Abstract

At terahertz (THz) frequencies, scattering-type scanning near-field optical microscopy (s-SNOM) based on continuous wave sources mostly relies on cryogenic and bulky detectors, which represents a major constraint for its practical application. Here, we devise a THz s-SNOM system that provides both amplitude and phase contrast and achieves nanoscale (60-70nm) in-plane spatial resolution. It features a quantum cascade laser that simultaneously emits THz frequency light and senses the backscattered optical field through a voltage modulation induced inherently through the self-mixing technique. We demonstrate its performance by probing a phonon-polariton-resonant CsBr crystal and doped black phosphorus flakes.

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

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References

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  28. Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
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    [Crossref]
  32. M. Rosch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
    [Crossref]
  33. N. Rotenberg and L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8(12), 919–926 (2014).
    [Crossref]
  34. S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
    [Crossref]
  35. L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014).
    [Crossref] [PubMed]
  36. M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
    [Crossref]
  37. M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
    [Crossref] [PubMed]

2018 (1)

2017 (3)

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
[Crossref] [PubMed]

M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
[Crossref] [PubMed]

2016 (5)

M. S. Vitiello and L. Viti, “Photonic Devices Based On Black-Phosphorus and Combined Hybrid 2D nanomaterials,” Riv. Nuovo Cim. 39, 371–398 (2016).

J. Abate, S. Gamage, Z. Li, V. Babicheva, M. H. Javani, H. Wang, S. B. Cronin, and M. I. Stockman, “Nanoscopy reveals surface-metallic black phosphorus,” Light Sci. Appl. 5(10), e16162 (2016).
[Crossref]

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

L. Viti, J. Hu, D. Coquillat, A. Politano, C. Consejo, W. Knap, and M. S. Vitiello, “Heterostructured hBN-BP-hBN Nanodetectors at Terahertz Frequencies,” Adv. Mater. 28(34), 7390–7396 (2016).
[Crossref] [PubMed]

P. Dean, O. Mitrofanov, J. Keeley, I. Kundu, L. Li, E. H. Linfield, and A. Giles Davies, “Apertureless near-field THz imaging using the self-mixing effect in a quantum cascade laser,” Appl. Phys. Lett. 108(9), 091113 (2016).
[Crossref]

2015 (5)

M. S. Vitiello, G. Scalari, B. S. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 8462–8475 (2015).
[Crossref] [PubMed]

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, C. Rizza, M. Brambilla, A. Ciattoni, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Photo-generated metamaterials induce modulation of CW terahertz quantum cascade lasers,” Sci. Rep. 5(1), 16207 (2015).
[Crossref] [PubMed]

L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
[Crossref] [PubMed]

M. Rosch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

2014 (6)

N. Rotenberg and L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8(12), 919–926 (2014).
[Crossref]

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014).
[Crossref] [PubMed]

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, and A. D. Rakić, “Methodology for materials analysis using swept-frequency feedback interferometry with terahertz frequency quantum cascade lasers,” Opt. Express 22(15), 18633–18647 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20(23), 25654–25661 (2012).
[Crossref] [PubMed]

2011 (3)

M. S. Vitiello and A. Tredicucci, “Tunable emission in Terahertz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol. 1(1), 76–84 (2011).
[Crossref]

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

A. J. L. Adam, “Review of Near-Field Terahertz Measurement Methods and Their Applications,” J. Infrared Millim. Terahertz Waves 32(8-9), 976–1019 (2011).
[Crossref]

2008 (2)

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz Near-Field Nanoscopy of Mobile Carriers in Single Semiconductor Nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

H. G. von Ribbeck, M. Brehm, D. W. van der Weide, S. Winnerl, O. Drachenko, M. Helm, and F. Keilmann, “Spectroscopic THz near-field microscope,” Opt. Express 16(5), 3430–3438 (2008).
[Crossref] [PubMed]

2007 (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

2006 (1)

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudo-heterodyne Detection for Background-Free Near-Field Spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

2004 (2)

H.-T. Chen, S. Kraatz, G. C. Cho, and R. Kersting, “Identification of a resonant imaging process in apertureless near-field microscopy,” Phys. Rev. Lett. 93(26), 267401 (2004).
[Crossref]

T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical Resonance Tuning and Phase Effects in Optical Near-Field Interaction,” Nano Lett. 4(9), 1669–1672 (2004).
[Crossref]

2000 (1)

R. Hillenbrand and F. Keilmann, “Complex Optical Constants on a Subwavelength Scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

1992 (1)

T. G. Fiske and L. B. Coleman, “Longitudinal-optical phonons in thin films of rubidium iodide, potassium iodide, rubidium bromide, cesium iodide, and cesium bromide,” Phys. Rev. B Condens. Matter 45(3), 1414–1424 (1992).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

Abate, J.

J. Abate, S. Gamage, Z. Li, V. Babicheva, M. H. Javani, H. Wang, S. B. Cronin, and M. I. Stockman, “Nanoscopy reveals surface-metallic black phosphorus,” Light Sci. Appl. 5(10), e16162 (2016).
[Crossref]

Adam, A. J. L.

A. J. L. Adam, “Review of Near-Field Terahertz Measurement Methods and Their Applications,” J. Infrared Millim. Terahertz Waves 32(8-9), 976–1019 (2011).
[Crossref]

Aizpurua, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz Near-Field Nanoscopy of Mobile Carriers in Single Semiconductor Nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Amarie, S.

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

Babicheva, V.

J. Abate, S. Gamage, Z. Li, V. Babicheva, M. H. Javani, H. Wang, S. B. Cronin, and M. I. Stockman, “Nanoscopy reveals surface-metallic black phosphorus,” Light Sci. Appl. 5(10), e16162 (2016).
[Crossref]

Bao, Q.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

Barbieri, S.

Bartalini, S.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
[Crossref]

Beck, M.

M. Rosch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

Beere, H. E.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref] [PubMed]

Bertling, K.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, and A. D. Rakić, “Methodology for materials analysis using swept-frequency feedback interferometry with terahertz frequency quantum cascade lasers,” Opt. Express 22(15), 18633–18647 (2014).
[Crossref] [PubMed]

Borri, S.

Bosch, T.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

Braeuninger-Weimer, P.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Brambilla, M.

F. P. Mezzapesa, L. L. Columbo, C. Rizza, M. Brambilla, A. Ciattoni, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Photo-generated metamaterials induce modulation of CW terahertz quantum cascade lasers,” Sci. Rep. 5(1), 16207 (2015).
[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014).
[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref] [PubMed]

Brehm, M.

Burgoff, D.

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Cai, X.

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Chan, C. W. I.

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Chan, W. L.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Chen, H.-T.

H.-T. Chen, S. Kraatz, G. C. Cho, and R. Kersting, “Identification of a resonant imaging process in apertureless near-field microscopy,” Phys. Rev. Lett. 93(26), 267401 (2004).
[Crossref]

Cho, G. C.

H.-T. Chen, S. Kraatz, G. C. Cho, and R. Kersting, “Identification of a resonant imaging process in apertureless near-field microscopy,” Phys. Rev. Lett. 93(26), 267401 (2004).
[Crossref]

Ciattoni, A.

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F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
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T. G. Fiske and L. B. Coleman, “Longitudinal-optical phonons in thin films of rubidium iodide, potassium iodide, rubidium bromide, cesium iodide, and cesium bromide,” Phys. Rev. B Condens. Matter 45(3), 1414–1424 (1992).
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M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
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R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
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C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica 5(2), 159 (2018).
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M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
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C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica 5(2), 159 (2018).
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L. Viti, J. Hu, D. Coquillat, A. Politano, C. Consejo, W. Knap, and M. S. Vitiello, “Heterostructured hBN-BP-hBN Nanodetectors at Terahertz Frequencies,” Adv. Mater. 28(34), 7390–7396 (2016).
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L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
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P. Dean, O. Mitrofanov, J. Keeley, I. Kundu, L. Li, E. H. Linfield, and A. Giles Davies, “Apertureless near-field THz imaging using the self-mixing effect in a quantum cascade laser,” Appl. Phys. Lett. 108(9), 091113 (2016).
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[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref] [PubMed]

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O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
[Crossref] [PubMed]

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[Crossref]

P. Dean, O. Mitrofanov, J. Keeley, I. Kundu, L. Li, E. H. Linfield, and A. Giles Davies, “Apertureless near-field THz imaging using the self-mixing effect in a quantum cascade laser,” Appl. Phys. Lett. 108(9), 091113 (2016).
[Crossref]

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W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
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M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
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N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudo-heterodyne Detection for Background-Free Near-Field Spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
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M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
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O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
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L. Viti, J. Hu, D. Coquillat, A. Politano, C. Consejo, W. Knap, and M. S. Vitiello, “Heterostructured hBN-BP-hBN Nanodetectors at Terahertz Frequencies,” Adv. Mater. 28(34), 7390–7396 (2016).
[Crossref] [PubMed]

L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
[Crossref] [PubMed]

Rakic, A. D.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, and A. D. Rakić, “Methodology for materials analysis using swept-frequency feedback interferometry with terahertz frequency quantum cascade lasers,” Opt. Express 22(15), 18633–18647 (2014).
[Crossref] [PubMed]

Ravaro, M.

Reno, J. L.

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Ritchie, D. A.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref] [PubMed]

Rizza, C.

F. P. Mezzapesa, L. L. Columbo, C. Rizza, M. Brambilla, A. Ciattoni, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Photo-generated metamaterials induce modulation of CW terahertz quantum cascade lasers,” Sci. Rep. 5(1), 16207 (2015).
[Crossref] [PubMed]

Rosch, M.

M. Rosch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

Rotenberg, N.

N. Rotenberg and L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8(12), 919–926 (2014).
[Crossref]

Sandner, F.

M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
[Crossref] [PubMed]

Santarelli, G.

Scalari, G.

M. S. Vitiello, G. Scalari, B. S. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 8462–8475 (2015).
[Crossref] [PubMed]

M. Rosch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

Scamarcio, G.

F. P. Mezzapesa, L. L. Columbo, C. Rizza, M. Brambilla, A. Ciattoni, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Photo-generated metamaterials induce modulation of CW terahertz quantum cascade lasers,” Sci. Rep. 5(1), 16207 (2015).
[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref] [PubMed]

Sirtori, C.

Sorba, L.

O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
[Crossref] [PubMed]

Stockman, M. I.

J. Abate, S. Gamage, Z. Li, V. Babicheva, M. H. Javani, H. Wang, S. B. Cronin, and M. I. Stockman, “Nanoscopy reveals surface-metallic black phosphorus,” Light Sci. Appl. 5(10), e16162 (2016).
[Crossref]

Taimre, T.

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

T. Taimre, K. Bertling, Y. L. Lim, P. Dean, D. Indjin, and A. D. Rakić, “Methodology for materials analysis using swept-frequency feedback interferometry with terahertz frequency quantum cascade lasers,” Opt. Express 22(15), 18633–18647 (2014).
[Crossref] [PubMed]

Taschin, A.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
[Crossref]

Taubner, T.

T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical Resonance Tuning and Phase Effects in Optical Near-Field Interaction,” Nano Lett. 4(9), 1669–1672 (2004).
[Crossref]

Tredicucci, A.

L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
[Crossref] [PubMed]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
[Crossref]

M. S. Vitiello and A. Tredicucci, “Tunable emission in Terahertz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol. 1(1), 76–84 (2011).
[Crossref]

van der Weide, D. W.

Viti, L.

O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
[Crossref] [PubMed]

M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
[Crossref] [PubMed]

M. S. Vitiello and L. Viti, “Photonic Devices Based On Black-Phosphorus and Combined Hybrid 2D nanomaterials,” Riv. Nuovo Cim. 39, 371–398 (2016).

L. Viti, J. Hu, D. Coquillat, A. Politano, C. Consejo, W. Knap, and M. S. Vitiello, “Heterostructured hBN-BP-hBN Nanodetectors at Terahertz Frequencies,” Adv. Mater. 28(34), 7390–7396 (2016).
[Crossref] [PubMed]

L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
[Crossref] [PubMed]

Vitiello, M. S.

M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
[Crossref] [PubMed]

O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
[Crossref] [PubMed]

M. S. Vitiello and L. Viti, “Photonic Devices Based On Black-Phosphorus and Combined Hybrid 2D nanomaterials,” Riv. Nuovo Cim. 39, 371–398 (2016).

L. Viti, J. Hu, D. Coquillat, A. Politano, C. Consejo, W. Knap, and M. S. Vitiello, “Heterostructured hBN-BP-hBN Nanodetectors at Terahertz Frequencies,” Adv. Mater. 28(34), 7390–7396 (2016).
[Crossref] [PubMed]

L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, C. Rizza, M. Brambilla, A. Ciattoni, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Photo-generated metamaterials induce modulation of CW terahertz quantum cascade lasers,” Sci. Rep. 5(1), 16207 (2015).
[Crossref] [PubMed]

M. S. Vitiello, G. Scalari, B. S. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 8462–8475 (2015).
[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013).
[Crossref] [PubMed]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
[Crossref]

M. S. Vitiello and A. Tredicucci, “Tunable emission in Terahertz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol. 1(1), 76–84 (2011).
[Crossref]

von Ribbeck, H. G.

Wallis, R.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Wang, H.

J. Abate, S. Gamage, Z. Li, V. Babicheva, M. H. Javani, H. Wang, S. B. Cronin, and M. I. Stockman, “Nanoscopy reveals surface-metallic black phosphorus,” Light Sci. Appl. 5(10), e16162 (2016).
[Crossref]

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

Wang, X.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

Wang, Y.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

Wei, B.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Williams, B. S.

Winnerl, S.

Wittborn, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz Near-Field Nanoscopy of Mobile Carriers in Single Semiconductor Nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Xia, F.

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

Xiao, L.

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Xu, Y.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

Yang, Y.

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Yuan, J.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

Zhang, K.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

Zhang, Y.

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

ACS Photonics (1)

R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017).
[Crossref]

Adv. Mater. (2)

L. Viti, J. Hu, D. Coquillat, A. Politano, C. Consejo, W. Knap, and M. S. Vitiello, “Heterostructured hBN-BP-hBN Nanodetectors at Terahertz Frequencies,” Adv. Mater. 28(34), 7390–7396 (2016).
[Crossref] [PubMed]

L. Viti, J. Hu, D. Coquillat, W. Knap, A. Tredicucci, A. Politano, and M. S. Vitiello, “Black Phosphorus Terahertz Photodetectors,” Adv. Mater. 27(37), 5567–5572 (2015).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

T. Taimre, M. Nikolić, K. Bertling, Y. L. Lim, T. Bosch, and A. D. Rakić, “Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing,” Adv. Opt. Photonics 7(3), 570–631 (2015).
[Crossref]

Appl. Phys. Lett. (3)

F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014).
[Crossref]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudo-heterodyne Detection for Background-Free Near-Field Spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

P. Dean, O. Mitrofanov, J. Keeley, I. Kundu, L. Li, E. H. Linfield, and A. Giles Davies, “Apertureless near-field THz imaging using the self-mixing effect in a quantum cascade laser,” Appl. Phys. Lett. 108(9), 091113 (2016).
[Crossref]

IEEE J. Quantum Electron. (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

IEEE Trans. Terahertz Sci. Technol. (1)

M. S. Vitiello and A. Tredicucci, “Tunable emission in Terahertz quantum cascade lasers,” IEEE Trans. Terahertz Sci. Technol. 1(1), 76–84 (2011).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

A. J. L. Adam, “Review of Near-Field Terahertz Measurement Methods and Their Applications,” J. Infrared Millim. Terahertz Waves 32(8-9), 976–1019 (2011).
[Crossref]

Light Sci. Appl. (1)

J. Abate, S. Gamage, Z. Li, V. Babicheva, M. H. Javani, H. Wang, S. B. Cronin, and M. I. Stockman, “Nanoscopy reveals surface-metallic black phosphorus,” Light Sci. Appl. 5(10), e16162 (2016).
[Crossref]

Nano Lett. (2)

T. Taubner, F. Keilmann, and R. Hillenbrand, “Nanomechanical Resonance Tuning and Phase Effects in Optical Near-Field Interaction,” Nano Lett. 4(9), 1669–1672 (2004).
[Crossref]

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz Near-Field Nanoscopy of Mobile Carriers in Single Semiconductor Nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[Crossref] [PubMed]

Nat. Commun. (1)

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

M. A. Huber, F. Mooshammer, M. Plankl, L. Viti, F. Sandner, L. Z. Kastner, T. Frank, J. Fabian, M. S. Vitiello, T. L. Cocker, and R. Huber, “Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures,” Nat. Nanotechnol. 12, 207 (2017).
[Crossref] [PubMed]

Nat. Photonics (4)

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6(8), 525–528 (2012).
[Crossref]

D. Burgoff, T.-Y. Kao, N. Han, C. W. I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

M. Rosch, G. Scalari, M. Beck, and J. Faist, “Octave spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2015).
[Crossref]

N. Rotenberg and L. Kuipers, “Mapping nanoscale light fields,” Nat. Photonics 8(12), 919–926 (2014).
[Crossref]

Opt. Express (6)

Optica (1)

Phys. Rev. B (1)

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

Phys. Rev. B Condens. Matter (1)

T. G. Fiske and L. B. Coleman, “Longitudinal-optical phonons in thin films of rubidium iodide, potassium iodide, rubidium bromide, cesium iodide, and cesium bromide,” Phys. Rev. B Condens. Matter 45(3), 1414–1424 (1992).
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Phys. Rev. Lett. (2)

H.-T. Chen, S. Kraatz, G. C. Cho, and R. Kersting, “Identification of a resonant imaging process in apertureless near-field microscopy,” Phys. Rev. Lett. 93(26), 267401 (2004).
[Crossref]

R. Hillenbrand and F. Keilmann, “Complex Optical Constants on a Subwavelength Scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Riv. Nuovo Cim. (1)

M. S. Vitiello and L. Viti, “Photonic Devices Based On Black-Phosphorus and Combined Hybrid 2D nanomaterials,” Riv. Nuovo Cim. 39, 371–398 (2016).

Sci. Rep. (2)

O. Mitrofanov, L. Viti, E. Dardanis, M. C. Giordano, D. Ercolani, A. Politano, L. Sorba, and M. S. Vitiello, “Near-field terahertz probes with room-temperature nanodetectors for subwavelength resolution imaging,” Sci. Rep. 7, 44240 (2017).
[Crossref] [PubMed]

F. P. Mezzapesa, L. L. Columbo, C. Rizza, M. Brambilla, A. Ciattoni, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Photo-generated metamaterials induce modulation of CW terahertz quantum cascade lasers,” Sci. Rep. 5(1), 16207 (2015).
[Crossref] [PubMed]

Small (1)

Y. Xu, J. Yuan, L. Fei, X. Wang, Q. Bao, Y. Wang, K. Zhang, and Y. Zhang, “Selenium-Doped Black Phosphorus for High-Responsivity 2D Photodetectors,” Small 12(36), 5000–5007 (2016).
[Crossref] [PubMed]

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G. Giuliani and S. Donati, “Laser interferometry”, in Unlocking Dynamical Diversity, John Wiley & Sons, Ltd, pp. 217–255 (2005).

F. Keilmann and R. Hillenbrand, “Near-Field Nanoscopy by Elastic Light Scattering from a Tip”, in Nano-Optics and Near-Field Optical Microscopy, Zayats, & A. D. Richards, eds., Artech House, Boston, London (2009).

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Figures (4)

Fig. 1
Fig. 1 Self-detection scattering type near field optical microscope with nanometer resolution at terahertz frequencies. (a) Schematic diagram showing the experimental arrangements. The same optical components (two paraboloid mirrors, an attenuator (A), one fixed mirror and one piezo-actuated mirror (PZM)) focus the THz beam emitted by the QCL onto the apex of a Pt tip sinusoidally dithered at frequency Ω in close proximity to the sample surface and feeds the scattered radiation back into the QCL cavity to produce self-mixing. The distance L ≈60 cm between the QCL front facet and the tip can be varied by translating the PZM. (b) Self-mixing induced modulation from a Au surface of the voltage drop across the QCL obtained using the experimental arrangement (a) and measured by a lock-in amplifier to the n = 3 demodulation order, as a function of ΔL. The dots are the experimental data and the solid line is the best-fitted curve obtained using Eq. (2). The ΔV3 signal show the expected λ/2 periodicity characteristic of self-mixing. (c) AFM topographic and (d) 3rd harmonic near-field THz imaging of the Au-on-silicon sample at a fixed mirror position. (e) Edge response profile extracted from (d) by averaging seven adjacent rows of pixels along the green horizontal line. The inset shows the corresponding spatial derivative, which has been fitted by a Gaussian function (red curve) with a full-width-at-half-maximum of 65 nm.
Fig. 2
Fig. 2 Amplitude and phase resolved THz nanoscopy on a resonant polar crystal. (a-b) Simulated, near-field resonant dielectric response of CsBr (red lines) and Au (blue lines): amplitude (s3) and phase (φ3) plots as a function of wave number. The dashed vertical line corresponds to the probing laser frequency. (c) Atomic force microscope image of a 5 μm x 5.5 μm area of the CsBr/Au sample. Step sizes of Δx = Δy = 41.6 nm were used. (d) Self-detected near field 3rd order signal. Every Δy = 0.5 μm the PZM mirror position is changed in order to shorten the optical path by ΔL = - 9.25 μm. (e-g) average topography (e), amplitude s3 (f), and phase φ3 (g) as a function of the position with respect to the CsBr/Au edge. The insets in Figs. 2(f) and 2(g) show the spatial derivative of the amplitude 2(f) and phase 2 (g) signals, which have been fitted by Gaussian functions (red curves) with full-width-at-half-maxima of 54 nm and 60 nm, respectively.
Fig. 3
Fig. 3 THz near field amplitude and phase as a function of tip-sample distance (approach curves). (a-b) Comparison between the experimental amplitude (a) and phase (b) of CsBr (red) and Au (blue), collected as a function of the tip-sample distance z, using dither amplitude 106 nm and setting L such that ΔV3 is maximum at z = 0; (c-d) Calculated near-field amplitudes (s3) (c) and phases (φ3) (d) of CsBr (red curves) and Au (blue curves) (see Appendix 2).
Fig. 4
Fig. 4 SD s-SNOM nanoscopy at THz frequencies of doped black-phosphorus. (a, c, e) AFM tomographic images and (b, d, f) corresponding ΔV3 near field optical signal collected on a set of representative Se-doped BP flakes having thickness 130 nm (a), 300 nm (c) 100 nm (e); (f) Self- detected near field 3rd order signal. Every Δy = 0.21 μm the PZM mirror position is changed in order to shorten the optical path by ΔL = 5.5 μm. (g-i) average topography (g), amplitude s3 (h), and phase φ3 (i) as a function of the position with respect to the Se-doped BP/ SiO2 edge. The sharp features in panels (h) and (i) at Δx = 0 are known edge artifacts arising at the sharp edges of the mechanical exfoliated black phosphorus flakes. The dashed vertical line in panels (h-i) corresponds to the BP/SiO2 edge. The horizontal dashed lines in panel (g) mark the amplitude contrast between the two materials. (l-m) ΔV3 profiles averaged over seven adjacent rows of pixels along the green lines in panels (b) and (d), respectively

Equations (9)

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ΔV scos( ω 0 2L c φ )
Δ V n     s n cos( ω 0 2L( t ) c φ n )
  α eff = a 2 L t L t ( ϵ t 1)(2 L t 1 a L t +aln      ( 1 1 a L t ) 2 a L t ) 2 L t 1 a L t  ( L t a ϵ t )a L t ( ϵ t 1)ln      ( 1 1 a L L t ) 2 Ra L t   (2+ β( g a+z L L t )ln( 4 L t 4z+2a ) ln( 4 L t a )β( g 3a+4z 4 L t )ln( 2 L t 2z+a ) ).
dE( t ) dt = 1 2 ( 1+ H )[ G n ( N( t ) N 0 ) 1 τ p ]E( t )+  γ τ c E( tτ ) e 0 τ dN(t) dt = Jη qd N( t ) τ e G n ( N( t ) N 0 ) | E( t ) | 2
γ( t )σ( t )= s( t ) e iφ( t ) =               n= + σ n e inΩt = n= + s n e i φ n e inΩt .
ΔN=2| γ | τ p τ c cos( ω 0 2L(t) c φ(t) )
ΔV(t) s(t)cos( ω 0 2L(t) c φ(t) )
ΔV( t ) n= + S n cos( ω 0 2L c φ   n Ω n t ) = n=0 [ s n cos( ω 0 2L c φ   n Ω n t )+ s n cos( ω 0 2L c φ   n + Ω n t ) ] s 0 cos( ω 0 2L c φ   0 )= n=0 s n [ cos( ω 0 2L c φ   n Ω n t )+cos( ω 0 2L c φ   n + Ω n t ) ] s 0 cos( ω 0 2L c φ   0 ) = n=0 2 s n [ cos( ω 0 2L c φ n )cos( Ω n t ) ] s 0 cos( ω 0 2L c φ   0 )
Δ V n     s n cos( ω 0 2L c φ   n ).

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