Abstract

The influence of a tapering on nanowire light-emission profiles is studied. We show that, for nanowires with divergent output beams, the introduction of a conical tapering with a small opening angle reduces the beam divergence and increases transmission. This results in a dramatic increase in the collection efficiency of the detection optics. For a realistic tapering and a modest NA, the collection efficiency is enhanced by more than a factor of 2. This improvement is ensured by the adiabatic expansion of the guided mode in the tapering.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (2)

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, Appl. Phys. Lett. 91, 011116 (2007).
[CrossRef]

2006 (3)

P. J. Pauzauskie and P. Yang, Mater. Today 9, 36 (2006).
[CrossRef]

L. Chen and E. Towe, Appl. Phys. Lett. 89, 053125 (2006).
[CrossRef]

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

2005 (2)

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, Nano Lett. 5, 1439 (2005).
[CrossRef] [PubMed]

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

2002 (1)

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

2001 (1)

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

1995 (1)

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Almeida, V. R.

Baets, R.

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989), Chap. 6.

Barnes, W. L.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Bi, W. G.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Bienstman, P.

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

Björk, G.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Borgström, M. T.

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, Nano Lett. 5, 1439 (2005).
[CrossRef] [PubMed]

Bukanov, M. I.

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

Chen, L.

L. Chen and E. Towe, Appl. Phys. Lett. 89, 053125 (2006).
[CrossRef]

Chu, D. Y.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Claudon, J.

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

Gérard, J. M.

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Gradecak, S.

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

Gregersen, N.

N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, Appl. Phys. Lett. 91, 011116 (2007).
[CrossRef]

Hahner, R.

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

Ho, S. T.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Imamoglu, A.

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, Nano Lett. 5, 1439 (2005).
[CrossRef] [PubMed]

Jonsson, P.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Lalanne, P.

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

Lecamp, G.

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

Li, Y.

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

Lieber, C. M.

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

Lipson, M.

Maslov, A. V.

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

A. V. Maslov and C. Z. Ning, Opt. Lett. 29, 572 (2004).
[CrossRef] [PubMed]

Mørk, J.

N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, Appl. Phys. Lett. 91, 011116 (2007).
[CrossRef]

Müller, E.

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, Nano Lett. 5, 1439 (2005).
[CrossRef] [PubMed]

Nielsen, T. R.

N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, Appl. Phys. Lett. 91, 011116 (2007).
[CrossRef]

Ning, C. Z.

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

A. V. Maslov and C. Z. Ning, Opt. Lett. 29, 572 (2004).
[CrossRef] [PubMed]

Nowicki-Bringuier, Y.-R.

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

Panepucci, R. R.

Pauzauskie, P. J.

P. J. Pauzauskie and P. Yang, Mater. Today 9, 36 (2006).
[CrossRef]

Qian, F.

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

Tiberio, R. C.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Towe, E.

L. Chen and E. Towe, Appl. Phys. Lett. 89, 053125 (2006).
[CrossRef]

Tromborg, B.

N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, Appl. Phys. Lett. 91, 011116 (2007).
[CrossRef]

Tu, C. W.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Wasey, J. A. E.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Wen, C.-Y.

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

Worthing, P. T.

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Wu, S. L.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Yang, P.

P. J. Pauzauskie and P. Yang, Mater. Today 9, 36 (2006).
[CrossRef]

Zhang, J. P.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Zwiller, V.

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, Nano Lett. 5, 1439 (2005).
[CrossRef] [PubMed]

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

Ann. Phys. Fr. (1)

Y.-R. Nowicki-Bringuier, R. Hahner, J. Claudon, G. Lecamp, P. Lalanne, and J. M. Gérard, Ann. Phys. Fr. 32, 151 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

L. Chen and E. Towe, Appl. Phys. Lett. 89, 053125 (2006).
[CrossRef]

N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, Appl. Phys. Lett. 91, 011116 (2007).
[CrossRef]

Eur. Phys. J. D (1)

W. L. Barnes, G. Björk, J. M. Gérard, P. Jonsson, J. A. E. Wasey, P. T. Worthing, and V. Zwiller, Eur. Phys. J. D 18, 197 (2002).

J. Appl. Phys. (1)

A. V. Maslov, M. I. Bukanov, and C. Z. Ning, J. Appl. Phys. 99, 024314 (2006).
[CrossRef]

Mater. Today (1)

P. J. Pauzauskie and P. Yang, Mater. Today 9, 36 (2006).
[CrossRef]

Nano Lett. (2)

M. T. Borgström, V. Zwiller, E. Müller, and A. Imamoglu, Nano Lett. 5, 1439 (2005).
[CrossRef] [PubMed]

F. Qian, S. Gradečak, Y. Li, C.-Y. Wen, and C. M. Lieber, Nano Lett. 5, 2287 (2005).
[CrossRef] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, Opt. Quantum Electron. 33, 327 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Other (1)

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989), Chap. 6.

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Figures (4)

Fig. 1
Fig. 1

Sketch of light emission from the nanowire (a) without and (b) with a conical taper and (c) with a truncated conical taper. (d) Scanning-electron micrograph of nanowire with conical taper.

Fig. 2
Fig. 2

(a) Far-field radiation pattern, (b) E φ mode profiles, and (c) total free-space transmission and collection efficiency as function of radius R nw for the fundamental guided mode.

Fig. 3
Fig. 3

(a) Far-field radiation pattern, (b) total free-space transmission and collection efficiency as function of opening angle α, and (c) of taper truncation parameter L L 0 for α = 5 ° .

Fig. 4
Fig. 4

(a) E φ field profile for conical and (b) truncated taper with L L 0 = 0.5 for α = 5 ° . (c) E φ field profile for nanowire without taper.

Equations (2)

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P t = 0 π P ( θ ) d θ .
ε E 2 d r = 1 .

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