Abstract

Plasmonic particle arrays enable unconventional miniature lasers by virtue of feedback by enhanced scattering, field confinement, and diffractive resonances. Here, we demonstrate lasing in quasi-periodic and aperiodic Galois, Thue–Morse, Fibonacci, paperfolding, Rudin–Shapiro, and randomized lattice arrangements of silver particles spanning the Fourier spectrum from discrete (period-like) to increasingly continuous (random-like). Through high-NA back-focal plane images we find that the laser output displays the rich Fourier spectrum of the lattice. Conversely, the real-space output at the laser plane is similar to speckle, yet with distinctly structured autocorrelations. Further, we identify many new lasing conditions on the basis of pseudo-Bragg conditions that do not occur for periodic arrays. This work enables controlled studies of lasing for any level of spatial correlation in the feedback mechanism going from periodic to random and shows that metasurface lasers offer new beam-shaping strategies.

© 2016 Optical Society of America

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References

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2015 (4)

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]

A. H. Schokker and A. F. Koenderink, “Statistics of randomized plasmonic lattice lasers,” ACS Photon. 2, 1289–1297 (2015).
[Crossref]

L. Langguth, A. H. Schokker, K. Guo, and A. F. Koenderink, “Plasmonic phase-gradient metasurface for spontaneous emission control,” Phys. Rev. B 92, 205401 (2015).
[Crossref]

H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Speckle correlation resolution enhancement of wide-field fluorescence imaging,” Optica 2, 424–429 (2015).
[Crossref]

2014 (4)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Y. Nishijima, J. B. Khurgin, L. Rosa, H. Fujiwara, and S. Juodkazis, “Tunable Raman selectivity via randomization of a rectangular pattern of nanodisks,” ACS Photon. 1, 1006–1012 (2014).
[Crossref]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8, 889–898 (2014).
[Crossref]

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

2013 (8)

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).

G. Lozano, D. J. Louwers, S. R. K. Rodriguez, S. Murai, O. T. A. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light 2, e66 (2013).
[Crossref]

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 177–187 (2013).
[Crossref]

C.-W. Lee, G. Singh, and Q. Wang, “Light extraction-a practical consideration for a plasmonic nano-ring laser,” Nanoscale 5, 10835–10838 (2013).
[Crossref]

Y. Nishijima, J. B. Khurgin, L. Rosa, H. Fujiwara, and S. Juodkazis, “Randomization of gold nano-brick arrays: a tool for SERS enhancement,” Opt. Express 21, 13502–13514 (2013).
[Crossref]

W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, E. Hashemizad, S. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast,” Opt. Express 21, 19972–19981 (2013).
[Crossref]

J. H. Lin, W. L. Chang, H.-Y. Lin, T.-H. Chou, H.-C. Kan, and C. C. Hsu, “Enhancing light extraction efficiency of polymer light-emitting diodes with a 12-fold photonic quasi crystal,” Opt. Express 21, 22090–22097 (2013).
[Crossref]

2012 (8)

Y. Nishijima, L. Rosa, and S. Juodkazis, “Surface plasmon resonances in periodic and random patterns of gold nano-disks for broadband light harvesting,” Opt. Express 20, 11466–11477 (2012).
[Crossref]

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

D. Luo, Q. G. Du, H. T. Dai, H. V. Demir, H. Z. Yang, W. Ji, and X. W. Sun, “Strongly linearly polarized low threshold lasing of all organic photonic quasicrystals,” Sci. Rep. 2, 627 (2012).

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

E. Maciá, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref]

S. Mokkapati and K. R. Catchpole, “Nanophotonic light trapping in solar cells,” J. Appl. Phys. 112, 101101 (2012).
[Crossref]

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]

2011 (3)

B. le Feber, J. Cesario, H. Zeijlemaker, N. Rotenberg, and L. Kuipers, “Exploiting long-ranged order in quasiperiodic structures for broadband plasmonic excitation,” Appl. Phys. Lett. 98, 201108 (2011).
[Crossref]

I. Sersic, C. Tuambilangana, and A. F. Koenderink, “Fourier microscopy of single plasmonic scatterers,” New J. Phys. 13, 083019 (2011).
[Crossref]

M. J. H. Marell, B. Smalbrugge, E. J. Geluk, P. J. van Veldhoven, B. Barcones, B. Koopmans, R. Nötzel, M. K. Smit, and M. T. Hill, “Plasmonic distributed feedback lasers at telecommunications wavelengths,” Opt. Express 19, 15109–15118 (2011).
[Crossref]

2010 (4)

J.-K. Yang, S. V. Boriskina, H. Noh, M. J. Rooks, G. S. Solomon, L. Dal Negro, and H. Cao, “Demonstration of laser action in a pseudorandom medium,” Appl. Phys. Lett. 97, 223101 (2010).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

S. Y. Lee, J. J. Amsden, S. V. Boriskina, A. Gopinath, A. Mitropolous, D. L. Kaplan, F. G. Omenetto, and L. Dal Negro, “Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles,” Proc. Natl. Acad. Sci. USA 107, 12086–12090 (2010).
[Crossref]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[Crossref]

2009 (5)

G. Vecchi, V. Giannini, and J. Gómez, Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102, 146807 (2009).
[Crossref]

A. Lagendijk, B. van Tiggelen, and D. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

S. V. Boriskina, A. Gopinath, and L. Dal Negro, “Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures,” Phys. Rev. E 41, 1102–1106 (2009).

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[Crossref]

C. Forestiere, G. F. Walsh, G. Miano, and L. Dal Negro, “Nanoplasmonics of prime number arrays,” Opt. Express 17, 24288–24303 (2009).
[Crossref]

2008 (8)

S. V. Boriskina and L. Dal Negro, “Sensitive label-free biosensing using critical modes in aperiodic photonic structures,” Opt. Express 16, 12511–12522 (2008).
[Crossref]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[Crossref]

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
[Crossref]

L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
[Crossref]

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8, 2423–2431 (2008).
[Crossref]

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. R. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[Crossref]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref]

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108, 494–521 (2008).
[Crossref]

2007 (1)

A. Barbe and F. Von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcation Chaos 17, 1265–1303 (2007).
[Crossref]

2006 (2)

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[Crossref]

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

2005 (1)

M. Ghulinyan, C. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
[Crossref]

2004 (1)

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref]

2003 (3)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref]

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[Crossref]

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D. Luo, Q. G. Du, H. T. Dai, H. V. Demir, H. Z. Yang, W. Ji, and X. W. Sun, “Strongly linearly polarized low threshold lasing of all organic photonic quasicrystals,” Sci. Rep. 2, 627 (2012).

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A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8, 2423–2431 (2008).
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Y. Nishijima, J. B. Khurgin, L. Rosa, H. Fujiwara, and S. Juodkazis, “Randomization of gold nano-brick arrays: a tool for SERS enhancement,” Opt. Express 21, 13502–13514 (2013).
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S. Y. Lee, J. J. Amsden, S. V. Boriskina, A. Gopinath, A. Mitropolous, D. L. Kaplan, F. G. Omenetto, and L. Dal Negro, “Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles,” Proc. Natl. Acad. Sci. USA 107, 12086–12090 (2010).
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L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
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D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
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M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108, 494–521 (2008).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
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Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
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J. Stehr, J. Crewett, F. Schindler, R. Sperling, G. von Plessen, U. Lemmer, J. M. Lupton, T. A. Klar, J. Feldmann, A. W. Holleitner, M. Forster, and U. Scherf, “A low threshold polymer laser based on metallic nanoparticle gratings,” Adv. Mater. 15, 1726 (2003).
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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).
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G. Lozano, D. J. Louwers, S. R. K. Rodriguez, S. Murai, O. T. A. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light 2, e66 (2013).
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D. Luo, Q. G. Du, H. T. Dai, H. V. Demir, H. Z. Yang, W. Ji, and X. W. Sun, “Strongly linearly polarized low threshold lasing of all organic photonic quasicrystals,” Sci. Rep. 2, 627 (2012).

Juodkazis, S.

Kan, H.-C.

Kaplan, D. L.

S. Y. Lee, J. J. Amsden, S. V. Boriskina, A. Gopinath, A. Mitropolous, D. L. Kaplan, F. G. Omenetto, and L. Dal Negro, “Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles,” Proc. Natl. Acad. Sci. USA 107, 12086–12090 (2010).
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O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
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L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[Crossref]

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Y. Nishijima, J. B. Khurgin, L. Rosa, H. Fujiwara, and S. Juodkazis, “Tunable Raman selectivity via randomization of a rectangular pattern of nanodisks,” ACS Photon. 1, 1006–1012 (2014).
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L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

Tuambilangana, C.

I. Sersic, C. Tuambilangana, and A. F. Koenderink, “Fourier microscopy of single plasmonic scatterers,” New J. Phys. 13, 083019 (2011).
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van Albada, M. P.

D. S. Wiersma, M. P. van Albada, and A. Lagendijk, “Random laser,” Nature 373, 203–204 (1995).
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Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
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Van Duyne, R. R.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. R. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
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van Soest, G.

G. van Soest, F. J. Poelwijk, and A. Lagendijk, “Speckle experiments in random lasers,” Phys. Rev. E 65, 046603 (2002).
[Crossref]

van Tiggelen, B.

A. Lagendijk, B. van Tiggelen, and D. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

van Veldhoven, P. J.

Vardeny, Z. V.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 177–187 (2013).
[Crossref]

Vecchi, G.

G. Vecchi, V. Giannini, and J. Gómez, Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102, 146807 (2009).
[Crossref]

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G. Lozano, D. J. Louwers, S. R. K. Rodriguez, S. Murai, O. T. A. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light 2, e66 (2013).
[Crossref]

Von Haeseler, F.

A. Barbe and F. Von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcation Chaos 17, 1265–1303 (2007).
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von Plessen, G.

J. Stehr, J. Crewett, F. Schindler, R. Sperling, G. von Plessen, U. Lemmer, J. M. Lupton, T. A. Klar, J. Feldmann, A. W. Holleitner, M. Forster, and U. Scherf, “A low threshold polymer laser based on metallic nanoparticle gratings,” Adv. Mater. 15, 1726 (2003).
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Vos, W. L.

Walsh, G. F.

Walther, C.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
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Wang, C. J. R.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
[Crossref]

Wang, Q.

C.-W. Lee, G. Singh, and Q. Wang, “Light extraction-a practical consideration for a plasmonic nano-ring laser,” Nanoscale 5, 10835–10838 (2013).
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H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
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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).

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]

Wiersma, D.

A. Lagendijk, B. van Tiggelen, and D. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

M. Ghulinyan, C. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
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D. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
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Wiersma, D. S.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
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D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
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D. S. Wiersma, M. P. van Albada, and A. Lagendijk, “Random laser,” Nature 373, 203–204 (1995).
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Williamson, S.

Yadak, P.

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, H. Z.

D. Luo, Q. G. Du, H. T. Dai, H. V. Demir, H. Z. Yang, W. Ji, and X. W. Sun, “Strongly linearly polarized low threshold lasing of all organic photonic quasicrystals,” Sci. Rep. 2, 627 (2012).

Yang, J.-K.

J.-K. Yang, S. V. Boriskina, H. Noh, M. J. Rooks, G. S. Solomon, L. Dal Negro, and H. Cao, “Demonstration of laser action in a pseudorandom medium,” Appl. Phys. Lett. 97, 223101 (2010).
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Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
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Zhao, L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
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H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
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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).

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).
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ACS Photon. (2)

A. H. Schokker and A. F. Koenderink, “Statistics of randomized plasmonic lattice lasers,” ACS Photon. 2, 1289–1297 (2015).
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Y. Nishijima, J. B. Khurgin, L. Rosa, H. Fujiwara, and S. Juodkazis, “Tunable Raman selectivity via randomization of a rectangular pattern of nanodisks,” ACS Photon. 1, 1006–1012 (2014).
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Adv. Mater. (1)

J. Stehr, J. Crewett, F. Schindler, R. Sperling, G. von Plessen, U. Lemmer, J. M. Lupton, T. A. Klar, J. Feldmann, A. W. Holleitner, M. Forster, and U. Scherf, “A low threshold polymer laser based on metallic nanoparticle gratings,” Adv. Mater. 15, 1726 (2003).
[Crossref]

Annu. Rev. Anal. Chem. (1)

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. R. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
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Appl. Phys. Lett. (2)

B. le Feber, J. Cesario, H. Zeijlemaker, N. Rotenberg, and L. Kuipers, “Exploiting long-ranged order in quasiperiodic structures for broadband plasmonic excitation,” Appl. Phys. Lett. 98, 201108 (2011).
[Crossref]

J.-K. Yang, S. V. Boriskina, H. Noh, M. J. Rooks, G. S. Solomon, L. Dal Negro, and H. Cao, “Demonstration of laser action in a pseudorandom medium,” Appl. Phys. Lett. 97, 223101 (2010).
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Biophys. J. (1)

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
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Int. J. Bifurcation Chaos (1)

A. Barbe and F. Von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcation Chaos 17, 1265–1303 (2007).
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J. Appl. Phys. (1)

S. Mokkapati and K. R. Catchpole, “Nanophotonic light trapping in solar cells,” J. Appl. Phys. 112, 101101 (2012).
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J. Opt. A (1)

L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
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J. Phys. Chem. B (1)

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
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Laser Photon. Rev. (1)

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).
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Light (1)

G. Lozano, D. J. Louwers, S. R. K. Rodriguez, S. Murai, O. T. A. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light 2, e66 (2013).
[Crossref]

Nano Lett. (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).
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A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8, 2423–2431 (2008).
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Nanoscale (1)

C.-W. Lee, G. Singh, and Q. Wang, “Light extraction-a practical consideration for a plasmonic nano-ring laser,” Nanoscale 5, 10835–10838 (2013).
[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]

Nat. Mater. (3)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
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H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[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).

Nat. Photonics (5)

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 177–187 (2013).
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E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
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O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
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L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8, 889–898 (2014).
[Crossref]

Nat. Phys. (2)

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
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M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
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Nature (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
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D. S. Wiersma, M. P. van Albada, and A. Lagendijk, “Random laser,” Nature 373, 203–204 (1995).
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New J. Phys. (1)

I. Sersic, C. Tuambilangana, and A. F. Koenderink, “Fourier microscopy of single plasmonic scatterers,” New J. Phys. 13, 083019 (2011).
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Opt. Express (7)

S. V. Boriskina and L. Dal Negro, “Sensitive label-free biosensing using critical modes in aperiodic photonic structures,” Opt. Express 16, 12511–12522 (2008).
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C. Forestiere, G. F. Walsh, G. Miano, and L. Dal Negro, “Nanoplasmonics of prime number arrays,” Opt. Express 17, 24288–24303 (2009).
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M. J. H. Marell, B. Smalbrugge, E. J. Geluk, P. J. van Veldhoven, B. Barcones, B. Koopmans, R. Nötzel, M. K. Smit, and M. T. Hill, “Plasmonic distributed feedback lasers at telecommunications wavelengths,” Opt. Express 19, 15109–15118 (2011).
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Y. Nishijima, L. Rosa, and S. Juodkazis, “Surface plasmon resonances in periodic and random patterns of gold nano-disks for broadband light harvesting,” Opt. Express 20, 11466–11477 (2012).
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Y. Nishijima, J. B. Khurgin, L. Rosa, H. Fujiwara, and S. Juodkazis, “Randomization of gold nano-brick arrays: a tool for SERS enhancement,” Opt. Express 21, 13502–13514 (2013).
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W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, E. Hashemizad, S. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast,” Opt. Express 21, 19972–19981 (2013).
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J. H. Lin, W. L. Chang, H.-Y. Lin, T.-H. Chou, H.-C. Kan, and C. C. Hsu, “Enhancing light extraction efficiency of polymer light-emitting diodes with a 12-fold photonic quasi crystal,” Opt. Express 21, 22090–22097 (2013).
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Optica (1)

Phys. Rev. B (5)

L. Langguth, A. H. Schokker, K. Guo, and A. F. Koenderink, “Plasmonic phase-gradient metasurface for spontaneous emission control,” Phys. Rev. B 92, 205401 (2015).
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M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
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A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90, 155452 (2014).
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M. Ghulinyan, C. Oton, L. Dal Negro, L. Pavesi, R. Sapienza, M. Colocci, and D. Wiersma, “Light-pulse propagation in Fibonacci quasicrystals,” Phys. Rev. B 71, 094204 (2005).
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Phys. Rev. E (4)

M. Stockman, “Inhomogeneous eigenmode localization, chaos, and correlations in large disordered clusters,” Phys. Rev. E 56, 6494–6507 (1997).
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S. V. Boriskina, A. Gopinath, and L. Dal Negro, “Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures,” Phys. Rev. E 41, 1102–1106 (2009).

D. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[Crossref]

G. van Soest, F. J. Poelwijk, and A. Lagendijk, “Speckle experiments in random lasers,” Phys. Rev. E 65, 046603 (2002).
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Phys. Rev. Lett. (5)

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
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H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

G. Vecchi, V. Giannini, and J. Gómez, Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102, 146807 (2009).
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Phys. Today (1)

A. Lagendijk, B. van Tiggelen, and D. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
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Proc. Natl. Acad. Sci. USA (1)

S. Y. Lee, J. J. Amsden, S. V. Boriskina, A. Gopinath, A. Mitropolous, D. L. Kaplan, F. G. Omenetto, and L. Dal Negro, “Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles,” Proc. Natl. Acad. Sci. USA 107, 12086–12090 (2010).
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D. Luo, Q. G. Du, H. T. Dai, H. V. Demir, H. Z. Yang, W. Ji, and X. W. Sun, “Strongly linearly polarized low threshold lasing of all organic photonic quasicrystals,” Sci. Rep. 2, 627 (2012).

Other (1)

L. Dal Negro, Optics of aperiodic structures (Pan Stanford, 2014).

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Figures (5)

Fig. 1.
Fig. 1.

Panel (a): SEM images of the arrays for a particle pitch of 380 nm; underneath it, the discrete Fourier transform of the corresponding array (Panel b). Red circles indicate the wave vector range available to a NA = 1.45 objective, assuming a 380 nm pitch and 590 nm emisson wavelength. Panel (c) shows a set-up diagram indicating Fourier imaging. Panel (d) shows spectra above the lasing threshold for periodic, Galois, Thue–Morse, Fibonacci, paperfolding, Rudin–Shapiro, and random arrays. The lasing wavelength is the same to within 1 nm for all arrays and corresponds to the wavelength for which the second-order Bragg diffraction condition holds for a pitch of 380 nm. Input–output curves are shown for all arrays in panel (e). From these curves, we obtain threshold pump powers of 12.5, 13.5, 15.6, 14.6, 12.5, 15.6, and 18.7 nJ.

Fig. 2.
Fig. 2.

Fourier images well above threshold for (a) periodic, (b) Galois, (c) Thue–Morse, (d) Fibonacci, (e) paperfolding, (f) Rudin–Shapiro (f), and random array (g). The Fourier images are obtained for an excitation energy of 0.05 μJ. For all quasi-periodic structures, extra peaks appear beside the second-order Bragg peak in the middle at k = 0 . These coincide with maxima in the Fourier transform of the structure. It should be noted that these single-shot images well above the threshold are saturated in their bright pixels.

Fig. 3.
Fig. 3.

Panels (a)–(d): Direct comparison of high dynamic range Fourier images of lasing in the Galois, Thue–Morse, paperfolding, and Fibonacci structures to the structure factors (DFTs). East-southeast quadrants (red): measured. Northern quadrants (blue): structure DFT (data and DFT normalized to the k = 0 peak, linear color scale). White circles: NA = 1 and 1.45 boundaries. White arrows: k x / k 0 values at which salient line traces along k y are taken for panels (e)–(h). In each panel, the top (red) traces are data, while the downward (blue) traces are theoretical.

Fig. 4.
Fig. 4.

Real-space images (a) and normalized autocorrelation (b) well above the threshold. The real-space images have 20 μm field of view, and a clipped colorscale [ranges always corresponding to 1.4 times the minimum number of counts to 0.6 times the maximum number of counts]. Color ranges for autocorrelations are from 1.0 (minimum, no excess correlation) to the maximum correlation a at ( x , y ) = ( 0 , 0 ) , which is 1.05, 1.12, 1.07, 1.14, 1.09, 1.07, resp. 1.1. This value mainly measures how far above threshold data was taken [46]. The scalebar is 3 μm in all panels in (b).

Fig. 5.
Fig. 5.

Fourier images above lasing threshold for a pitch of 300 nm (a)–(g) and spectra for all arrays at the maximum pump power. As can be seen in panel (h), the lasing wavelength is different for each structure. The periodic system does not show a lasing peak. Panel (j): calculated band diagrams for Galois, Fibonacci, and paperfolding arrays. Horizontal colored lines represent measured lasing peak frequencies for the lattices with 380, 190, and 300 nm pitch plotted in normalized units n WG d / λ (where λ is measured wavelength, d is the nominal pitch, and n WG = 1.54 , assumed to be fixed). Solid (dashed) cyan lines represent the d = 380    nm ( d = 190    nm ) samples, lasing at second- resp. first-order Bragg diffraction ( n WG d / λ equals 1 resp. 0.5). The other lines (around 0.7–0.85) correspond to various lasing conditions for d = 300    nm .

Tables (1)

Tables Icon

Table 1. Calculated Spectral Flatness (SF) and Measured Threshold Pump Power P th Required to Obtain Lasing for Pitch 380 nm. Also Reported Is Whether the k-Space Spectrum of the Structure is Pure-Point (PP), Singular Continuous (SC), or Absolutely Continuous (AC)

Equations (1)

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SF = n , m N , M | DFT { s ( n , m ) } | N M 1 N M n , m N , M | DFT { s ( n , m ) } | .

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