Abstract

We theoretically investigate the interaction of a single quantum dipole with the modes of a fiber-coupled semiconductor waveguide. Through a combination of tight modal confinement and phase-matched evanescent coupling, we predict that 70% of the dipole’s emission can be collected into a single-mode optical fiber. We further show that the dipole strongly modifies resonant light transmission through the system, with a change of over 1 order of magnitude for an appropriate choice of fiber-waveguide coupler geometry.

© 2009 Optical Society of America

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  1. H. J. Kimble, Phys. Scr., T 76, 127 (1998).
    [CrossRef]
  2. S. J. van Enk, Phys. Rev. A 69, 043813 (2004).
    [CrossRef]
  3. P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A 65, 033832 (2002).
    [CrossRef]
  4. J. T. Shen and S. Fan, Opt. Lett. 30, 2001 (2005).
    [CrossRef] [PubMed]
  5. D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).
  6. B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
    [CrossRef]
  7. G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
    [CrossRef] [PubMed]
  8. V. S. C. M. Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).
    [CrossRef]
  9. G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
    [CrossRef] [PubMed]
  10. Resonant fluorescence can also be studied, for example, through emission into the backward traveling WG mode.
  11. M. I. Davanço and K. Srinivasan, Opt. Express 17, 10542 (2009).
    [CrossRef] [PubMed]
  12. W.-P. Huang, J. Opt. Soc. Am. A 11, 963 (1994).
    [CrossRef]
  13. K. Srinivasan and O. Painter, Nature 450, 862 (2007).
    [CrossRef] [PubMed]
  14. Far from cutoff, channel WG Epqx,y modes are predominantly x or y polarized, with p and q maxima in the x and y directions respectively.
  15. F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
    [CrossRef]

2009 (1)

2008 (1)

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
[CrossRef] [PubMed]

2007 (5)

V. S. C. M. Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).
[CrossRef]

G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

K. Srinivasan and O. Painter, Nature 450, 862 (2007).
[CrossRef] [PubMed]

2005 (2)

F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
[CrossRef]

J. T. Shen and S. Fan, Opt. Lett. 30, 2001 (2005).
[CrossRef] [PubMed]

2004 (1)

S. J. van Enk, Phys. Rev. A 69, 043813 (2004).
[CrossRef]

2002 (1)

P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A 65, 033832 (2002).
[CrossRef]

1998 (1)

H. J. Kimble, Phys. Scr., T 76, 127 (1998).
[CrossRef]

1994 (1)

Agio, M.

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
[CrossRef] [PubMed]

Badolato, A.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Balykin, V. I.

F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
[CrossRef]

Chang, D. E.

D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).

Dalgarno, P. A.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Davanço, M. I.

Demler, E. A.

D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).

Domokos, P.

P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A 65, 033832 (2002).
[CrossRef]

Fan, S.

Gerardot, B. D.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Gupta, S. D.

F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
[CrossRef]

Hakuta, K.

F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
[CrossRef]

Horak, P.

P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A 65, 033832 (2002).
[CrossRef]

Huang, W.-P.

Hughes, S.

V. S. C. M. Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).
[CrossRef]

Hugonin, J. P.

G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
[CrossRef] [PubMed]

Karrai, K.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Kimble, H. J.

H. J. Kimble, Phys. Scr., T 76, 127 (1998).
[CrossRef]

Kroner, M.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Lalanne, P.

G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
[CrossRef] [PubMed]

Le Kien, F.

F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
[CrossRef]

Lecamp, G.

G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
[CrossRef] [PubMed]

Lukin, M. D.

D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).

Mojarad, N. M.

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
[CrossRef] [PubMed]

Painter, O.

K. Srinivasan and O. Painter, Nature 450, 862 (2007).
[CrossRef] [PubMed]

Petroff, P. M.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Rao, V. S. C. M.

V. S. C. M. Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).
[CrossRef]

Ritsch, H.

P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A 65, 033832 (2002).
[CrossRef]

Sandoghdar, V.

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
[CrossRef] [PubMed]

Seidl, S.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Shen, J. T.

Srensen, A. S.

D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).

Srinivasan, K.

van Enk, S. J.

S. J. van Enk, Phys. Rev. A 69, 043813 (2004).
[CrossRef]

Warburton, R. J.

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

Zumofen, G.

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

B. D. Gerardot, S. Seidl, P. A. Dalgarno, R. J. Warburton, M. Kroner, K. Karrai, A. Badolato, and P. M. Petroff, Appl. Phys. Lett. 90, 221106 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (2)

K. Srinivasan and O. Painter, Nature 450, 862 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Srensen, E. A. Demler, and M. D. Lukin, Nature 3, 807 (2007).

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (3)

S. J. van Enk, Phys. Rev. A 69, 043813 (2004).
[CrossRef]

P. Domokos, P. Horak, and H. Ritsch, Phys. Rev. A 65, 033832 (2002).
[CrossRef]

F. Le Kien, S. D. Gupta, V. I. Balykin, and K. Hakuta, Phys. Rev. A 72, 032509 (2005).
[CrossRef]

Phys. Rev. B (1)

V. S. C. M. Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
[CrossRef] [PubMed]

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, Phys. Rev. Lett. 101, 180404 (2008).
[CrossRef] [PubMed]

Phys. Scr., T (1)

H. J. Kimble, Phys. Scr., T 76, 127 (1998).
[CrossRef]

Other (2)

Resonant fluorescence can also be studied, for example, through emission into the backward traveling WG mode.

Far from cutoff, channel WG Epqx,y modes are predominantly x or y polarized, with p and q maxima in the x and y directions respectively.

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Figures (4)

Fig. 1
Fig. 1

Fiber taper/channel WG directional coupler scheme. (a) 3D schematic and coupler cross section. (b) Hybrid hE 11 x , I and hE 11 x , II coupler supermodes for W ch = 190 nm and λ = 1.3 μ m . (c) Nonresonant single-dipole PL collection configuration.

Fig. 2
Fig. 2

Effective index n eff , m , fiber mode fraction f m , β-factor γ m , and PL collection contribution η PL , m as functions of channel WG width W ch for (a)–(d) hE 11 x , m ( m = I or II) and (e)–(h) hE 11 y , m supermodes ( m = I , II, or III).

Fig. 3
Fig. 3

Maximum spontaneous emission collection efficiencies for (a) x- and (b) z-polarized dipole moments as a function of W ch , calculated with FDTD and supermode expansion.

Fig. 4
Fig. 4

Normalized, off- and on-resonance transmission ( F 0 and F) and contrast Δ T = ( F F 0 ) F 0 as functions of separation from a single dipole at z 0 , for (a) W ch = 220 nm and (b) W ch = 300 nm .

Equations (2)

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E ( + ) ( z , t ) = i 2 π m ω 4 π S m e m e i ( ω t β m z ) × [ a ̂ in m ( t n m z c ) + Γ m * σ ̂ ( t n m z c ) ] .
F ̂ = { S d S ( E ( ) × h f ) z S d S ( e f * × H ( + ) ) z + S d S ( H ( ) × e f * ) z S d S ( h f * × E ( + ) ) z } S f 1 ,

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