Abstract

Distributed feedback plasmonic laser based on the periodic array of holes in the silver half-space and covered with gain medium is considered. Square, hexagonal and several rectangular lattices are studied. It is demonstrated that the bound states in the continuum provide substantially lower threshold than radiating modes. Moreover, it is shown that while the hole size increases the lasing threshold of some modes decreases. Among the studied types of lattices, lasing in the hexagonal lattice requires the lowest material gain of only 18 cm−1. Our results pave the way to the development of the efficient low-threshold distributed feedback plasmonic lasers.

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

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2017 (5)

P. Melentiev, A. Kalmykov, A. Gritchenko, A. Afanasiev, V. Balykin, A. Baburin, E. Ryzhova, I. Filippov, I. Rodionov, I. Nechepurenko, and et al., “Plasmonic nanolaser for intracavity spectroscopy and sensorics,” Appl. Phys. Lett. 111, 213104 (2017).
[Crossref]

S. J. Kress, J. Cui, P. Rohner, D. K. Kim, F. V. Antolinez, K.-A. Zaininger, S. V. Jayanti, P. Richner, K. M. McPeak, D. Poulikakos, and et al., “A customizable class of colloidal-quantum-dot spasers and plasmonic amplifiers,” Sci. Adv. 3, e1700688 (2017).
[Crossref] [PubMed]

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[Crossref]

T. Hakala, H. Rekola, A. Väkeväinen, J.-P. Martikainen, M. Nečada, A. Moilanen, and P. Törmä, “Lasing in dark and bright modes of a finite-sized plasmonic lattice,” Nat. communications 8, 13687 (2017).
[Crossref]

E. Chubchev and A. Vinogradov, “Amplifying of surface plasmon-polariton in a metal–gain medium–vacuum structure,” J. Commun. Technol. Electron. 62, 119–122 (2017).
[Crossref]

2016 (4)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

V. T. Tenner, M. J. de Dood, and M. P. van Exter, “Measurement of the phase and intensity profile of surface plasmon laser emission,” ACS Photonics 3, 942–946 (2016).
[Crossref]

N. Arnold, C. Hrelescu, and T. A. Klar, “Minimal spaser threshold within electrodynamic framework: Shape, size and modes,” Annalen der Physik 528, 295–306 (2016).
[Crossref] [PubMed]

K. Liu, N. Li, D. K. Sadana, and V. J. Sorger, “Integrated nanocavity plasmon light sources for on-chip optical interconnects,” ACS Photonics 3, 233–242 (2016).
[Crossref]

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] [PubMed]

N. Arnold, K. Piglmayer, A. V. Kildishev, and T. A. Klar, “Spasers with retardation and gain saturation: electrodynamic description of fields and optical cross-sections,” Opt. Mater. Express 5, 2546–2577 (2015).
[Crossref]

K. M. McPeak, S. V. Jayanti, S. J. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photonics 2, 326–333 (2015).
[Crossref] [PubMed]

2014 (6)

E. K. Keshmarzi, R. N. Tait, and P. Berini, “Near infrared amplified spontaneous emission in a dye-doped polymeric waveguide for active plasmonic applications,” Opt. Express 22, 12452–12460 (2014).
[Crossref] [PubMed]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

N. Zhou, X. Xu, A. T. Hammack, B. C. Stipe, K. Gao, W. Scholz, and E. C. Gage, “Plasmonic near-field transducer for heat-assisted magnetic recording,” Nanophotonics 3, 141–155 (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 & Photonics Rev. 8, 896–903 (2014).
[Crossref]

Y. E. Lozovik, I. Nechepurenko, A. Dorofeenko, E. Andrianov, and A. Pukhov, “Highly sensitive spectroscopy based on a surface plasmon polariton quantum generator,” Laser Phys. Lett. 11, 125701 (2014).
[Crossref]

2013 (7)

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110, 106803 (2013).
[Crossref] [PubMed]

K. Ding, M. Hill, Z. Liu, L. Yin, P. Van Veldhoven, and C. Ning, “Record performance of electrical injection sub-wavelength metallic-cavity semiconductor lasers at room temperature,” Opt. Express 21, 4728–4733 (2013).
[Crossref] [PubMed]

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

X. Meng, A. V. Kildishev, K. Fujita, K. Tanaka, and V. M. Shalaev, “Wavelength-tunable spasing in the visible,” Nano Lett. 13, 4106–4112 (2013).
[Crossref] [PubMed]

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

M. Van Exter, V. Tenner, F. van Beijnum, M. de Dood, P. van Veldhoven, E. Geluk, and et al., “Surface plasmon dispersion in metal hole array lasers,” Opt. express 21, 27422–27437 (2013).
[Crossref] [PubMed]

D. Baranov, E. Andrianov, A. Vinogradov, and A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21, 10779–10791 (2013).
[Crossref] [PubMed]

2012 (2)

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref] [PubMed]

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37, 728–738 (2012).
[Crossref]

2011 (2)

2010 (2)

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic fret lasers via dna scaffolds,” Proc. Natl. Acad. Sci. 107, 16039–16042 (2010).
[Crossref] [PubMed]

L. Ge, Y. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

2009 (5)

W. Challener, C. Peng, A. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. Gokemeijer, Y.-T. Hsia, and et al., “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. photonics 3, 220 (2009).
[Crossref]

P. Zijlstra, J. W. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459, 410 (2009).
[Crossref] [PubMed]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide- si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[Crossref] [PubMed]

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

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 (2009).
[Crossref] [PubMed]

2003 (1)

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] [PubMed]

Afanasiev, A.

P. Melentiev, A. Kalmykov, A. Gritchenko, A. Afanasiev, V. Balykin, A. Baburin, E. Ryzhova, I. Filippov, I. Rodionov, I. Nechepurenko, and et al., “Plasmonic nanolaser for intracavity spectroscopy and sensorics,” Appl. Phys. Lett. 111, 213104 (2017).
[Crossref]

Andrianov, E.

Y. E. Lozovik, I. Nechepurenko, A. Dorofeenko, E. Andrianov, and A. Pukhov, “Highly sensitive spectroscopy based on a surface plasmon polariton quantum generator,” Laser Phys. Lett. 11, 125701 (2014).
[Crossref]

D. Baranov, E. Andrianov, A. Vinogradov, and A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21, 10779–10791 (2013).
[Crossref] [PubMed]

Antolinez, F. V.

S. J. Kress, J. Cui, P. Rohner, D. K. Kim, F. V. Antolinez, K.-A. Zaininger, S. V. Jayanti, P. Richner, K. M. McPeak, D. Poulikakos, and et al., “A customizable class of colloidal-quantum-dot spasers and plasmonic amplifiers,” Sci. Adv. 3, e1700688 (2017).
[Crossref] [PubMed]

Arnold, N.

N. Arnold, C. Hrelescu, and T. A. Klar, “Minimal spaser threshold within electrodynamic framework: Shape, size and modes,” Annalen der Physik 528, 295–306 (2016).
[Crossref] [PubMed]

N. Arnold, K. Piglmayer, A. V. Kildishev, and T. A. Klar, “Spasers with retardation and gain saturation: electrodynamic description of fields and optical cross-sections,” Opt. Mater. Express 5, 2546–2577 (2015).
[Crossref]

Arnold, S.

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic fret lasers via dna scaffolds,” Proc. Natl. Acad. Sci. 107, 16039–16042 (2010).
[Crossref] [PubMed]

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide- si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[Crossref] [PubMed]

Baburin, A.

P. Melentiev, A. Kalmykov, A. Gritchenko, A. Afanasiev, V. Balykin, A. Baburin, E. Ryzhova, I. Filippov, I. Rodionov, I. Nechepurenko, and et al., “Plasmonic nanolaser for intracavity spectroscopy and sensorics,” Appl. Phys. Lett. 111, 213104 (2017).
[Crossref]

Bakker, R.

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

Balykin, V.

P. Melentiev, A. Kalmykov, A. Gritchenko, A. Afanasiev, V. Balykin, A. Baburin, E. Ryzhova, I. Filippov, I. Rodionov, I. Nechepurenko, and et al., “Plasmonic nanolaser for intracavity spectroscopy and sensorics,” Appl. Phys. Lett. 111, 213104 (2017).
[Crossref]

Baranov, D.

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 (2009).
[Crossref] [PubMed]

Belgrave, A.

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

Bergman, D. J.

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] [PubMed]

Berini, P.

Challener, W.

W. Challener, C. Peng, A. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. Gokemeijer, Y.-T. Hsia, and et al., “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. photonics 3, 220 (2009).
[Crossref]

Chon, J. W.

P. Zijlstra, J. W. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459, 410 (2009).
[Crossref] [PubMed]

Chong, Y.

L. Ge, Y. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Chubchev, E.

E. Chubchev and A. Vinogradov, “Amplifying of surface plasmon-polariton in a metal–gain medium–vacuum structure,” J. Commun. Technol. Electron. 62, 119–122 (2017).
[Crossref]

Co, D. T.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref] [PubMed]

Cui, J.

S. J. Kress, J. Cui, P. Rohner, D. K. Kim, F. V. Antolinez, K.-A. Zaininger, S. V. Jayanti, P. Richner, K. M. McPeak, D. Poulikakos, and et al., “A customizable class of colloidal-quantum-dot spasers and plasmonic amplifiers,” Sci. Adv. 3, e1700688 (2017).
[Crossref] [PubMed]

Dai, L.

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[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 (2009).
[Crossref] [PubMed]

de Dood, M.

de Dood, M. J.

V. T. Tenner, M. J. de Dood, and M. P. van Exter, “Measurement of the phase and intensity profile of surface plasmon laser emission,” ACS Photonics 3, 942–946 (2016).
[Crossref]

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

Deeb, C.

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] [PubMed]

Diest, K.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide- si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[Crossref] [PubMed]

Ding, K.

Dionne, J. A.

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[Crossref] [PubMed]

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[Crossref]

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

Shalaev, V. M.

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

X. Meng, A. V. Kildishev, K. Fujita, K. Tanaka, and V. M. Shalaev, “Wavelength-tunable spasing in the visible,” Nano Lett. 13, 4106–4112 (2013).
[Crossref] [PubMed]

Shopova, S. I.

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic fret lasers via dna scaffolds,” Proc. Natl. Acad. Sci. 107, 16039–16042 (2010).
[Crossref] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Soljacic, M.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Sorger, V. J.

K. Liu, N. Li, D. K. Sadana, and V. J. Sorger, “Integrated nanocavity plasmon light sources for on-chip optical interconnects,” ACS Photonics 3, 233–242 (2016).
[Crossref]

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37, 728–738 (2012).
[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 (2009).
[Crossref] [PubMed]

Stipe, B. C.

N. Zhou, X. Xu, A. T. Hammack, B. C. Stipe, K. Gao, W. Scholz, and E. C. Gage, “Plasmonic near-field transducer for heat-assisted magnetic recording,” Nanophotonics 3, 141–155 (2014).
[Crossref]

Stockman, M. I.

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110, 106803 (2013).
[Crossref] [PubMed]

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] [PubMed]

Stone, A. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

L. Ge, Y. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Stout, S.

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

Suh, J. Y.

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

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref] [PubMed]

Sun, Y.

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic fret lasers via dna scaffolds,” Proc. Natl. Acad. Sci. 107, 16039–16042 (2010).
[Crossref] [PubMed]

Suteewong, T.

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

Sweatlock, L. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide- si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[Crossref] [PubMed]

Tait, R. N.

Tanaka, K.

X. Meng, A. V. Kildishev, K. Fujita, K. Tanaka, and V. M. Shalaev, “Wavelength-tunable spasing in the visible,” Nano Lett. 13, 4106–4112 (2013).
[Crossref] [PubMed]

Tenner, V.

Tenner, V. T.

V. T. Tenner, M. J. de Dood, and M. P. van Exter, “Measurement of the phase and intensity profile of surface plasmon laser emission,” ACS Photonics 3, 942–946 (2016).
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Törmä, P.

T. Hakala, H. Rekola, A. Väkeväinen, J.-P. Martikainen, M. Nečada, A. Moilanen, and P. Törmä, “Lasing in dark and bright modes of a finite-sized plasmonic lattice,” Nat. communications 8, 13687 (2017).
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Väkeväinen, A.

T. Hakala, H. Rekola, A. Väkeväinen, J.-P. Martikainen, M. Nečada, A. Moilanen, and P. Törmä, “Lasing in dark and bright modes of a finite-sized plasmonic lattice,” Nat. communications 8, 13687 (2017).
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M. Van Exter, V. Tenner, F. van Beijnum, M. de Dood, P. van Veldhoven, E. Geluk, and et al., “Surface plasmon dispersion in metal hole array lasers,” Opt. express 21, 27422–27437 (2013).
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F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. de Dood, W. Gert, and M. P. van Exter, “Surface plasmon lasing observed in metal hole arrays,” Phys. Rev. Lett. 110, 206802 (2013).
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Van Exter, M.

van Exter, M. P.

V. T. Tenner, M. J. de Dood, and M. P. van Exter, “Measurement of the phase and intensity profile of surface plasmon laser emission,” ACS Photonics 3, 942–946 (2016).
[Crossref]

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

Van Veldhoven, P.

van Veldhoven, P. J.

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

Vinogradov, A.

E. Chubchev and A. Vinogradov, “Amplifying of surface plasmon-polariton in a metal–gain medium–vacuum structure,” J. Commun. Technol. Electron. 62, 119–122 (2017).
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D. Baranov, E. Andrianov, A. Vinogradov, and A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21, 10779–10791 (2013).
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Wang, S.

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[Crossref]

Wang, X.-Y.

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[Crossref]

Wang, Y.-L.

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[Crossref]

Wasielewski, M. R.

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

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref] [PubMed]

Wiesner, U.

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

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton university press, 2011).

Wu, C.-S.

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic fret lasers via dna scaffolds,” Proc. Natl. Acad. Sci. 107, 16039–16042 (2010).
[Crossref] [PubMed]

Xu, X.

N. Zhou, X. Xu, A. T. Hammack, B. C. Stipe, K. Gao, W. Scholz, and E. C. Gage, “Plasmonic near-field transducer for heat-assisted magnetic recording,” Nanophotonics 3, 141–155 (2014).
[Crossref]

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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Yang, X.

W. Challener, C. Peng, A. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. Gokemeijer, Y.-T. Hsia, and et al., “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. photonics 3, 220 (2009).
[Crossref]

Yin, L.

Yun, S. H.

Zaininger, K.-A.

S. J. Kress, J. Cui, P. Rohner, D. K. Kim, F. V. Antolinez, K.-A. Zaininger, S. V. Jayanti, P. Richner, K. M. McPeak, D. Poulikakos, and et al., “A customizable class of colloidal-quantum-dot spasers and plasmonic amplifiers,” Sci. Adv. 3, e1700688 (2017).
[Crossref] [PubMed]

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 (2009).
[Crossref] [PubMed]

Zhang, X.

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37, 728–738 (2012).
[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 (2009).
[Crossref] [PubMed]

Zhang, X.-W.

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[Crossref]

Zhen, B.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Zhou, N.

N. Zhou, X. Xu, A. T. Hammack, B. C. Stipe, K. Gao, W. Scholz, and E. C. Gage, “Plasmonic near-field transducer for heat-assisted magnetic recording,” Nanophotonics 3, 141–155 (2014).
[Crossref]

Zhou, W.

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

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref] [PubMed]

Zhu, G.

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

Zhu, X.

W. Challener, C. Peng, A. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. Gokemeijer, Y.-T. Hsia, and et al., “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. photonics 3, 220 (2009).
[Crossref]

Zijlstra, P.

P. Zijlstra, J. W. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459, 410 (2009).
[Crossref] [PubMed]

ACS Photonics (3)

K. Liu, N. Li, D. K. Sadana, and V. J. Sorger, “Integrated nanocavity plasmon light sources for on-chip optical interconnects,” ACS Photonics 3, 233–242 (2016).
[Crossref]

V. T. Tenner, M. J. de Dood, and M. P. van Exter, “Measurement of the phase and intensity profile of surface plasmon laser emission,” ACS Photonics 3, 942–946 (2016).
[Crossref]

K. M. McPeak, S. V. Jayanti, S. J. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photonics 2, 326–333 (2015).
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Annalen der Physik (1)

N. Arnold, C. Hrelescu, and T. A. Klar, “Minimal spaser threshold within electrodynamic framework: Shape, size and modes,” Annalen der Physik 528, 295–306 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

P. Melentiev, A. Kalmykov, A. Gritchenko, A. Afanasiev, V. Balykin, A. Baburin, E. Ryzhova, I. Filippov, I. Rodionov, I. Nechepurenko, and et al., “Plasmonic nanolaser for intracavity spectroscopy and sensorics,” Appl. Phys. Lett. 111, 213104 (2017).
[Crossref]

J. Commun. Technol. Electron. (1)

E. Chubchev and A. Vinogradov, “Amplifying of surface plasmon-polariton in a metal–gain medium–vacuum structure,” J. Commun. Technol. Electron. 62, 119–122 (2017).
[Crossref]

Laser & Photonics Rev. (1)

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

Laser Phys. Lett. (1)

Y. E. Lozovik, I. Nechepurenko, A. Dorofeenko, E. Andrianov, and A. Pukhov, “Highly sensitive spectroscopy based on a surface plasmon polariton quantum generator,” Laser Phys. Lett. 11, 125701 (2014).
[Crossref]

MRS Bull. (1)

V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37, 728–738 (2012).
[Crossref]

Nano Lett. (3)

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide- si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref] [PubMed]

X. Meng, A. V. Kildishev, K. Fujita, K. Tanaka, and V. M. Shalaev, “Wavelength-tunable spasing in the visible,” Nano Lett. 13, 4106–4112 (2013).
[Crossref] [PubMed]

Nanophotonics (2)

X.-Y. Wang, Y.-L. Wang, S. Wang, B. Li, X.-W. Zhang, L. Dai, and R.-M. Ma, “Lasing enhanced surface plasmon resonance sensing,” Nanophotonics 6, 472–478 (2017).
[Crossref]

N. Zhou, X. Xu, A. T. Hammack, B. C. Stipe, K. Gao, W. Scholz, and E. C. Gage, “Plasmonic near-field transducer for heat-assisted magnetic recording,” Nanophotonics 3, 141–155 (2014).
[Crossref]

Nat. Commun. (1)

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] [PubMed]

Nat. communications (1)

T. Hakala, H. Rekola, A. Väkeväinen, J.-P. Martikainen, M. Nečada, A. Moilanen, and P. Törmä, “Lasing in dark and bright modes of a finite-sized plasmonic lattice,” Nat. communications 8, 13687 (2017).
[Crossref]

Nat. Nanotechnol. (1)

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

Nat. photonics (1)

W. Challener, C. Peng, A. Itagi, D. Karns, W. Peng, Y. Peng, X. Yang, X. Zhu, N. Gokemeijer, Y.-T. Hsia, and et al., “Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer,” Nat. photonics 3, 220 (2009).
[Crossref]

M. C. Gather and S. H. Yun, “Single-cell biological lasers,” Nat. Photonics 5, 406 (2011).
[Crossref]

Nat. Rev. Mater. (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Nature (3)

P. Zijlstra, J. W. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459, 410 (2009).
[Crossref] [PubMed]

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

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 (2009).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. A (1)

L. Ge, Y. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (4)

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

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

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] [PubMed]

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110, 106803 (2013).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. (1)

Y. Sun, S. I. Shopova, C.-S. Wu, S. Arnold, and X. Fan, “Bioinspired optofluidic fret lasers via dna scaffolds,” Proc. Natl. Acad. Sci. 107, 16039–16042 (2010).
[Crossref] [PubMed]

Sci. Adv. (1)

S. J. Kress, J. Cui, P. Rohner, D. K. Kim, F. V. Antolinez, K.-A. Zaininger, S. V. Jayanti, P. Richner, K. M. McPeak, D. Poulikakos, and et al., “A customizable class of colloidal-quantum-dot spasers and plasmonic amplifiers,” Sci. Adv. 3, e1700688 (2017).
[Crossref] [PubMed]

Other (3)

A. E. Siegman, Lasers (University Science Books, 1986).

I. I. Khanin, Fundamentals of laser dynamics (Cambridge International Science Publishing, 2006).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton university press, 2011).

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic view of several lattice periods of the distributed feedback plasmonic laser. It consists of a periodic array of holes in the silver half-space covered by the dielectric host medium with active molecules. (b–d) Electric field norm distribution of the eigenmodes of the plasmonic lattice above the metal surface: non-radiating or BIC modes (b, c) and one of the radiating modes (d). Non-radiating modes decay exponentially away from the metal surface in contrast to radiating mode.
Fig. 2
Fig. 2 Geometries of the distributed feedback plasmon lasers, xz cross-section through the center of the holes. Infinite dielectric with finite gain layer thickness (a), finite dielectric host with gain (b).
Fig. 3
Fig. 3 Lattice shapes under study: (a) square, (b) hexagonal, (c) rectangular with TxTy = Δ, where Tx,y are lattice pitches along the x and y directions, respectively; Δ = 10, 15 and 30 nm. Hole diameter is d.
Fig. 4
Fig. 4 Surface plasmon dispersion on the silver-PVA interface in the empty lattice approximation in the square lattice with T = 561 nm. Different colors show different (n, m) combinations. Black dashed lines show light cone in the air.
Fig. 5
Fig. 5 Position of the eigenmodes in the (r, T) coordinates at fixed wavelength in the square (a), hexagonal (b), rectangular with Δ = 10 nm (c), 15 nm (d), 30 nm (e) lattices. The lattice is covered with infinite dielectric (see Fig. 2(a)), ε″g = 0. Blue line correspond to radiating modes (annotated by r), red line — to the non-radiative modes (nr). Horizontal black lines show the position of the Wood anomaly. Eigenmode above the Wood anomaly is shown as dotted line. Color on the background shows the logarithm of the absorptance (blue — low absorption, yellow — high absorption).
Fig. 6
Fig. 6 Scheme that shows the eigenmodes and their radiation channels in the rectangular lattice with TxTy = Δ. Red arrows show the standing waves in the ±x direction (left) and ±y direction (right). The lattice pitch Tx on the right happens to be above the Wood anomaly so there are the diffraction orders that the eigenmode is scattered into (shown as green arrows).
Fig. 7
Fig. 7 Gain required to reach the lasing threshold for eigenmodes in the square (a), hexagonal (b), rectangular with Δ = 10 nm (c), 15 nm (d), 30 nm (e) lattices. Lattice pitches can be found in Fig. 5. The lattice is covered with the infinite dielectric (see Fig. 2(a)). Blue lines correspond to the radiating modes (annotated by r), red lines — to the non-radiative modes (nr). Solid lines correspond to the threshold found by solving equation for the eigenmodes and complex eigenfrequencies (r and nr), dashed lines ( n r ˜) correspond to the thresholds found through the singularity in absorption coefficient for the incident plane waves (above the Wood anomaly).
Fig. 8
Fig. 8 Gain required to reach lasing threshold for the lowest threshold eigenmodes in square (blue line) and hexagonal (red line) lattices vs. penetration depth of the eigenmodes into the dielectric half-space for a range of hole radii from 0 nm (indicated by the black dot) to 200 nm (arrows show the direction of increasing radius). The lattice is covered with the infinite dielectric (see Fig. 2(a)).
Fig. 9
Fig. 9 (a) Threshold gain for the topmost modes from Fig. 5 for each lattice type (with infinite dielectric covering the metal, see Fig. 2(a)). (b) Threshold gain for the eigenmodes that have the lowest threshold for each lattice type (thickness of the gain medium covering the metal is 400 nm, see Fig. 2(b)). Figure parts (a) and (b) share the same legend.

Equations (10)

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× × E 1 c 2 2 t 2 [ ^ ( r , t ) E ] = C ( r ) c 2 0 2 P t 2 , 2 P t 2 + 2 τ p P t + ω 21 2 P = 2 ω 21 | μ 21 | 2 3 n E , n t + n n 0 τ n = 2 ω 21 E P t ,
× × E + ω 2 c 2 ( ε ( r , ω ) + ε g ( r , ω ) ) E = 0 ,
ε g ( r , ω ) = C ( r ) α ω 21 ω τ p 2 ω [ ω 2 ω 21 2 ] i 1 + β | E | 2 + ( τ p 2 ω [ ω 2 ω 21 2 ] ) 2
× × E + ω 21 2 c 2 ( ε ( r , ω 21 ) + i ε g ( r ) ) E = 0 ,
× × E + Ω n m 2 c 2 ( ε ( r , ω 21 , ξ n ) + i ε g , m ψ ( r , ξ n ) ) E = 0 ,
× × E + ω 21 2 c 2 ( ε ( r , ω 21 , ξ n ) + i ε g , m ψ ( r , ξ n ) ) E = i ω 21 μ 0 J source ( r ) ,
g = 2 ω c Im ε h + i ε g ,
k ˜ eig = ± k eig ( ω ) + n G 1 + m G 2 ,
L = 2 Im k z eig ,
k z eig = k 2 ( n G 1 + m G 2 ) 2 ,

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