Abstract

Analytical modelling of hysteresis is used to provide crucial prediction and insight for phase transitions in materials. Here we present a modified Maxwell Garnett model for analysing electromagnetic hysteresis. The model uses an asymmetric effective medium approximation to describe intermediate states in the phase change, establishing a link between effective medium and hysteresis analysis. Numerical calculation was performed on an example material, vanadium dioxide, for quantitative demonstration and future experimental verification. The model is easy to use, requires very few input parameters, and provides a phenomenological approach to describing electromagnetic hysteresis in various phase change materials.

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

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References

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    [Crossref]

2018 (1)

2017 (5)

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically reconfigurable metadevice employing nanostructured phase-change materials,” Nano Lett. 17(8), 4881–4885 (2017).
[Crossref] [PubMed]

O. Najera, M. Civelli, V. Dobrosavljevic, and M. J. Rozenberg, “Resolving the VO2 controversy: Mott mechanism dominates the insulator-to-metal transition,” Phys. Rev. B 95(3), 035113 (2017).
[Crossref]

A. Hatef, N. Zamani, and W. Johnston, “Coherent control of optical absorption and the energy transfer pathway of an infrared quantum dot hybridized with a VO2 nanoparticle,” J. Phys. Condens. Matter 29(15), 155305 (2017).
[Crossref] [PubMed]

2016 (2)

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

K. Ito, K. Nishikawa, and H. Iizuka, “Multilevel radiative thermal memory realized by the hysteretic metal-insulator transition of vanadium dioxide,” Appl. Phys. Lett. 108(5), 053507 (2016).
[Crossref]

2015 (1)

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

2014 (3)

N. Dávila, E. Merced, and N. Sepulveda, “Emmanuelle Merced, and Nelson Sepúlveda, “Electronically variable optical attenuator enabled by self-sensing in vanadium dioxide,” IEEE Photonics Technol. Lett. 26(10), 1011–1014 (2014).
[Crossref]

J. Zhang, E. Merced, N. Sepulveda, and X. B. Tan, “Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model,” Smart Mater. Struct. 23(12), 125017 (2014).
[Crossref]

J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, “Overview of emerging nonvolatile memory technologies,” Nanoscale Res. Lett. 9(1), 526 (2014).
[Crossref] [PubMed]

2013 (3)

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

G. Leahu, R. L. Voti, C. Sibilia, and M. Bertolotti, “Anomalous optical switching and thermal hysteresis during semiconductor-metal phase transition of VO2 films on Si substrate,” Appl. Phys. Lett. 103(23), 231114 (2013).
[Crossref]

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

2012 (1)

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

2011 (1)

Z. Yang, C. Y. Ko, and S. Ramanathan, “Oxide electronics utilizing ultrafast metal-insulator transitions,” Annu. Rev. Mater. Res. 41(1), 337–367 (2011).
[Crossref]

2009 (1)

2008 (1)

I. Pirozhenko and A. Lambrecht, “Influence of slab thickness on the Casimir force,” Phys. Rev. A 77(1), 013811 (2008).
[Crossref]

2007 (1)

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

2002 (1)

L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, “Modeling of the hysteretic metal-insulator transition in a vanadium dioxide infrared detector,” Opt. Eng. 41(10), 2582–2588 (2002).
[Crossref]

2001 (1)

T. Ung, L. M. Liz-Marzan, and P. Mulvaney, “Optical properties of thin films of Au@SiO2 particles,” J. Phys. Chem. B 105(17), 3441–3452 (2001).
[Crossref]

1968 (1)

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172(3), 788–798 (1968).
[Crossref]

Andreev, G. O.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Ang, S. S.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Atwater, H. A.

Aydin, K.

Balatsky, A. V.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Barker, A. S.

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172(3), 788–798 (1968).
[Crossref]

Basov, D. N.

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Berglund, C. N.

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172(3), 788–798 (1968).
[Crossref]

Bertolotti, M.

G. Leahu, R. L. Voti, C. Sibilia, and M. Bertolotti, “Anomalous optical switching and thermal hysteresis during semiconductor-metal phase transition of VO2 films on Si substrate,” Appl. Phys. Lett. 103(23), 231114 (2013).
[Crossref]

Bhaskaran, H.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Blanchard, R.

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

Boyd, E. M.

Brehm, M.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Cao, C. X.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Capasso, F.

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

Chae, B. G.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Chand, U.

J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, “Overview of emerging nonvolatile memory technologies,” Nanoscale Res. Lett. 9(1), 526 (2014).
[Crossref] [PubMed]

Chen, Z.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Civelli, M.

O. Najera, M. Civelli, V. Dobrosavljevic, and M. J. Rozenberg, “Resolving the VO2 controversy: Mott mechanism dominates the insulator-to-metal transition,” Phys. Rev. B 95(3), 035113 (2017).
[Crossref]

Dávila, N.

N. Dávila, E. Merced, and N. Sepulveda, “Emmanuelle Merced, and Nelson Sepúlveda, “Electronically variable optical attenuator enabled by self-sensing in vanadium dioxide,” IEEE Photonics Technol. Lett. 26(10), 1011–1014 (2014).
[Crossref]

de Almeida, L. A. L.

L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, “Modeling of the hysteretic metal-insulator transition in a vanadium dioxide infrared detector,” Opt. Eng. 41(10), 2582–2588 (2002).
[Crossref]

Deep, G. S.

L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, “Modeling of the hysteretic metal-insulator transition in a vanadium dioxide infrared detector,” Opt. Eng. 41(10), 2582–2588 (2002).
[Crossref]

Dicken, M. J.

Dobrosavljevic, V.

O. Najera, M. Civelli, V. Dobrosavljevic, and M. J. Rozenberg, “Resolving the VO2 controversy: Mott mechanism dominates the insulator-to-metal transition,” Phys. Rev. B 95(3), 035113 (2017).
[Crossref]

Du, J.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Evans, P. G.

Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically reconfigurable metadevice employing nanostructured phase-change materials,” Nano Lett. 17(8), 4881–4885 (2017).
[Crossref] [PubMed]

Gao, Y. F.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Genevet, P.

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Gholipour, B.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Gu, T.

Haglund, R. F.

Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically reconfigurable metadevice employing nanostructured phase-change materials,” Nano Lett. 17(8), 4881–4885 (2017).
[Crossref] [PubMed]

Hashemi, M. R. M.

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

Hatef, A.

A. Hatef, N. Zamani, and W. Johnston, “Coherent control of optical absorption and the energy transfer pathway of an infrared quantum dot hybridized with a VO2 nanoparticle,” J. Phys. Condens. Matter 29(15), 155305 (2017).
[Crossref] [PubMed]

Ho, P. C.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Hosseini, P.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Hu, J.

Huang, K.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Iizuka, H.

K. Ito, K. Nishikawa, and H. Iizuka, “Multilevel radiative thermal memory realized by the hysteretic metal-insulator transition of vanadium dioxide,” Appl. Phys. Lett. 108(5), 053507 (2016).
[Crossref]

Ito, K.

K. Ito, K. Nishikawa, and H. Iizuka, “Multilevel radiative thermal memory realized by the hysteretic metal-insulator transition of vanadium dioxide,” Appl. Phys. Lett. 108(5), 053507 (2016).
[Crossref]

Jarrahi, M.

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

Johnston, W.

A. Hatef, N. Zamani, and W. Johnston, “Coherent control of optical absorption and the energy transfer pathway of an infrared quantum dot hybridized with a VO2 nanoparticle,” J. Phys. Condens. Matter 29(15), 155305 (2017).
[Crossref] [PubMed]

Kanehira, M.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Kang, L. T.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Kats, M. A.

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

Keilmann, F.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Kiang, K. S.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Kim, B. J.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Kim, H. T.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Ko, C. H.

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Ko, C. Y.

Z. Yang, C. Y. Ko, and S. Ramanathan, “Oxide electronics utilizing ultrafast metal-insulator transitions,” Annu. Rev. Mater. Res. 41(1), 337–367 (2011).
[Crossref]

Lambrecht, A.

I. Pirozhenko and A. Lambrecht, “Influence of slab thickness on the Casimir force,” Phys. Rev. A 77(1), 013811 (2008).
[Crossref]

Leahu, G.

G. Leahu, R. L. Voti, C. Sibilia, and M. Bertolotti, “Anomalous optical switching and thermal hysteresis during semiconductor-metal phase transition of VO2 films on Si substrate,” Appl. Phys. Lett. 103(23), 231114 (2013).
[Crossref]

Li, J.

Lima, A. M. N.

L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, “Modeling of the hysteretic metal-insulator transition in a vanadium dioxide infrared detector,” Opt. Eng. 41(10), 2582–2588 (2002).
[Crossref]

Liz-Marzan, L. M.

T. Ung, L. M. Liz-Marzan, and P. Mulvaney, “Optical properties of thin films of Au@SiO2 particles,” J. Phys. Chem. B 105(17), 3441–3452 (2001).
[Crossref]

Luo, H. J.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Ma, J.

Maple, M. B.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Meena, J. S.

J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, “Overview of emerging nonvolatile memory technologies,” Nanoscale Res. Lett. 9(1), 526 (2014).
[Crossref] [PubMed]

Merced, E.

J. Zhang, E. Merced, N. Sepulveda, and X. B. Tan, “Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model,” Smart Mater. Struct. 23(12), 125017 (2014).
[Crossref]

N. Dávila, E. Merced, and N. Sepulveda, “Emmanuelle Merced, and Nelson Sepúlveda, “Electronically variable optical attenuator enabled by self-sensing in vanadium dioxide,” IEEE Photonics Technol. Lett. 26(10), 1011–1014 (2014).
[Crossref]

Mulvaney, P.

T. Ung, L. M. Liz-Marzan, and P. Mulvaney, “Optical properties of thin films of Au@SiO2 particles,” J. Phys. Chem. B 105(17), 3441–3452 (2001).
[Crossref]

Najera, O.

O. Najera, M. Civelli, V. Dobrosavljevic, and M. J. Rozenberg, “Resolving the VO2 controversy: Mott mechanism dominates the insulator-to-metal transition,” Phys. Rev. B 95(3), 035113 (2017).
[Crossref]

Neff, H.

L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, “Modeling of the hysteretic metal-insulator transition in a vanadium dioxide infrared detector,” Opt. Eng. 41(10), 2582–2588 (2002).
[Crossref]

Nishikawa, K.

K. Ito, K. Nishikawa, and H. Iizuka, “Multilevel radiative thermal memory realized by the hysteretic metal-insulator transition of vanadium dioxide,” Appl. Phys. Lett. 108(5), 053507 (2016).
[Crossref]

Pernice, W. H. P.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Pirozhenko, I.

I. Pirozhenko and A. Lambrecht, “Influence of slab thickness on the Casimir force,” Phys. Rev. A 77(1), 013811 (2008).
[Crossref]

Pryce, I. M.

Qazilbash, M. M.

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Ramanathan, S.

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

M. A. Kats, R. Blanchard, P. Genevet, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Thermal tuning of mid-infrared plasmonic antenna arrays using a phase change material,” Opt. Lett. 38(3), 368–370 (2013).
[Crossref] [PubMed]

Z. Yang, C. Y. Ko, and S. Ramanathan, “Oxide electronics utilizing ultrafast metal-insulator transitions,” Annu. Rev. Mater. Res. 41(1), 337–367 (2011).
[Crossref]

Rios, C.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Rogers, E. T. F.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Rozenberg, M. J.

O. Najera, M. Civelli, V. Dobrosavljevic, and M. J. Rozenberg, “Resolving the VO2 controversy: Mott mechanism dominates the insulator-to-metal transition,” Phys. Rev. B 95(3), 035113 (2017).
[Crossref]

Scherer, T.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Sepulveda, N.

J. Zhang, E. Merced, N. Sepulveda, and X. B. Tan, “Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model,” Smart Mater. Struct. 23(12), 125017 (2014).
[Crossref]

N. Dávila, E. Merced, and N. Sepulveda, “Emmanuelle Merced, and Nelson Sepúlveda, “Electronically variable optical attenuator enabled by self-sensing in vanadium dioxide,” IEEE Photonics Technol. Lett. 26(10), 1011–1014 (2014).
[Crossref]

Sepúlveda, N.

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

Sibilia, C.

G. Leahu, R. L. Voti, C. Sibilia, and M. Bertolotti, “Anomalous optical switching and thermal hysteresis during semiconductor-metal phase transition of VO2 films on Si substrate,” Appl. Phys. Lett. 103(23), 231114 (2013).
[Crossref]

Soref, R.

Stegmaier, M.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Sun, K.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Sweatlock, L. A.

Sze, S. M.

J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, “Overview of emerging nonvolatile memory technologies,” Nanoscale Res. Lett. 9(1), 526 (2014).
[Crossref] [PubMed]

Tan, X. B.

J. Zhang, E. Merced, N. Sepulveda, and X. B. Tan, “Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model,” Smart Mater. Struct. 23(12), 125017 (2014).
[Crossref]

Taubner, T.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Teng, J. H.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Tseng, T. Y.

J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, “Overview of emerging nonvolatile memory technologies,” Nanoscale Res. Lett. 9(1), 526 (2014).
[Crossref] [PubMed]

Ung, T.

T. Ung, L. M. Liz-Marzan, and P. Mulvaney, “Optical properties of thin films of Au@SiO2 particles,” J. Phys. Chem. B 105(17), 3441–3452 (2001).
[Crossref]

Valentine, J. G.

Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically reconfigurable metadevice employing nanostructured phase-change materials,” Nano Lett. 17(8), 4881–4885 (2017).
[Crossref] [PubMed]

Verleur, H. W.

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172(3), 788–798 (1968).
[Crossref]

Voti, R. L.

G. Leahu, R. L. Voti, C. Sibilia, and M. Bertolotti, “Anomalous optical switching and thermal hysteresis during semiconductor-metal phase transition of VO2 films on Si substrate,” Appl. Phys. Lett. 103(23), 231114 (2013).
[Crossref]

Walavalkar, S.

Wang, D.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Wang, Q.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Wang, T.

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

Wright, C. D.

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Wuttig, M.

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

Yang, S. H.

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

Yang, Z.

Yuan, G. H.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Yun, S. J.

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Zamani, N.

A. Hatef, N. Zamani, and W. Johnston, “Coherent control of optical absorption and the energy transfer pathway of an infrared quantum dot hybridized with a VO2 nanoparticle,” J. Phys. Condens. Matter 29(15), 155305 (2017).
[Crossref] [PubMed]

Zhang, J.

J. Zhang, E. Merced, N. Sepulveda, and X. B. Tan, “Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model,” Smart Mater. Struct. 23(12), 125017 (2014).
[Crossref]

Zhang, Q.

Zhang, S. Y.

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Zhang, Y.

Zhang, Z. T.

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Zheludev, N. I.

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

Zhu, Z.

Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically reconfigurable metadevice employing nanostructured phase-change materials,” Nano Lett. 17(8), 4881–4885 (2017).
[Crossref] [PubMed]

Annu. Rev. Mater. Res. (1)

Z. Yang, C. Y. Ko, and S. Ramanathan, “Oxide electronics utilizing ultrafast metal-insulator transitions,” Annu. Rev. Mater. Res. 41(1), 337–367 (2011).
[Crossref]

Appl. Phys. Lett. (3)

Q. Wang, G. H. Yuan, K. S. Kiang, K. Sun, B. Gholipour, E. T. F. Rogers, K. Huang, S. S. Ang, N. I. Zheludev, and J. H. Teng, “Reconfigurable phase-change photomask for grayscale photolithography,” Appl. Phys. Lett. 110(20), 201110 (2017).
[Crossref]

K. Ito, K. Nishikawa, and H. Iizuka, “Multilevel radiative thermal memory realized by the hysteretic metal-insulator transition of vanadium dioxide,” Appl. Phys. Lett. 108(5), 053507 (2016).
[Crossref]

G. Leahu, R. L. Voti, C. Sibilia, and M. Bertolotti, “Anomalous optical switching and thermal hysteresis during semiconductor-metal phase transition of VO2 films on Si substrate,” Appl. Phys. Lett. 103(23), 231114 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

N. Dávila, E. Merced, and N. Sepulveda, “Emmanuelle Merced, and Nelson Sepúlveda, “Electronically variable optical attenuator enabled by self-sensing in vanadium dioxide,” IEEE Photonics Technol. Lett. 26(10), 1011–1014 (2014).
[Crossref]

J. Phys. Chem. B (1)

T. Ung, L. M. Liz-Marzan, and P. Mulvaney, “Optical properties of thin films of Au@SiO2 particles,” J. Phys. Chem. B 105(17), 3441–3452 (2001).
[Crossref]

J. Phys. Condens. Matter (1)

A. Hatef, N. Zamani, and W. Johnston, “Coherent control of optical absorption and the energy transfer pathway of an infrared quantum dot hybridized with a VO2 nanoparticle,” J. Phys. Condens. Matter 29(15), 155305 (2017).
[Crossref] [PubMed]

Nano Energy (1)

Y. F. Gao, H. J. Luo, Z. T. Zhang, L. T. Kang, Z. Chen, J. Du, M. Kanehira, and C. X. Cao, “Nanoceramic VO2 thermochromic smart glass: A review on progress in solution processing,” Nano Energy 1(2), 221–246 (2012).
[Crossref]

Nano Lett. (1)

Z. Zhu, P. G. Evans, R. F. Haglund, and J. G. Valentine, “Dynamically reconfigurable metadevice employing nanostructured phase-change materials,” Nano Lett. 17(8), 4881–4885 (2017).
[Crossref] [PubMed]

Nanoscale Res. Lett. (1)

J. S. Meena, S. M. Sze, U. Chand, and T. Y. Tseng, “Overview of emerging nonvolatile memory technologies,” Nanoscale Res. Lett. 9(1), 526 (2014).
[Crossref] [PubMed]

Nat. Photonics (2)

M. Wuttig, H. Bhaskaran, and T. Taubner, “Phase-change materials for non-volatile photonic applications,” Nat. Photonics 11(8), 465–476 (2017).
[Crossref]

C. Rios, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Opt. Eng. (1)

L. A. L. de Almeida, G. S. Deep, A. M. N. Lima, and H. Neff, “Modeling of the hysteretic metal-insulator transition in a vanadium dioxide infrared detector,” Opt. Eng. 41(10), 2582–2588 (2002).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172(3), 788–798 (1968).
[Crossref]

Phys. Rev. A (1)

I. Pirozhenko and A. Lambrecht, “Influence of slab thickness on the Casimir force,” Phys. Rev. A 77(1), 013811 (2008).
[Crossref]

Phys. Rev. B (1)

O. Najera, M. Civelli, V. Dobrosavljevic, and M. J. Rozenberg, “Resolving the VO2 controversy: Mott mechanism dominates the insulator-to-metal transition,” Phys. Rev. B 95(3), 035113 (2017).
[Crossref]

Phys. Rev. X (1)

M. A. Kats, R. Blanchard, S. Y. Zhang, P. Genevet, C. H. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Sci. Rep. (1)

M. R. M. Hashemi, S. H. Yang, T. Wang, N. Sepúlveda, and M. Jarrahi, “Electronically-controlled beam-steering through vanadium dioxide metasurfaces,” Sci. Rep. 6(1), 35439 (2016).
[Crossref] [PubMed]

Science (1)

M. M. Qazilbash, M. Brehm, B. G. Chae, P. C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H. T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007).
[Crossref] [PubMed]

Smart Mater. Struct. (1)

J. Zhang, E. Merced, N. Sepulveda, and X. B. Tan, “Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model,” Smart Mater. Struct. 23(12), 125017 (2014).
[Crossref]

Other (4)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 2012).

A. Visintin, Differential Models of Hysteresis (Springer, 1994).

I. D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications (Academic, 2003).

T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University, 2015).

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Figures (6)

Fig. 1
Fig. 1 Viewing hysteresis as an asymmetric structural change. A VO2 thin film grown on a substrate is used as an example to illustrate the change. The transition between the two homogeneous states shows distinct structural differences in heating and cooling. The embedded spheres approximate the complex, inhomogeneous growth of one pure phase inside another. This view may be adopted for various materials if the modified Maxwell Garnett model is used as a phenomenological approach.
Fig. 2
Fig. 2 Complex permittivity of VO2 calculated based on the modified Maxwell Garnett model. (a) The real part of the permittivity in heating ( ε eff,h , lines) and cooling ( ε eff,c , dots) with f euqals 0 (black), 0.25 (magenta), 0.5 (dark yellow), 0.75 (olive) and 1 (orange). ε eff,h are labelled for further clarification. ε eff,h = ε eff,c at f=0 and f=1. (b) Corresponding imaginary part of the permittivity. (c) ε eff,h (red) and ε eff,c (blue) at wavelength 1.55 µm. The real part is drawn in solid lines, and the imaginary part dashed lines. (d) Corresponding values at 10 µm.
Fig. 3
Fig. 3 Reflection of a thin VO2 film on top of a bulk sapphire substrate. The film thickness is (a) 100 nm, (b) 50 nm, and (c) 500 nm. The light wavelength is 10 µm.
Fig. 4
Fig. 4 Dependence of light reflection from a 50 nm thick VO2 film on the complex permittivity of the material. The permittivity of either one or both of the pure phases is changed by 20% before applying the modified Maxwell Garnett model. From the standard values of ε m and ε d , the changes are (a) 1.2× ε m , (b) 1.2× ε d , (c) 1.2× ε m and 1.2× ε d , (d) 0.8× ε m , (e) 0.8× ε d , and (f)  0.8× ε m and 0.8× ε d .
Fig. 5
Fig. 5 Reflection of a thin VO2 film on top of a bulk silicon substrate. The film thickness is (a) 100 nm, (b) 50 nm, and (c) 500 nm. The light wavelength is 10 µm.
Fig. 6
Fig. 6 Data corresponding to Fig. 4 with the Al2O3 substrate replaced by Si.

Equations (3)

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ε eff = ε 2 ε 1 ( 1+2f )+ ε 2 ( 22f ) ε 1 ( 1f )+ ε 2 ( 2+f )
ε eff,h = ε d ε m ( 1+2f )+ ε d ( 22f ) ε m ( 1f )+ ε d ( 2+f )
ε eff,  c = ε m ε m *2f+ ε d ( 32f ) ε m ( 3f )+ ε d *f

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