Abstract

Plasmonic lasers (spasers) generate coherent surface plasmon polaritons (SPPs) and could be realized at subwavelength dimensions in metallic cavities for applications in nanoscale optics. Plasmonic cavities are also utilized for terahertz quantum-cascade lasers (QCLs), which are the brightest available solid-state sources of terahertz radiation. A long standing challenge for spasers that are utilized as nanoscale sources of radiation, is their poor coupling to the far-field radiation. Unlike conventional lasers that could produce directional beams, spasers have highly divergent radiation patterns due to their subwavelength apertures. Here, we theoretically and experimentally demonstrate a new technique for implementing distributed feedback (DFB) that is distinct from any other previously utilized DFB schemes for semiconductor lasers. The so-termed antenna-feedback scheme leads to single-mode operation in plasmonic lasers, couples the resonant SPP mode to a highly directional far-field radiation pattern, and integrates hybrid SPPs in surrounding medium into the operation of the DFB lasers. Experimentally, the antenna-feedback method, which does not require the phase matching to a well-defined effective index, is implemented for terahertz QCLs, and single-mode terahertz QCLs with a beam divergence as small as 4°×4° are demonstrated, which is the narrowest beam reported for any terahertz QCL to date. Moreover, in contrast to a negligible radiative field in conventional photonic band-edge lasers, in which the periodicity follows the integer multiple of half-wavelengths inside the active medium, antenna-feedback breaks this integer limit for the first time and enhances the radiative field of the lasing mode. Terahertz lasers with narrow-beam emission will find applications for integrated as well as standoff terahertz spectroscopy and sensing. The antenna-feedback scheme is generally applicable to any plasmonic laser with a Fabry–Perot cavity irrespective of its operating wavelength and could bring plasmonic lasers closer to practical applications.

© 2016 Optical Society of America

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References

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2015 (3)

A. Yang, T. B. Hoang, M. Dridi, C. Deeb, M. H. Mikkelsen, G. C. Schatz, and T. W. Odom, “Real-time tunable lasing from plasmonic nanocavity arrays,” Nat. Commun. 6, 6939 (2015).
[Crossref]

L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107, 221105 (2015).
[Crossref]

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23, 6915–6923 (2015).
[Crossref]

2014 (5)

Y. Halioua, G. Xu, S. Moumdji, L. H. Li, A. G. Davies, E. H. Linfield, and R. Colombelli, “THz quantum cascade lasers operating on the radiative modes of a 2D photonic crystal,” Opt. Lett. 39, 3962–3965 (2014).
[Crossref]

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
[Crossref]

A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90, 155452 (2014).
[Crossref]

X. Meng, J. Liu, A. V. Kildishev, and V. M. Shalaev, “Highly directional spaser array for the red wavelength region,” Laser Photon. Rev. 8, 896–903 (2014).
[Crossref]

M. T. Hill and M. C. Gather, “Advances in small lasers,” Nat. Photonics 8, 908–918 (2014).
[Crossref]

2013 (4)

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[Crossref]

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’tHooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110, 206802 (2013).
[Crossref]

C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
[Crossref]

A. V. Dorofeenko, A. A. Zyablovsky, A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, and A. A. Lisyansky, “Steady state superradiance of a 2D-spaser array,” Opt. Express 21, 14539–14547 (2013).
[Crossref]

2012 (5)

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
[Crossref]

T. Y. Kao, Q. Hu, and J. L. Reno, “Perfectly phase-matched third-order DFB THz quantum-cascade lasers,” Opt. Lett. 37, 2070–2072 (2012).
[Crossref]

R. F. Oulton, “Surface plasmon lasers: sources of nanoscopic light,” Mater. Today 15(1–2), 26–34 (2012).
[Crossref]

P. Berini and I. D. Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6, 16–24 (2012).
[Crossref]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

2011 (1)

L. Mahler and A. Tredicucci, “Photonic engineering of surface-emitting terahertz quantum cascade lasers,” Laser Photon. Rev. 5, 647–658 (2011).
[Crossref]

2010 (4)

M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence terahertz photonic-wire laser,” Opt. Express 18, 6390–6395 (2010).
[Crossref]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9, 730–735 (2010).
[Crossref]

A. Babuty, A. Bousseksou, J.-P. Tetienne, I. M. Doyen, C. Sirtori, G. Beaudoin, I. Sagnes, Y. D. Wilde, and R. Colombelli, “Semiconductor surface plasmon sources,” Phys. Rev. Lett. 104, 226806 (2010).
[Crossref]

T.-Y. Kao, Q. Hu, and J. L. Reno, “Phase-locked arrays of surface-emitting terahertz quantum-cascade lasers,” Appl. Phys. Lett. 96, 101106 (2010).
[Crossref]

2009 (6)

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3, 586–590 (2009).
[Crossref]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174–178 (2009).
[Crossref]

P. Lalanne, J. Hugonin, H. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-λ metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[Crossref]

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[Crossref]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[Crossref]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[Crossref]

2007 (3)

2006 (3)

O. Demichel, L. Mahler, T. Losco, C. Mauro, R. Green, A. Tredicucci, J. Xu, F. Beltram, H. E. Beere, D. A. Ritchie, and V. Tamošinuas, “Surface plasmon photonic structures in terahertz quantum cascade lasers,” Opt. Express 14, 5335–5345 (2006).
[Crossref]

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

E. E. Orlova, J. N. Hovenier, T. O. Klaassen, I. Kašalynas, A. J. L. Adam, J. R. Gao, T. M. Klapwijk, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Antenna model for wire lasers,” Phys. Rev. Lett. 96, 173904 (2006).
[Crossref]

2005 (1)

2003 (2)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ∼100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

2002 (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref]

’tHooft, G. W.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’tHooft, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110, 206802 (2013).
[Crossref]

Adam, A. J. L.

E. E. Orlova, J. N. Hovenier, T. O. Klaassen, I. Kašalynas, A. J. L. Adam, J. R. Gao, T. M. Klapwijk, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Antenna model for wire lasers,” Phys. Rev. Lett. 96, 173904 (2006).
[Crossref]

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
[Crossref]

Amanti, M. I.

M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence terahertz photonic-wire laser,” Opt. Express 18, 6390–6395 (2010).
[Crossref]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3, 586–590 (2009).
[Crossref]

Andrianov, E. S.

Babuty, A.

A. Babuty, A. Bousseksou, J.-P. Tetienne, I. M. Doyen, C. Sirtori, G. Beaudoin, I. Sagnes, Y. D. Wilde, and R. Colombelli, “Semiconductor surface plasmon sources,” Phys. Rev. Lett. 104, 226806 (2010).
[Crossref]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[Crossref]

Ban, D.

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
[Crossref]

Barbieri, S.

C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
[Crossref]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174–178 (2009).
[Crossref]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[Crossref]

Beaudoin, G.

A. Babuty, A. Bousseksou, J.-P. Tetienne, I. M. Doyen, C. Sirtori, G. Beaudoin, I. Sagnes, Y. D. Wilde, and R. Colombelli, “Semiconductor surface plasmon sources,” Phys. Rev. Lett. 104, 226806 (2010).
[Crossref]

Beck, M.

M. I. Amanti, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Low divergence terahertz photonic-wire laser,” Opt. Express 18, 6390–6395 (2010).
[Crossref]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3, 586–590 (2009).
[Crossref]

Beere, H. E.

Y. Halioua, G. Xu, S. Moumdji, L. Li, J. Zhu, E. H. Linfield, A. G. Davies, H. E. Beere, D. A. Ritchie, and R. Colombelli, “Phase-locked arrays of surface-emitting graded-photonic-heterostructure terahertz semiconductor lasers,” Opt. Express 23, 6915–6923 (2015).
[Crossref]

G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
[Crossref]

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Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Wang, Q. J.

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
[Crossref]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9, 730–735 (2010).
[Crossref]

Wasielewski, M. R.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[Crossref]

Wasilewski, Z. R.

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
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Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[Crossref]

Wilde, Y. D.

A. Babuty, A. Bousseksou, J.-P. Tetienne, I. M. Doyen, C. Sirtori, G. Beaudoin, I. Sagnes, Y. D. Wilde, and R. Colombelli, “Semiconductor surface plasmon sources,” Phys. Rev. Lett. 104, 226806 (2010).
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Williams, B. S.

L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107, 221105 (2015).
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B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
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S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
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A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
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E. E. Orlova, J. N. Hovenier, T. O. Klaassen, I. Kašalynas, A. J. L. Adam, J. R. Gao, T. M. Klapwijk, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Antenna model for wire lasers,” Phys. Rev. Lett. 96, 173904 (2006).
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Wu, C.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Xu, G.

Xu, J.

Xu, L.

L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107, 221105 (2015).
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Yang, A.

A. Yang, T. B. Hoang, M. Dridi, C. Deeb, M. H. Mikkelsen, G. C. Schatz, and T. W. Odom, “Real-time tunable lasing from plasmonic nanocavity arrays,” Nat. Commun. 6, 6939 (2015).
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Yu, N.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9, 730–735 (2010).
[Crossref]

Yu, S. F.

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
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Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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Zhang, Y.

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
[Crossref]

Zhou, W.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[Crossref]

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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Zhu, J.

Zhu, Y.

Zyablovsky, A. A.

Appl. Phys. Lett. (4)

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at λ∼100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

A. J. L. Adam, I. Kašalynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions,” Appl. Phys. Lett. 88, 151105 (2006).
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T.-Y. Kao, Q. Hu, and J. L. Reno, “Phase-locked arrays of surface-emitting terahertz quantum-cascade lasers,” Appl. Phys. Lett. 96, 101106 (2010).
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L. Xu, C. A. Curwen, P. W. Hon, Q.-S. Chen, T. Itoh, and B. S. Williams, “Metasurface external cavity laser,” Appl. Phys. Lett. 107, 221105 (2015).
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L. Mahler and A. Tredicucci, “Photonic engineering of surface-emitting terahertz quantum cascade lasers,” Laser Photon. Rev. 5, 647–658 (2011).
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R. F. Oulton, “Surface plasmon lasers: sources of nanoscopic light,” Mater. Today 15(1–2), 26–34 (2012).
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Nat. Commun. (2)

A. Yang, T. B. Hoang, M. Dridi, C. Deeb, M. H. Mikkelsen, G. C. Schatz, and T. W. Odom, “Real-time tunable lasing from plasmonic nanocavity arrays,” Nat. Commun. 6, 6939 (2015).
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G. Xu, R. Colombelli, S. P. Khanna, A. Belarouci, X. Letartre, L. Li, E. H. Linfield, A. G. Davies, H. E. Beere, and D. A. Ritchie, “Efficient power extraction in surface-emitting semiconductor lasers using graded photonic heterostructures,” Nat. Commun. 3, 952 (2012).
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Nat. Mater. (1)

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9, 730–735 (2010).
[Crossref]

Nat. Nanotechnol. (1)

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[Crossref]

Nat. Photonics (5)

C. Sirtori, S. Barbieri, and R. Collombelli, “Wave engineering with THz quantum cascade lasers,” Nat. Photonics 7, 691–701 (2013).
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P. Berini and I. D. Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics 6, 16–24 (2012).
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M. T. Hill and M. C. Gather, “Advances in small lasers,” Nat. Photonics 8, 908–918 (2014).
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B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
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M. I. Amanti, M. Fischer, G. Scalari, M. Beck, and J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3, 586–590 (2009).
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Nature (4)

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174–178 (2009).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[Crossref]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
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Opt. Express (7)

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S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, Q. Hu, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
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Sci. Rep. (1)

G. Liang, E. Dupont, S. Fathololoumi, Z. R. Wasilewski, D. Ban, H. K. Liang, Y. Zhang, S. F. Yu, L. H. Li, A. G. Davies, E. H. Linfield, H. C. Liu, and Q. J. Wang, “Planar integrated metasurfaces for highly-collimated terahertz quantum cascade lasers,” Sci. Rep. 4, 7083 (2014).
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Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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COMSOL 4.4, a finite-element partial differential equation solver from COMSOL Inc.

Supplementary Material (1)

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» Supplement 1: PDF (2746 KB)      Supplementary material

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Figures (4)

Fig. 1.
Fig. 1.

Antenna-feedback concept for spasers. (a) The general principle of conventional DFB that could be implemented in a spaser by introducing periodicity in its metallic cladding. A parallel-plate metallic cavity is illustrated; however, the principle is equally applicable to spaser cavities with a single-metal cladding. (b) If the periodicity in (a) is implemented by making holes or slits in the metal cladding, the guided SPP wave diffracts out through the apertures and generates single-sided SPP waves on the cladding in the surrounding medium. The figure shows a phase mismatch between successive apertures for SPP waves on either side of the cladding. Coherent single-sided SPP waves in the surrounding medium cannot therefore be sustained owing to destructive interference with the guided SPP wave inside the cavity, as illustrated in (c). (d) The principle of an antenna-feedback grating. If the periodicity in the metal film allows the guided SPP mode to diffract outside the cavity, a grating period could be chosen that leads to the first-order Bragg diffraction in the opposite direction, but in the surrounding medium rather than inside the active medium itself. Similarly, the single-sided SPP mode in the surrounding medium undergoes first-order Bragg diffraction to couple with the guided SPP wave in the opposite direction inside the cavity. (e) The grating in (d) leads to a fixed phase condition at each aperture between counterpropagating SPP waves on the either side of metal cladding. First, this leads to a significant buildup of amplitude in the single-sided SPP wave in the surrounding medium, as illustrated in (f). Second, emission from each aperture adds constructively to couple to far-field radiation in the end-fire ( z ) direction. As argued in the text, both of these aspects lead to a narrow far-field emission profile in the x y plane.

Fig. 2.
Fig. 2.

Comparison between conventional DFB (third-order DFB as an example) and antenna-feedback schemes for terahertz QCL cavities. The figure shows a SPP eigenmode spectrum and electric field for the eigenmode with lowest loss calculated by finite-element simulations of parallel-plate metallic cavities, as in Fig. 1, with GaAs as the dielectric ( n a = 3.6 ) and air as the surrounding medium ( n s = 1 ). Simulations are done in 2D (i.e., cavities of infinite width) for 10 μm thick and 1.4 mm long cavities, and metal and active layers are considered lossless. Lossy sections are implemented in the cavities at both longitudinal ends of the cavity as absorbing boundaries, which eliminates the reflection of guided SPP modes from the end facets. A periodic grating with apertures of (somewhat arbitrary) width 0.2 Λ in the top-metal cladding are implemented for DFB. Λ is chosen to excite the lowest-loss DFB mode at similar frequencies close to 3    THz . The eigenmode spectrum shows frequencies and loss for the resonant-cavity modes, which reflects a combination of radiation loss and the loss at longitudinal absorbing regions. (a) The results from a third-order DFB grating with Λ = 41.7    μm and (b) the results from antenna-feedback grating with Λ = 21.7    μm . Radiation loss occurs through diffraction from apertures, and the amplitude of the in-plane electric-field E z is indicative of the outcoupling efficiency. The major fraction of EM energy for the resonant modes exists in the TM polarized ( E y ) electric field. A photonic bandgap in the eigenmode spectrum is indicative of the DFB effect due to the grating. The antenna-feedback grating excites a strong single-sided SPP standing wave on top of the metallic grating (in air), as also illustrated in Fig. 1(f). Also, the radiative loss for the third-order DFB grating is smaller since the lowest-loss eigenmode has zeros of E z under the apertures, which leads to a smaller net outcoupling of radiation. The loss is 6.7    cm 1 and 10.6    cm 1 for the lowest loss resonant cavity mode of the third-order DFB and antenna-feedback scheme, respectively.

Fig. 3.
Fig. 3.

Lasing characteristics of terahertz QCLs with antenna-feedback. (a) The schematic on the left shows the QCL’s metallic cavity with an antenna-feedback grating implemented in the top metal cladding. The active medium is 10 μm thick and based on a 3    THz    GaAs / Al 0.10 Ga 0.90 As QCL design (details in the Supplement 1, Section S1). A scanning electron microscope image of the fabricated QCLs is shown on the right. (b) Experimental light-current-voltage characteristics of a representative QCL with antenna-feedback of dimensions 1.4    mm × 100    μm at different heat-sink temperatures. The QCL is biased with low duty cycle current pulses of 200 ns duration and 100 kHz repetition rate. Inset shows the lasing spectra for different biases where the spectral linewidth is limited by instrument’s resolution. The emitted optical power is measured without any cone collecting optics inside the cryostat. (c) Measured spectra for four different antenna-feedback QCLs with varying grating periods Λ , but similar overall cavity dimensions. The QCLs are biased at a current density of 440    A / cm 2 at 78 K.

Fig. 4.
Fig. 4.

Far-field radiation patterns of terahertz QCLs with antenna-feedback. (a) Schematic showing the orientation of the QCLs and definition of angles. The QCLs were operated at 78 K in pulsed mode and biased at 440    A / cm 2 while lasing in single mode. The plots are for QCLs with 1.4    mm long cavities and (b) 70 μm width and Λ = 21    μm grating emitting at 3.1    THz , (c) 100 μm width and Λ = 21    μm grating emitting at 3.1    THz , and (d) 100 μm width and Λ = 24    μm grating emitting at 2.9    THz , respectively.

Equations (2)

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k i = p 2 π Λ + k d ,
2 π n a λ = 2 π Λ 2 π n s λ ,

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