystal via oxidation,” J. Quant. Spectrosc. Radiat. Transf. 207(1), 23–31 (2018).
[Crossref]

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 50–57 (2014).
[Crossref]

B. Zhao, L. P. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transf. 67(1), 637–645 (2013).
[Crossref]

Sobnack, M. B.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80(25), 5667–5670 (1998).
[Crossref]

Solymar, L.

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

Soukoulis, C. M.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[Crossref] [PubMed]

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]

Suh, Y. D.

D. K. Lim, K. S. Jeon, H. M. Kim, J. M. Nam, and Y. D. Suh, “Nanogap-engineerable Raman-active nanodumbbells for single-molecule detection,” Nat. Mater. 9(1), 60–67 (2010).
[Crossref] [PubMed]

Tan, G.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Tan, H.

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 50–57 (2014).
[Crossref]

Tan, H. P.

Z. X. Jia, Y. Shuai, M. Li, Y. Guo, and H. P. Tan, “Enhancement radiative cooling performance of nanoparticle crystal via oxidation,” J. Quant. Spectrosc. Radiat. Transf. 207(1), 23–31 (2018).
[Crossref]

Tan, W. C.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80(25), 5667–5670 (1998).
[Crossref]

Wang, A.

Z. H. Zheng, X. L. Liu, A. Wang, and Y. M. Xuan, “Graphene-assisted near-field radiative thermal rectifier based on phase transition of vanadium dioxide (VO2),” Int. J. Heat Mass Transf. 109(1), 63–72 (2017).
[Crossref]

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Wang, H.

J. Y. Chang, H. Wang, and L. Wang, “Tungsten nanowire metamaterials as selective solar thermal absorbers by excitation of magnetic polaritons,” J. Heat Transf. 139(5), 052401 (2017).
[Crossref]

H. Wang and L. Wang, “Tailoring thermal radiative properties with film-coupled concave grating metamaterials,” J. Quant. Spectrosc. Radiat. Transf. 158(1), 127–135 (2015).
[Crossref]

Wang, L.

J. Y. Chang, H. Wang, and L. Wang, “Tungsten nanowire metamaterials as selective solar thermal absorbers by excitation of magnetic polaritons,” J. Heat Transf. 139(5), 052401 (2017).
[Crossref]

H. Wang and L. Wang, “Tailoring thermal radiative properties with film-coupled concave grating metamaterials,” J. Quant. Spectrosc. Radiat. Transf. 158(1), 127–135 (2015).
[Crossref]

L. Wang and Z. Zhang, “Resonance transmission or absorption in deep gratings explained by magnetic polaritons,” Appl. Phys. Lett. 95(11), 111904 (2009).
[Crossref]

Wang, L. P.

B. Zhao, L. P. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transf. 67(1), 637–645 (2013).
[Crossref]

Z. M. Zhang and L. P. Wang, “Measurements and modeling of the spectral and directional radiative properties of micro/nanostructured materials,” Int. J. Thermophys. 34(12), 2209–2242 (2013).
[Crossref]

B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328–11336 (2008).
[Crossref] [PubMed]

Wanstall, N. P.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80(25), 5667–5670 (1998).
[Crossref]

Wu, Y.

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Xuan, Y. M.

Z. H. Zheng, X. L. Liu, A. Wang, and Y. M. Xuan, “Graphene-assisted near-field radiative thermal rectifier based on phase transition of vanadium dioxide (VO2),” Int. J. Heat Mass Transf. 109(1), 63–72 (2017).
[Crossref]

Yang, R.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Yin, X.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Zhai, Y.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Zhang, Z.

L. Wang and Z. Zhang, “Resonance transmission or absorption in deep gratings explained by magnetic polaritons,” Appl. Phys. Lett. 95(11), 111904 (2009).
[Crossref]

Zhang, Z. M.

J. M. Zhao and Z. M. Zhang, “Electromagnetic energy storage and power dissipation in nanostructures,” J. Quant. Spectrosc. Radiat. Transf. 151(1), 49–57 (2015).
[Crossref]

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transf. 149(1), 33–40 (2014).
[Crossref]

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 81–89 (2014).
[Crossref]

Z. M. Zhang and L. P. Wang, “Measurements and modeling of the spectral and directional radiative properties of micro/nanostructured materials,” Int. J. Thermophys. 34(12), 2209–2242 (2013).
[Crossref]

X. L. Liu, B. Zhao, and Z. M. Zhang, “Wide-angle near infrared polarizer with extremely high extinction ratio,” Opt. Express 21(9), 10502–10510 (2013).
[Crossref] [PubMed]

B. Zhao, L. P. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transf. 67(1), 637–645 (2013).
[Crossref]

B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328–11336 (2008).
[Crossref] [PubMed]

Y. B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269(2), 411–417 (2007).
[Crossref]

Zhao, B.

B. Zhao, K. Chen, S. Buddhiraju, G. Bhatt, M. Lipson, and S. Fan, “High-performance near-field thermophotovoltaics for waste heat recovery,” Nano Energy 41(1), 344–350 (2017).
[Crossref]

B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transf. 135(1), 81–89 (2014).
[Crossref]

A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transf. 149(1), 33–40 (2014).
[Crossref]

B. Zhao, L. P. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transf. 67(1), 637–645 (2013).
[Crossref]

X. L. Liu, B. Zhao, and Z. M. Zhang, “Wide-angle near infrared polarizer with extremely high extinction ratio,” Opt. Express 21(9), 10502–10510 (2013).
[Crossref] [PubMed]

Zhao, D.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref] [PubMed]

Zhao, J. M.

J. M. Zhao and Z. M. Zhang, “Electromagnetic energy storage and power dissipation in nanostructures,” J. Quant. Spectrosc. Radiat. Transf. 151(1), 49–57 (2015).
[Crossref]

Zhao, Y.

Y. Zhao and C. J. Fu, “Design of multiband selective near-perfect metamaterial absorbers with SiO2 cylinder/rectangle shell horizontally embedded in opaque silver substrate,” Int. J. Heat Mass Transf. 113(1), 281–285 (2017).
[Crossref]

Zheng, Z. H.

Z. H. Zheng, X. L. Liu, A. Wang, and Y. M. Xuan, “Graphene-assisted near-field radiative thermal rectifier based on phase transition of vanadium dioxide (VO2),” Int. J. Heat Mass Transf. 109(1), 63–72 (2017).
[Crossref]

Zhou, J.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[Crossref] [PubMed]

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]

Appl. Phys. Lett. (1)

L. Wang and Z. Zhang, “Resonance transmission or absorption in deep gratings explained by magnetic polaritons,” Appl. Phys. Lett. 95(11), 111904 (2009).
[Crossref]

Energy Environ. Sci. (1)

J. Baxter, Z. Bian, G. Chen, D. Danielson, M. S. Dresselhaus, A. G. Fedorov, T. S. Fisher, C. W. Jones, E. Maginn, U. Kortshagen, A. Manthiram, A. Nozik, D. R. Rolison, T. Sands, L. Shi, D. Sholl, and Y. Wu, “Nanoscale design to enable the revolution in renewable energy,” Energy Environ. Sci. 2(6), 559–588 (2009).
[Crossref]

Int. J. Heat Mass Transf. (4)

Z. H. Zheng, X. L. Liu, A. Wang, and Y. M. Xuan, “Graphene-assisted near-field radiative thermal rectifier based on phase transition of vanadium dioxide (VO2),” Int. J. Heat Mass Transf. 109(1), 63–72 (2017).
[Crossref]

Y. Zhao and C. J. Fu, “Design of multiband selective near-perfect metamaterial absorbers with SiO2 cylinder/rectangle shell horizontally embedded in opaque silver substrate,” Int. J. Heat Mass Transf. 113(1), 281–285 (2017).
[Crossref]

B. Zhao, L. P. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transf. 67(1), 637–645 (2013).
[Crossref]

Y. B. Liu, R. Jin, J. Qiu, and L. H. Liu, “Spectral radiative properties of a nickel porous microstructure and magnetic polariton resonance for light trapping,” Int. J. Heat Mass Transf. 98(1), 833–844 (2016).
[Crossref]

Int. J. Thermophys. (1)

Z. M. Zhang and L. P. Wang, “Measurements and modeling of the spectral and directional radiative properties of micro/nanostructured materials,” Int. J. Thermophys. 34(12), 2209–2242 (2013).
[Crossref]

J. Heat Transf. (2)

J. Y. Chang, H. Wang, and L. Wang, “Tungsten nanowire metamaterials as selective solar thermal absorbers by excitation of magnetic polaritons,” J. Heat Transf. 139(5), 052401 (2017).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic of a slit array in the present study.
Fig. 2
Fig. 2 Reflectance ρ, transmittance τ and absorptance α at normal incidence for TM waves.
Fig. 3
Fig. 3 Electromagnetic field distributions at the MP1 resonant frequencies: (a) h = 1000nm at 3475 cm−1; (b) h = 400nm at 7914 cm−1; (c) h = 200nm at 13377 cm−1; (d) h = 100nm at 17961 cm−1. The contour plots indicate the magnitude of magnetic field and the arrows represent the direction of the electric field vectors.
Fig. 4
Fig. 4 Electromagnetic field distributions at the MP4 excitation frequencies: (a) h = 600nm at 19060 cm−1; (b) h = 1000nm at 13474 cm−1. The contour plots indicate the magnitude of magnetic field and the arrows represent the direction of the electric field vectors.
Fig. 5
Fig. 5 The MLC circuit model for MP1.
Fig. 6
Fig. 6 The MLC circuit model for MPn.
Fig. 7
Fig. 7 Illustration of the comparison between the previous LC model and MLC model with the geometric values: (a) Λ = 0.5μm, b = 0.05μm and h varies from 2nm to 1μm; (b) h = 0.4μm, b = 0.05μm and Λ varies from 52nm to 1450nm. The green line are the results calculated from the previous LC model [28] and the cyan-blue lines are calculated from the MLC circuit model.
Fig. 8
Fig. 8 Demonstration of incident angle effect on the magnetic resonance conditions with slit height h = 400nm, slit width b = 50nm and period Λ = 0.5μm. The cyan-blue lines are calculated from the MLC circuit model and yellow line is curve of SPP.

Tables (2)

Tables Icon

Table 1 Numerical values of the electric field and current density on Fig. 3. For location 1, the electric field vectors and current density only have z components; while for location 2, they only have x components.

Tables Icon

Table 2 MPn paramters of Fig. 7.

Equations (13)

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ε(ω)= ε +i ε = ε ω p 2 ω(ω+iγ)
k SPP = ω c ε ε+1
L= 0.5 μ 0 hb l h ε 0 ω 2 lδ ε ε 2 + ε 2
C= c 1 ε d ε 0 hl b
L w = w ε 0 ω( ω SPP ω )lδ ε ε 2 + ε 2
M= k 1 L L w
Z=2i[ ω(L+M) 1 ωC ]
ω MP1 = 1 (L+M)C
L n = 0.5 μ 0 b l h n 1 ε 0 ω 2 lδ h n ε ε 2 + ε 2
C n = c 1 ε d ε 0 l b h n
M= k 1 L n L w
Z=2in[ ω( L n +M ) 1 ω C n ]
ω MPn = 1 ( L n +M ) C n

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