Abstract

Hyperbolic materials can sustain propagating modes with very large wave vectors and are thus characterized by a very large density of states. In practice, it is possible to mimic a hyperbolic material using a periodic stack of metallic and dielectric layers that can support surface plasmons with large wave vectors. This raises the question of the nature of the modes in the hyperbolic metamaterial medium and their connection to surface plasmons. Here, we address this question experimentally and theoretically by considering an interface separating a hyperbolic metamaterial from a vacuum. We image the local density of states outside the medium at different distances. By carefully analyzing the spectral and spatial structure of the local density of states as the sample is approached from the vacuum, we establish the connection between the two points of view. We find that the homogenized hyperbolic metamaterial picture is valid outside the material for distances larger than a/2π, where a is the period of the multilayer. For smaller distances, the local density of states displays spatial and spectral peaks pointing to the role of surface plasmons propagating along the interfaces in the layer stack.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

14 November 2017: A typographical correction was made to the author listing.


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References

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    [Crossref]
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    [Crossref]
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2017 (1)

A. Jarzembski and K. Park, “Finite dipole model for extreme near-field thermal radiation between a tip and planar sic substrate,” J. Quantum Spectrosc. Radiat. Transfer 191, 67–74 (2017).
[Crossref]

2016 (4)

2015 (1)

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

2014 (3)

F. Peragut, J.-B. Brubach, P. Roy, and Y. DeWilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Phys. Rev. Lett. 110, 251118 (2014).
[Crossref]

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

2013 (5)

T. A. Morgado, S. I. Maslovski, and M. G. Silveirinha, “Ultrahigh Casimir interaction torque in nanowire systems,” Opt. Express 21, 14943–14955 (2013).
[Crossref]

Y. Guo and Z. Jakob, “Thermal hyperbolic metamaterials,” Opt. Express 21, 15014–15019 (2013).
[Crossref]

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

M. Tschikin, S. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15, 105101 (2013).
[Crossref]

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

2012 (4)

A. Jones and M. Raschke, “Thermal infrared near-field spectroscopy,” Nano Lett. 12, 1475–1481 (2012).
[Crossref]

S. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109, 104301 (2012).
[Crossref]

Y. Guo, C. Cortes, S. Molesky, and Z. Jakob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
[Crossref]

C. Cortes, W. Newman, S. Molesky, and Z. Jakob, “Negative refraction in semiconductor metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

2011 (1)

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

2009 (1)

A. Archambault, T. V. Teperik, F. Marquier, and J.-J. Greffet, “Surface plasmons Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

2007 (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

2006 (3)

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

L. Piper, T. Veal, M. Lowe, and C. McConville, “Electron depletion at InAs free surfaces: doping-induced acceptorlike gap states,” Phys. Rev. B 73, 195321 (2006).
[Crossref]

Z. Jakob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

2005 (2)

J. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22, 1844–1849 (2005).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

2003 (4)

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003).
[Crossref]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

Y. DeWilde, F. Formanek, and L. Aigouy, “Apertureless near-field scanning optical microscope based on a quartz tuning fork,” Rev. Sci. Instrum. 74, 3889–3891 (2003).
[Crossref]

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

2000 (1)

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000).
[Crossref]

Aigouy, L.

Y. DeWilde, F. Formanek, and L. Aigouy, “Apertureless near-field scanning optical microscope based on a quartz tuning fork,” Rev. Sci. Instrum. 74, 3889–3891 (2003).
[Crossref]

Alekseyev, L.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Alekseyev, L. V.

Apostol, A.

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

Archambault, A.

A. Archambault, T. V. Teperik, F. Marquier, and J.-J. Greffet, “Surface plasmons Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Babuty, A.

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

Barho, F.

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

F. Barho, F. Gonzalez-Posada, M.-J. Milla-Rodrigo, M. Bomers, L. Cerutti, and T. Taliercio, “All-semiconductor plasmonic gratings for biosensing applications in the mid-infrared spectral range,” Opt. Express 24, 16175–16190 (2016).

Ben-Abdallah, P.

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

M. Tschikin, S. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15, 105101 (2013).
[Crossref]

S. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109, 104301 (2012).
[Crossref]

Biehs, S.

M. Tschikin, S. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15, 105101 (2013).
[Crossref]

S. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109, 104301 (2012).
[Crossref]

Binard, G.

Bomers, M.

F. Barho, F. Gonzalez-Posada, M.-J. Milla-Rodrigo, M. Bomers, L. Cerutti, and T. Taliercio, “All-semiconductor plasmonic gratings for biosensing applications in the mid-infrared spectral range,” Opt. Express 24, 16175–16190 (2016).

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Bourdillon, C.

Brubach, J.-B.

F. Peragut, J.-B. Brubach, P. Roy, and Y. DeWilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Phys. Rev. Lett. 110, 251118 (2014).
[Crossref]

Cao, D.

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

Carminati, R.

V. Parigi, E. Perros, G. Binard, C. Bourdillon, A. Maitre, R. Carminati, V. Krachmalnicoff, and Y. DeWilde, “Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials,” Opt. Express 24, 7019–7027 (2016).
[Crossref]

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003).
[Crossref]

Cazé, A.

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

Cerutti, L.

F. Barho, F. Gonzalez-Posada, M.-J. Milla-Rodrigo, M. Bomers, L. Cerutti, and T. Taliercio, “All-semiconductor plasmonic gratings for biosensing applications in the mid-infrared spectral range,” Opt. Express 24, 16175–16190 (2016).

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Chapuis, P.

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

Chapuis, P.-O.

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

Chen, Y.

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

Cortes, C.

C. Cortes, W. Newman, S. Molesky, and Z. Jakob, “Negative refraction in semiconductor metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Y. Guo, C. Cortes, S. Molesky, and Z. Jakob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
[Crossref]

DeWilde, Y.

V. Parigi, E. Perros, G. Binard, C. Bourdillon, A. Maitre, R. Carminati, V. Krachmalnicoff, and Y. DeWilde, “Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials,” Opt. Express 24, 7019–7027 (2016).
[Crossref]

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

F. Peragut, J.-B. Brubach, P. Roy, and Y. DeWilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Phys. Rev. Lett. 110, 251118 (2014).
[Crossref]

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

Y. DeWilde, F. Formanek, and L. Aigouy, “Apertureless near-field scanning optical microscope based on a quartz tuning fork,” Rev. Sci. Instrum. 74, 3889–3891 (2003).
[Crossref]

Dogariu, A.

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

Formanek, F.

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

Y. DeWilde, F. Formanek, and L. Aigouy, “Apertureless near-field scanning optical microscope based on a quartz tuning fork,” Rev. Sci. Instrum. 74, 3889–3891 (2003).
[Crossref]

Franz, K.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Fullerton, E. E.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Gmachl, C.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Gonzalez-Posada, F.

González-Posada, F.

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Gosztola, D.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Gralak, B.

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

Greffet, J.-J.

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J.-J. Greffet, “Surface plasmons Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003).
[Crossref]

Guo, Y.

Y. Guo and Z. Jakob, “Thermal hyperbolic metamaterials,” Opt. Express 21, 15014–15019 (2013).
[Crossref]

Y. Guo, C. Cortes, S. Molesky, and Z. Jakob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
[Crossref]

Hendren, W.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Henkel, C.

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

Hoffman, A.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Howard, S.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Hugonin, J.

Irudayaraj, J.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Ishii, S.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Jakob, Z.

Y. Guo and Z. Jakob, “Thermal hyperbolic metamaterials,” Opt. Express 21, 15014–15019 (2013).
[Crossref]

C. Cortes, W. Newman, S. Molesky, and Z. Jakob, “Negative refraction in semiconductor metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Y. Guo, C. Cortes, S. Molesky, and Z. Jakob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
[Crossref]

Z. Jakob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

Jarzembski, A.

A. Jarzembski and K. Park, “Finite dipole model for extreme near-field thermal radiation between a tip and planar sic substrate,” J. Quantum Spectrosc. Radiat. Transfer 191, 67–74 (2017).
[Crossref]

Jones, A.

A. Jones and M. Raschke, “Thermal infrared near-field spectroscopy,” Nano Lett. 12, 1475–1481 (2012).
[Crossref]

Joulain, K.

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003).
[Crossref]

Kan, J. J.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Keilmann, F.

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000).
[Crossref]

Khurgin, J.

Kildishev, A. V.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Knoll, B.

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000).
[Crossref]

Krachmalnicoff, V.

V. Parigi, E. Perros, G. Binard, C. Bourdillon, A. Maitre, R. Carminati, V. Krachmalnicoff, and Y. DeWilde, “Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials,” Opt. Express 24, 7019–7027 (2016).
[Crossref]

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

Lagutchev, A.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Lalanne, P.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

Lemoine, P.-A.

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

Li, Y.

Liu, J.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Liu, Z.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

Lowe, M.

L. Piper, T. Veal, M. Lowe, and C. McConville, “Electron depletion at InAs free surfaces: doping-induced acceptorlike gap states,” Phys. Rev. B 73, 195321 (2006).
[Crossref]

Lu, D.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Maitre, A.

Marquier, F.

A. Archambault, T. V. Teperik, F. Marquier, and J.-J. Greffet, “Surface plasmons Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

Maslovski, S. I.

McConville, C.

L. Piper, T. Veal, M. Lowe, and C. McConville, “Electron depletion at InAs free surfaces: doping-induced acceptorlike gap states,” Phys. Rev. B 73, 195321 (2006).
[Crossref]

Messina, R.

M. Tschikin, S. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15, 105101 (2013).
[Crossref]

Milla, M. J.

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Milla-Rodrigo, M.-J.

Molesky, S.

Y. Guo, C. Cortes, S. Molesky, and Z. Jakob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
[Crossref]

C. Cortes, W. Newman, S. Molesky, and Z. Jakob, “Negative refraction in semiconductor metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Morgado, T. A.

Mulet, J.-P.

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003).
[Crossref]

Narimanov, E.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Z. Jakob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

Newman, W.

C. Cortes, W. Newman, S. Molesky, and Z. Jakob, “Negative refraction in semiconductor metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

Parigi, V.

Park, K.

A. Jarzembski and K. Park, “Finite dipole model for extreme near-field thermal radiation between a tip and planar sic substrate,” J. Quantum Spectrosc. Radiat. Transfer 191, 67–74 (2017).
[Crossref]

Peragut, F.

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

F. Peragut, J.-B. Brubach, P. Roy, and Y. DeWilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Phys. Rev. Lett. 110, 251118 (2014).
[Crossref]

Perros, E.

Pierrat, R.

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

Piper, L.

L. Piper, T. Veal, M. Lowe, and C. McConville, “Electron depletion at InAs free surfaces: doping-induced acceptorlike gap states,” Phys. Rev. B 73, 195321 (2006).
[Crossref]

Podolskiy, V.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Pollard, R.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Raschke, M.

A. Jones and M. Raschke, “Thermal infrared near-field spectroscopy,” Nano Lett. 12, 1475–1481 (2012).
[Crossref]

Rodriguez, J.-B.

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Roy, P.

F. Peragut, J.-B. Brubach, P. Roy, and Y. DeWilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Phys. Rev. Lett. 110, 251118 (2014).
[Crossref]

Schurig, D.

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

Shalaev, V. M.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Shalaginov, M. Y.

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Silveirinha, M. G.

Sivco, D.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Smith, D.

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

Taliercio, T.

F. Barho, F. Gonzalez-Posada, M.-J. Milla-Rodrigo, M. Bomers, L. Cerutti, and T. Taliercio, “All-semiconductor plasmonic gratings for biosensing applications in the mid-infrared spectral range,” Opt. Express 24, 16175–16190 (2016).

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Teperik, T. V.

A. Archambault, T. V. Teperik, F. Marquier, and J.-J. Greffet, “Surface plasmons Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Tournié, E.

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Tschikin, M.

M. Tschikin, S. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15, 105101 (2013).
[Crossref]

S. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109, 104301 (2012).
[Crossref]

Veal, T.

L. Piper, T. Veal, M. Lowe, and C. McConville, “Electron depletion at InAs free surfaces: doping-induced acceptorlike gap states,” Phys. Rev. B 73, 195321 (2006).
[Crossref]

Wasserman, D.

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Wiederrecht, G.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Wurtz, G.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

Zayats, A.

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

Appl. Phys. Lett. (2)

M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildishev, and V. M. Shalaev, “Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,” Appl. Phys. Lett. 102, 173114 (2013).
[Crossref]

Y. Guo, C. Cortes, S. Molesky, and Z. Jakob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
[Crossref]

J. Opt. (2)

C. Cortes, W. Newman, S. Molesky, and Z. Jakob, “Negative refraction in semiconductor metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

M. Tschikin, S. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15, 105101 (2013).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Quantum Spectrosc. Radiat. Transfer (2)

K. Joulain, P. Ben-Abdallah, P. Chapuis, Y. DeWilde, A. Babuty, and C. Henkel, “Strong tip-sample coupling in thermal radiation scanning tunneling microscopy,” J. Quantum Spectrosc. Radiat. Transfer 136, 1–15 (2014).
[Crossref]

A. Jarzembski and K. Park, “Finite dipole model for extreme near-field thermal radiation between a tip and planar sic substrate,” J. Quantum Spectrosc. Radiat. Transfer 191, 67–74 (2017).
[Crossref]

Nano Lett. (1)

A. Jones and M. Raschke, “Thermal infrared near-field spectroscopy,” Nano Lett. 12, 1475–1481 (2012).
[Crossref]

Nanotechnology (1)

M. J. Milla, F. Barho, F. González-Posada, L. Cerutti, M. Bomers, J.-B. Rodriguez, E. Tournié, and T. Taliercio, “Localized surface plasmon resonance frequency tuning in highly doped InAsSb/GaSb one-dimensional nanostructures,” Nanotechnology 27, 425201 (2016).
[Crossref]

Nat. Mater. (1)

A. Hoffman, L. Alekseyev, S. Howard, K. Franz, D. Wasserman, V. Podolskiy, E. Narimanov, D. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[Crossref]

Nat. Nanotechnol. (1)

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Nature (1)

Y. DeWilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[Crossref]

Nature Nanotechnol. (1)

G. Wurtz, R. Pollard, W. Hendren, G. Wiederrecht, D. Gosztola, V. Podolskiy, and A. Zayats, “Negative refraction in semiconductor metamaterials,” Nature Nanotechnol. 6, 107–111 (2011).
[Crossref]

Opt. Commun. (1)

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000).
[Crossref]

Opt. Express (5)

Optica (1)

Phys. Rev. B (3)

L. Piper, T. Veal, M. Lowe, and C. McConville, “Electron depletion at InAs free surfaces: doping-induced acceptorlike gap states,” Phys. Rev. B 73, 195321 (2006).
[Crossref]

K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, “Definition and measurement of the local density of electromagnetic states close to an interface,” Phys. Rev. B 68, 245405 (2003).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J.-J. Greffet, “Surface plasmons Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Phys. Rev. Lett. (5)

A. Babuty, K. Joulain, P.-O. Chapuis, J.-J. Greffet, and Y. DeWilde, “Blackbody spectrum revisited in the near field,” Phys. Rev. Lett. 110, 146103 (2013).
[Crossref]

F. Peragut, J.-B. Brubach, P. Roy, and Y. DeWilde, “Infrared near-field imaging and spectroscopy based on thermal or synchrotron radiation,” Phys. Rev. Lett. 110, 251118 (2014).
[Crossref]

S. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109, 104301 (2012).
[Crossref]

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

Rev. Sci. Instrum. (1)

Y. DeWilde, F. Formanek, and L. Aigouy, “Apertureless near-field scanning optical microscope based on a quartz tuning fork,” Rev. Sci. Instrum. 74, 3889–3891 (2003).
[Crossref]

Science (1)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction limited objects,” Science 315, 1686 (2007).
[Crossref]

Surf. Sci. Rep. (2)

R. Carminati, A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. DeWilde, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41 (2015).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

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Figures (7)

Fig. 1.
Fig. 1.

Multilayer sample. (a) Schematic view of the sample. It consists of a multilayer of five pairs of 370 nm thick Si-doped InAs and 290 nm thick undoped InAs layers, grown on an undoped InAs substrate. A 2 μm ZnS layer terminates the multilayered structure. Red, doped InAs; gray, undoped InAs; green, ZnS (not on scale). Thermal radiation scanning tunneling microscopy measurements of the electromagnetic local density of states are performed by scattering the near-field thermal radiation at the surface of the cleaved edge of the sample with a tungsten tip, which can be scanned on the sample. The scattered radiation is directed toward a mid-IR detection (IR detection), which consists of either a mercury-cadmium-telluride detector or a Fourier transform IR spectrometer. (b) Optical microscope image of the layers under visible light illumination before deposition of the 2 μm ZnS layer. We can see the multilayered structure (five pairs of doped and undoped InAs layers) of the sample. The dark gray parts correspond to the highly doped InAs (InAs n++, thickness 370 nm) and the light gray part to the non-intentionally doped InAs (InAs nid, thickness 290 nm).

Fig. 2.
Fig. 2.

Reflectance spectra (red open circles) of the sample obtained under normal incidence of the HMM. The dark solid line corresponds to the simulation of the sample reflectivity using the transfer matrix method. The doped InAs is modeled with a Drude function using the parameters given. The undoped InAs is modeled using ω p = 310 13    rad · s 1 , γ = 10 12    rad · s 1 , and ε r = 12.3 , which correspond to a residual doping of 810 16    cm 3 . Inset: Representation of the sample structure.

Fig. 3.
Fig. 3.

Effective permittivity as a function of wavenumber. It can be seen that the sample behaves as a type II HMM for low energy and as a type I HMM for high energy. In the interval 998 1140    cm 1 , both permittivities are negative. Note that the permittivity ε has been multiplied by 10 for clarity.

Fig. 4.
Fig. 4.

Investigation of the electromagnetic local density of states (EM-LDOS) at various heights using a thermal radiation scanning tunneling microscope (TRSTM). (a) Sketch of the scanned area of 2.0    μm × 0.7    μm . Red, doped InAs; gray, undoped InAs. (b) The TRSTM images are measured with the tip at various heights H over the scanned area between 200 and 0 nm, which corresponds to the tip in intermittent contact with the sample; (c)–(f) the TRSTM images ( X Y scans) show a homogeneous EM-LDOS over the sample when the tip is above 100 nm; (g)–(j) at heights below a few tens of nanometers, the detailed structure of the doped/undoped multilayer can be resolved. The temperature of the sample in the measurements is T = 433    K . The signal is spectrally integrated over the interval 800 1500    cm 1 .

Fig. 5.
Fig. 5.

Spectral image of the EM-LDOS recorded with the TRSTM at H = 0    nm along a line of 1.65 μm that perpendicularly crosses 2.5 periods of the sample. The positions of the doped and undoped InAs layers are indicated.

Fig. 6.
Fig. 6.

(a) Schematic structure of the sample used for the numerical simulation of the EM-LDOS. (b) Spectral modeling of the EM-LDOS at a distance of 100 nm above the interface. The signal presents a strong peak at 1040    cm 1 . We also observe that the signal is at its maximum at the interfaces between the doped and undoped regions. These two observations indicate that BSPPs are responsible for the enhanced EM-LDOS above the multilayer sample.

Fig. 7.
Fig. 7.

TRSTM profile obtained by scanning the tip at H = 0    nm perpendicular to the first three pairs of doped/undoped InAs layers of the sample, starting from the undoped substrate. Here the signal, which is spectrally integrated in the range 800 1500    cm 1 , is demodulated at the third harmonic of the tip oscillation frequency, 3 Ω , to achieve the highest possible spatial resolution. The TRSTM signal, S 3 Ω , is compared with the spectrally integrated EM-LDOS. The red vertical arrows indicate the location of the local EM-LDOS maxima due to the contribution of surface plasmons that propagate at each of the interfaces between doped and undoped InAs layers. The six peaks are located at the positions of the six interfaces of the system of three doped layers.

Equations (1)

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k 2 ε + k 2 ε = ω 2 c 2 .