Abstract

We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction of emission rates into different modal channels for waveguides with arbitrary cross-sections. We compare our method with dyadic Green’s function for the light emission in single mode metallic nanowire, which yields an excellent agreement. This method is applied in multi-mode waveguides, as well as multi-core waveguides. We further show that our method has the full capability of including dipole orientations, as illustrated via a rotating dipole, which leads to unidirectional excitation of guide modes. The 2.5D Finite Element Method (FEM) approach proposed here can be applied for various waveguides, thus it is useful to interface single-photon single-emitter in nano-structures, as well as for other scenarios involving coupled waveguide-emitters.

© 2015 Optical Society of America

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2015 (4)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref] [PubMed]

B. le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref] [PubMed]

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kirsanska, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nature Nanotechnology 10, 775–778 (2015).
[Crossref] [PubMed]

2014 (2)

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref] [PubMed]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

2013 (7)

S. Kumar, A. Huck, Y. T. Chen, and U. L. Andersen, “Coupling of a single quantum emitter to end-to-end aligned silver nanowires,” Appl. Phys. Lett. 102, 103106 (2013).
[Crossref]

J. R. de Lasson, J. Mørk, and P. T. Kristensen, “Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes,” J. Opt. Soc. Am. B 30, 1996–2007 (2013).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref] [PubMed]

X. Guo, Y. Ma, Y. Wang, and L. Tong, “Nanowire plasmonic waveguides, circuits and devices,” Laser Photon. Rev. 7, 855–881 (2013).
[Crossref]

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B 87, 115419 (2013).
[Crossref]

Y. Bian and Q. Gong, “Metallic nanowire-loaded plasmonic slot waveguide for highly confined light transport at telecom wavelength,” IEEE J. Quantum Electron. 49, 870–876 (2013).
[Crossref]

S. Kumar, A. Huck, Y. W. Lu, and U. L. Andersen, “Coupling of single quantum emitters to plasmons propagating on mechanically etched wires,” Opt. Lett. 38, 3838–3841 (2013).
[Crossref] [PubMed]

2012 (2)

J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, and S. Matsuo, “Design and analysis of large-effective-area heterogeneous trench-assisted multi-core fiber,” Opt. Express,  20, 15157–15170 (2012).
[Crossref] [PubMed]

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J.-M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[Crossref] [PubMed]

2011 (1)

M. Frimmer, Y. Chen, and A. F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett. 107, 123602 (2011).
[Crossref] [PubMed]

2010 (4)

G. C. des Francs, P. Bramant, J. Grandidier, A. Bouhelier, J. C. Weeber, and A. Dereux, “Optical gain, spontaneous and stimulated emission of surface plasmon polaritons in confined plasmonic waveguide,” Opt. Express 18, 16327–16334 (2010).
[Crossref]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

D. Dzsotjan, A. S. Sørensen, and M. Fleischhauer, “Quantum emitters coupled to surface plasmons of a nanowire: A Green’s function approach,” Phys. Rev. B 82, 075427 (2010).
[Crossref]

2009 (3)

N. Gregersen and J. Mørk, “An improved perfectly matched layer for the eigenmode expansion technique,” Opt. Quantum Electron. 40, 957–966 (2009).
[Crossref]

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009).
[Crossref]

X. W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9, 3756–3761 (2009).
[Crossref] [PubMed]

2008 (4)

J. Johansen, S. Stobbe, I. S. Nikolaev, T. Lund-Hansen, P. T. Kristensen, J. M. Hvam, W. L. Vos, and P. Lodahl, “Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements,” Phys. Rev. B 77, 073303 (2008).
[Crossref]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

D. Pardo, L. Demkowicz, C. Torres-Verdín, and C. Michler, “PML enhanced with a self-adaptive goal-oriented hp-finite element method: simulation of through-casing borehole resistivity measurements,” SIAM J. Sci. Comput. 30, 2948–2964 (2008).
[Crossref]

P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Lgsgaard, and Y. S. Kivshar, “Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers,” Opt. Express 165878–5891 (2008).
[Crossref] [PubMed]

2007 (2)

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244 (10), 3448–3462 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

2006 (3)

S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref]

A. F. Koenderink, M. Kafesaki, C. M. Soukoulis, and V. Sandoghdar, “Spontaneous emission rates of dipoles in photonic crystal membranes,” J. Opt. Soc. Am. B 23, 1196–1206 (2006).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

2004 (1)

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004).
[Crossref]

2003 (1)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[Crossref]

2002 (1)

2001 (1)

T. Søndergaard and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: Example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001).
[Crossref]

1999 (1)

N. E. Hecker, R. A. Hopfel, N. Sawaki, T. Maier, and G. Strasser, “Surface plasmon enhanced photoluminescence from a single quantum well,” Appl. Phys. Lett. 75, 1577–1579 (1999).
[Crossref]

1997 (1)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[Crossref]

Agio, M.

X. W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9, 3756–3761 (2009).
[Crossref] [PubMed]

Akimov, A. V.

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009).
[Crossref]

Andersen, U. L.

S. Kumar, A. Huck, Y. T. Chen, and U. L. Andersen, “Coupling of a single quantum emitter to end-to-end aligned silver nanowires,” Appl. Phys. Lett. 102, 103106 (2013).
[Crossref]

S. Kumar, A. Huck, Y. W. Lu, and U. L. Andersen, “Coupling of single quantum emitters to plasmons propagating on mechanically etched wires,” Opt. Lett. 38, 3838–3841 (2013).
[Crossref] [PubMed]

Arcari, M.

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Bang, O.

Bian, Y.

Y. Bian and Q. Gong, “Metallic nanowire-loaded plasmonic slot waveguide for highly confined light transport at telecom wavelength,” IEEE J. Quantum Electron. 49, 870–876 (2013).
[Crossref]

Bleuse, J.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J.-M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[Crossref] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref] [PubMed]

Bouhelier, A.

Bramant, P.

Chang, D. E.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Chen, X. W.

X. W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9, 3756–3761 (2009).
[Crossref] [PubMed]

Chen, Y.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J.-M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[Crossref] [PubMed]

M. Frimmer, Y. Chen, and A. F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett. 107, 123602 (2011).
[Crossref] [PubMed]

Y. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18, 12489–12498 (2010).
[Crossref] [PubMed]

Chen, Y. T.

S. Kumar, A. Huck, Y. T. Chen, and U. L. Andersen, “Coupling of a single quantum emitter to end-to-end aligned silver nanowires,” Appl. Phys. Lett. 102, 103106 (2013).
[Crossref]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

Claudon, J.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J.-M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[Crossref] [PubMed]

Crozier, K. B.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[Crossref]

Dasari, R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[Crossref]

de Lasson, J. R.

Demkowicz, L.

D. Pardo, L. Demkowicz, C. Torres-Verdín, and C. Michler, “PML enhanced with a self-adaptive goal-oriented hp-finite element method: simulation of through-casing borehole resistivity measurements,” SIAM J. Sci. Comput. 30, 2948–2964 (2008).
[Crossref]

Dereux, A.

des Francs, G. C.

Dupuy, E.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J.-M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[Crossref] [PubMed]

Dzsotjan, D.

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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref] [PubMed]

Overgaag, K.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004).
[Crossref]

Pardo, D.

D. Pardo, L. Demkowicz, C. Torres-Verdín, and C. Michler, “PML enhanced with a self-adaptive goal-oriented hp-finite element method: simulation of through-casing borehole resistivity measurements,” SIAM J. Sci. Comput. 30, 2948–2964 (2008).
[Crossref]

Park, H.

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009).
[Crossref]

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[Crossref]

Petersen, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref] [PubMed]

Pregnolato, T.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kirsanska, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nature Nanotechnology 10, 775–778 (2015).
[Crossref] [PubMed]

Quate, C. F.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[Crossref]

Rasmussen, P. D.

Rauschenbeutel, A.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref] [PubMed]

Rodríguez-Fortuño, F. J.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref] [PubMed]

Rogobete, L.

S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref]

Rotenberg, N.

B. le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref] [PubMed]

Saitoh, K.

Sandoghdar, V.

X. W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9, 3756–3761 (2009).
[Crossref] [PubMed]

S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref]

A. F. Koenderink, M. Kafesaki, C. M. Soukoulis, and V. Sandoghdar, “Spontaneous emission rates of dipoles in photonic crystal membranes,” J. Opt. Soc. Am. B 23, 1196–1206 (2006).
[Crossref]

Sawaki, N.

N. E. Hecker, R. A. Hopfel, N. Sawaki, T. Maier, and G. Strasser, “Surface plasmon enhanced photoluminescence from a single quantum well,” Appl. Phys. Lett. 75, 1577–1579 (1999).
[Crossref]

Smirnova, D.

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref] [PubMed]

Snapp, N. D.

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, New York, 1983).

Söllner, I.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kirsanska, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nature Nanotechnology 10, 775–778 (2015).
[Crossref] [PubMed]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Søndergaard, T.

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244 (10), 3448–3462 (2007).
[Crossref]

T. Søndergaard and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: Example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001).
[Crossref]

Song, J. D.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kirsanska, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nature Nanotechnology 10, 775–778 (2015).
[Crossref] [PubMed]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Sørensen, A. S.

D. Dzsotjan, A. S. Sørensen, and M. Fleischhauer, “Quantum emitters coupled to surface plasmons of a nanowire: A Green’s function approach,” Phys. Rev. B 82, 075427 (2010).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Soukoulis, C. M.

Stobbe, S.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kirsanska, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nature Nanotechnology 10, 775–778 (2015).
[Crossref] [PubMed]

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

J. Johansen, S. Stobbe, I. S. Nikolaev, T. Lund-Hansen, P. T. Kristensen, J. M. Hvam, W. L. Vos, and P. Lodahl, “Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements,” Phys. Rev. B 77, 073303 (2008).
[Crossref]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Strasser, G.

N. E. Hecker, R. A. Hopfel, N. Sawaki, T. Maier, and G. Strasser, “Surface plasmon enhanced photoluminescence from a single quantum well,” Appl. Phys. Lett. 75, 1577–1579 (1999).
[Crossref]

Sukhorukov, A. A.

Sundaramurthy, A.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[Crossref]

Sünner, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Takenaga, K.

Thyrrestrup, H.

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

Tong, L.

X. Guo, Y. Ma, Y. Wang, and L. Tong, “Nanowire plasmonic waveguides, circuits and devices,” Laser Photon. Rev. 7, 855–881 (2013).
[Crossref]

Torres-Verdín, C.

D. Pardo, L. Demkowicz, C. Torres-Verdín, and C. Michler, “PML enhanced with a self-adaptive goal-oriented hp-finite element method: simulation of through-casing borehole resistivity measurements,” SIAM J. Sci. Comput. 30, 2948–2964 (2008).
[Crossref]

Tromborg, B.

T. Søndergaard and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: Example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001).
[Crossref]

Tu, J.

van Driel, A. F.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004).
[Crossref]

Vanmaekelbergh, D.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004).
[Crossref]

Volz, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref] [PubMed]

Vos, W. L.

J. Johansen, S. Stobbe, I. S. Nikolaev, T. Lund-Hansen, P. T. Kristensen, J. M. Hvam, W. L. Vos, and P. Lodahl, “Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements,” Phys. Rev. B 77, 073303 (2008).
[Crossref]

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004).
[Crossref]

Wang, Y.

X. Guo, Y. Ma, Y. Wang, and L. Tong, “Nanowire plasmonic waveguides, circuits and devices,” Laser Photon. Rev. 7, 855–881 (2013).
[Crossref]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[Crossref]

Weeber, J. C.

Wurtz, G. A.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref] [PubMed]

Yu, C. L.

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009).
[Crossref]

Zayats, A. V.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref] [PubMed]

Zueco, D.

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B 87, 115419 (2013).
[Crossref]

Appl. Phys. Lett. (2)

N. E. Hecker, R. A. Hopfel, N. Sawaki, T. Maier, and G. Strasser, “Surface plasmon enhanced photoluminescence from a single quantum well,” Appl. Phys. Lett. 75, 1577–1579 (1999).
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S. Kumar, A. Huck, Y. T. Chen, and U. L. Andersen, “Coupling of a single quantum emitter to end-to-end aligned silver nanowires,” Appl. Phys. Lett. 102, 103106 (2013).
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IEEE J. Quantum Electron. (1)

Y. Bian and Q. Gong, “Metallic nanowire-loaded plasmonic slot waveguide for highly confined light transport at telecom wavelength,” IEEE J. Quantum Electron. 49, 870–876 (2013).
[Crossref]

J. Appl. Phys. (1)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[Crossref]

J. Opt. Soc. Am. B (3)

Laser Photon. Rev. (1)

X. Guo, Y. Ma, Y. Wang, and L. Tong, “Nanowire plasmonic waveguides, circuits and devices,” Laser Photon. Rev. 7, 855–881 (2013).
[Crossref]

Nano Lett. (1)

X. W. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9, 3756–3761 (2009).
[Crossref] [PubMed]

Nat. Commun. (1)

B. le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref] [PubMed]

Nat. Phys. (1)

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009).
[Crossref]

Nature (London) (1)

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654–657 (2004).
[Crossref]

Nature Nanotechnology (1)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kirsanska, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nature Nanotechnology 10, 775–778 (2015).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

N. Gregersen and J. Mørk, “An improved perfectly matched layer for the eigenmode expansion technique,” Opt. Quantum Electron. 40, 957–966 (2009).
[Crossref]

Phys. Rev. A (1)

T. Søndergaard and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: Example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001).
[Crossref]

Phys. Rev. B (5)

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[Crossref]

J. Johansen, S. Stobbe, I. S. Nikolaev, T. Lund-Hansen, P. T. Kristensen, J. M. Hvam, W. L. Vos, and P. Lodahl, “Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements,” Phys. Rev. B 77, 073303 (2008).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B 87, 115419 (2013).
[Crossref]

D. Dzsotjan, A. S. Sørensen, and M. Fleischhauer, “Quantum emitters coupled to surface plasmons of a nanowire: A Green’s function approach,” Phys. Rev. B 82, 075427 (2010).
[Crossref]

Phys. Rev. Lett. (7)

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J.-M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[Crossref] [PubMed]

M. Frimmer, Y. Chen, and A. F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett. 107, 123602 (2011).
[Crossref] [PubMed]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101, 113903 (2008).
[Crossref] [PubMed]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[Crossref]

S. Kühn, U. Hakanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna,” Phys. Rev. Lett. 97, 017402 (2006).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref] [PubMed]

Phys. Status Solidi B (1)

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244 (10), 3448–3462 (2007).
[Crossref]

Rev. Mod. Phys. (1)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

Science (3)

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref] [PubMed]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref] [PubMed]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref] [PubMed]

SIAM J. Sci. Comput. (1)

D. Pardo, L. Demkowicz, C. Torres-Verdín, and C. Michler, “PML enhanced with a self-adaptive goal-oriented hp-finite element method: simulation of through-casing borehole resistivity measurements,” SIAM J. Sci. Comput. 30, 2948–2964 (2008).
[Crossref]

Other (4)

J. M. Jin, The Finite Element Method in Electromagnetics (Wiley, 1993).

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).
[Crossref]

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, New York, 1983).

J. Jackson, Classical Electrodynamics3rd ed. (Wiley, New York, 1999).

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Figures (4)

Fig. 1
Fig. 1 Spontaneous emission in a single nanowire. (a) Schematic of the coupling between a metallic nanowire and a quantum emitter oriented in the radial direction. (b) Normalized differential energy dissipation rate P(knz)/P0 and normalized differential spontaneous emission rate γ(knz)0 as functions of the effective index of different modes. The normalized differential dissipation rate of the emitter coupled to each mode calculated by the 2.5D FEM (red circle line), fully agree with the normalized differential emission rate calculated by the dyadic Green’s function method (blue line). The insets of (b) is the enlarged view of the shadow region of (b). (c) Length dependence of computation time for the 3D FEM and for the 2.5D FEM when solving an infinite nanowire with different parallel computations.
Fig. 2
Fig. 2 SE in an infinite elliptical photonic nanowire. (a) Rate of differential energy dissipation as a function of the effective index. The four guided modes have been excited, i.e., modes A, B, C, and D. (b) The fraction of the emission coupled to each of the four guided eigen modes (β factor) as a function of source distance D from the center of the nanowire. (c)–(f) The electric field distributions of the four guided modes, where the arrows denote the field intensity and orientation.
Fig. 3
Fig. 3 SE into a multi-core waveguide. (a) Differential energy dissipation rate of a single dipole relative to the homogeneous material (ε2 = 2) dissipation rate as a function of effective index. The guided modes propagating along the same direction have been excited, i.e., modes A, B, C, and D. (b)–(e) Electric field distributions of the four guided modes, where the arrows indicate the field of each guided mode in the dipole position. The β factors of the four guided plasmonic modes are also shown within the profile of each mode.
Fig. 4
Fig. 4 Perfectly unidirectional excitation. The blue line and red line of (a) show the perfect unidirectional excitation of guided modes, in the case of a wire of radius R1 = 20nm and R2 = 60nm respectively. (b) The P + k z S P P / P k z S P P as a function of polarization of the dipole for the two case. In each case, there is an optimal α where the mode with k z S P P suppressed completely.

Equations (9)

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[ × 1 μ ¯ r × k 0 2 ε ¯ r ( r ) ] E ( r , ω ) ω 2 μ 0 p ( r 0 , ω ) = 0 ,
L = V [ × 1 μ ¯ r × k 0 2 ε ¯ r ( r ) ] E ( r , ω ) F ( r , ω ) d v V ω 2 μ 0 p ( ω , r 0 ) F ( r , ω ) d v = V 1 μ ¯ r ( × E ( r , ω ) ) ( × F ( r , ω ) ) d v V k 0 2 ε ¯ r ( r ) E ( r , ω ) F ( r , ω ) d v V ω 2 μ 0 p ( ω , r 0 ) F ( r , ω ) d v + V F ( r , ω ) [ 1 μ ¯ r n × × E ( r , ω ) ] d s ,
L = X , Y d x d y { 1 μ ¯ r CurrlE ( x , y , k n z ) Currl E n ( x , y , k n z ) k 0 2 ε ¯ r ( r ) E ( x , y , k n z ) F n ( x , y , k n z ) } X , Y d x d y { ω 2 μ 0 p ( x 0 , y 0 ) F n ( x , y , k n z ) } + V F n ( r , ω ) [ 1 μ ¯ r n × × E ( r , ω ) ] d s ,
P = d W d t = ω 2 Im { p * E ( r 0 ) } ,
P ( k n z ) = ω 2 Im { p * E ( x 0 , y 0 ; k n z ) } ,
γ ( k n z ) γ 0 = 6 π c ω 0 [ n p T Im { G ¯ ( r 0 , r 0 , ω ; k n z ) } n p ] ,
P + k z S p p = ω 2 Im ( p * E d i p ( r 0 ) ) = ω 2 [ Im ( E x d i p ) + α Re ( E x d i p ) ] ,
P k z S p p = ω 2 Im ( p * E d i p ( r 0 ) ) = ω 2 [ Im ( E x d i p ) α Re ( E x d i p ) ] ,
α = Re ( E x e i g ) / Im ( E z e i g ) ,

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