Abstract

Vanadium dioxide (VO2) is a material that undergoes thermal phase transition resulting in drastic changes in its material properties. The phase change can also be brought on by optical pumping. Several experimental results have been presented in the literature dealing with such phase transitions brought on by optical pumping. In this manuscript we present a theoretical framework, which addresses this problem by self consistently solving the electromagnetic problem and the thermodynamic problem using a multiphysics approach when such transitions are thermally mediated, as is the case with continuous-wave optical pumps. Such an analysis provides us with insights into the transition process and also helps explain the conditions under which some of the observed experimental results like bistability takes place. Such optically induced phase transition materials also present the intriguing possibility of ultrahigh nonlinearity where the input optical signal essentially converts a dielectric into a plasmonic material. These materials can find significant applications in nonlinear metatronics.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2013 (1)

2012 (1)

G. Seo, B.-J. Kim, Y. W. Lee, and H.-T. Kim, “Photo-assisted bistable switching using Mott transition in two-terminal VO2 device,” Appl. Phys. Lett. 100(1), 011908 (2012).
[Crossref]

2010 (1)

2009 (1)

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

2008 (1)

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (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]

2001 (1)

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

2000 (1)

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

1996 (1)

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[Crossref] [PubMed]

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]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

Ahn, J. S.

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[Crossref] [PubMed]

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]

Ashrit, P. V.

S. Bonora, U. Bortolozzo, S. Residori, R. Balu, and P. V. Ashrit, “Mid-IR to near-IR image conversion by thermally induced optical switching in Vanadium Dioxide,” Opt. Lett. 35(2), 103–105 (2010).
[Crossref] [PubMed]

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

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]

Balu, R.

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.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[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]

Becker, M. F.

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

Ben-Messaoud, T.

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

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]

Bonora, S.

Bortolozzo, U.

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]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

Brun, A.

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

Buckman, A. B.

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

Cavalleri, A.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Chae, B.-G.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[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]

Choi, H. S.

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[Crossref] [PubMed]

Dayal, G.

Di Ventra, M.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Driscoll, T.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Forget, P.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Gariépy, J. P.

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

Georges, P.

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

Haché, A.

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

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]

Jokerst, N. M.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Jung, J. H.

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[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]

Kieffer, J. C.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Kim, B.-J.

G. Seo, B.-J. Kim, Y. W. Lee, and H.-T. Kim, “Photo-assisted bistable switching using Mott transition in two-terminal VO2 device,” Appl. Phys. Lett. 100(1), 011908 (2012).
[Crossref]

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[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]

Kim, D. H.

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[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]

Kim, H.-T.

G. Seo, B.-J. Kim, Y. W. Lee, and H.-T. Kim, “Photo-assisted bistable switching using Mott transition in two-terminal VO2 device,” Appl. Phys. Lett. 100(1), 011908 (2012).
[Crossref]

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Landry, G.

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

Lee, Y. W.

G. Seo, B.-J. Kim, Y. W. Lee, and H.-T. Kim, “Photo-assisted bistable switching using Mott transition in two-terminal VO2 device,” Appl. Phys. Lett. 100(1), 011908 (2012).
[Crossref]

Lee, Y.-W.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Lépine, T.

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

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]

Noh, T. W.

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[Crossref] [PubMed]

Palit, S.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Qazilbash, M. 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]

Ráksi, F.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Ramakrishna, S. A.

Ramamoorthy, B.

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

Residori, S.

Seo, G.

G. Seo, B.-J. Kim, Y. W. Lee, and H.-T. Kim, “Photo-assisted bistable switching using Mott transition in two-terminal VO2 device,” Appl. Phys. Lett. 100(1), 011908 (2012).
[Crossref]

Siders, C. W.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Smith, D. R.

T. Driscoll, H.-T. Kim, B.-G. Chae, B.-J. Kim, Y.-W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Squier, J. A.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Tóth, C.

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[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]

Walser, R. M.

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

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]

Ann. Phys. (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen,” Ann. Phys. 416(7), 636–664 (1935).
[Crossref]

Appl. Phys. Lett. (1)

G. Seo, B.-J. Kim, Y. W. Lee, and H.-T. Kim, “Photo-assisted bistable switching using Mott transition in two-terminal VO2 device,” Appl. Phys. Lett. 100(1), 011908 (2012).
[Crossref]

J. Appl. Phys. (1)

M. F. Becker, A. B. Buckman, R. M. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation of the semiconductor-metal phase transition in VO2,” J. Appl. Phys. 65(12), 1507–1509 (2000).

Opt. Commun. (1)

T. Ben-Messaoud, G. Landry, J. P. Gariépy, B. Ramamoorthy, P. V. Ashrit, and A. Haché, “High contrast optical switching in vanadium dioxide thin films,” Opt. Commun. 281(24), 6024–6027 (2008).
[Crossref]

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. B Condens. Matter (1)

H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B Condens. Matter 54(7), 4621–4628 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett. 87(23), 237401 (2001).
[Crossref] [PubMed]

Science (2)

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]

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[Crossref] [PubMed]

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T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. Dewitt, Fundamentals of Heat and Mass Transfer, 7th Ed. (John Wiley, 2011).

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A. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 2008).

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Figures (3)

Fig. 1
Fig. 1 (a) Schematic of the structure. (b) The metal filling fraction of VO2 film as a function of the temperature. (c) Real part and (d) imaginary part of the permittivity of VO2 for various values of f.
Fig. 2
Fig. 2 (a) Real part and (b) imaginary part of the permittivity of VO2 as a function of the incident intensity when the incident wavelength is 500 nm and 900 nm. (c). The wavelength and incident intensity map showing the regions where the VO2 film exhibits a bistable behavior.
Fig. 3
Fig. 3 (a) Real part and (b) imaginary part of the permittivity of VO2 as a function of the incident intensity when the incident wavelength is set to 500 nm and 900 nm. Simulation and analytical results. (c) Field map showing |Ez| when the wavelength and the intensity are set to 900 nm and 5W/cm2 during the heating and cooling cycle. During the heating cycle we see weaker reflections and a reasonable transmission indicating that the VO2 slab is in the dielectric phase, while during the cooling cycle the reflections are much stronger and the transmittance is near zero indicating that the VO2 slab is in the metallic phase.

Equations (6)

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Q=kT
q=h( T s T a )
ΔT T f T ref = 1 1+ k hΔx
T=4 n g | n( f ) in( f )( 1+ n g )+( n 2 + n g )tan( k 0 t f n( f ) ) | 2 R= | in( f )( 1 n g )+( n 2 ( f )+ n g )tan( k 0 t f n( f ) ) in( f )( 1+ n g )+( n 2 ( f )+ n g )tan( k 0 t f n( f ) ) | 2 A=1T( f )R( f ):=ϕ( f )
A= 4 k 0 t f ε ( f ) ( 1+ n g + k 0 t f ε ( f ) ) 2 + ( k 0 t f ε ( f ) ) 2 :=ϕ( f )
I inc = h eff ( T f T a ) ϕ( θ( T f ) )

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