Abstract

The polarization properties and angular distribution of intensity of the far fields from a nanowire laser are investigated. The far-field emission depends strongly on the mode type (HE11, TE01, TM01) and the radius of the nanowire. The emission is weakly directional, and a large part of it can be emitted in the backward direction. Our results can be applied for experimental determination of a lasing mode by its far fields as well as for optimization of laser emission.

© 2004 Optical Society of America

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References

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  1. J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
    [CrossRef]
  2. X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
    [CrossRef] [PubMed]
  3. R. E. Collin, Field Theory of Guided Waves (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1991), p. 721.
  4. R. K. Boncek and D. L. Rode, J. Lightwave Technol. 9, 18 (1991).
    [CrossRef]
  5. K. S. Yee, D. Ingham, and K. Shlager, IEEE Trans. Antennas Propag. 39, 410 (1991).
    [CrossRef]

2003 (1)

X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
[CrossRef] [PubMed]

2002 (1)

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

1991 (2)

R. K. Boncek and D. L. Rode, J. Lightwave Technol. 9, 18 (1991).
[CrossRef]

K. S. Yee, D. Ingham, and K. Shlager, IEEE Trans. Antennas Propag. 39, 410 (1991).
[CrossRef]

Agarval, R.

X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
[CrossRef] [PubMed]

Boncek, R. K.

R. K. Boncek and D. L. Rode, J. Lightwave Technol. 9, 18 (1991).
[CrossRef]

Choi, H. J.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1991), p. 721.

Duan, X.

X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
[CrossRef] [PubMed]

Huang, Y.

X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
[CrossRef] [PubMed]

Ingham, D.

K. S. Yee, D. Ingham, and K. Shlager, IEEE Trans. Antennas Propag. 39, 410 (1991).
[CrossRef]

Johnson, J. C.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Knutsen, K. P.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Lieber, C. M.

X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
[CrossRef] [PubMed]

Rode, D. L.

R. K. Boncek and D. L. Rode, J. Lightwave Technol. 9, 18 (1991).
[CrossRef]

Saykally, R. J.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Schaller, R. D.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Shlager, K.

K. S. Yee, D. Ingham, and K. Shlager, IEEE Trans. Antennas Propag. 39, 410 (1991).
[CrossRef]

Yang, P.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Yee, K. S.

K. S. Yee, D. Ingham, and K. Shlager, IEEE Trans. Antennas Propag. 39, 410 (1991).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, D. Ingham, and K. Shlager, IEEE Trans. Antennas Propag. 39, 410 (1991).
[CrossRef]

J. Lightwave Technol. (1)

R. K. Boncek and D. L. Rode, J. Lightwave Technol. 9, 18 (1991).
[CrossRef]

Nature (1)

X. Duan, Y. Huang, R. Agarval, and C. M. Lieber, Nature 421, 241 (2003).
[CrossRef] [PubMed]

Nature Mater. (1)

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang, and R. J. Saykally, Nature Mater. 1, 106 (2002).
[CrossRef]

Other (1)

R. E. Collin, Field Theory of Guided Waves (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1991), p. 721.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the FDTD computational domain. Far-field radiation in the direction of r has two polarizations: Eθ and Eϕ (only Eθ is shown). The dashed line is the cross section of the surface used in the near-to-far-field transformation.

Fig. 2
Fig. 2

Ratio of the propagation wave vector and the frequency for the first three guided modes of a nanowire with =6 surrounded by air. The crosses mark the frequencies at which the far-field intensities are shown in Fig. 3. The top axis shows the nanowire radius for a typical bandgap energy of 3.3 eV for GaN.

Fig. 3
Fig. 3

Normalized intensity Srˆ,ω of the far fields as a function of θ for (a) TE01, TM01 and (b) HE11 modes.

Equations (7)

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Strˆ,t=cr2/4π/μEθ2r,t+Eϕ2r,t.
Wrˆ=-+dtStrˆ,t=0dωSωrˆ,ω,
Sωrˆ,ω=cr2/μE˜θr,ω2+E˜ϕr,ω2.
Er,t=μc2rtrˆ×dσJE-μdσJH,
Sωrˆ,ω=cω2/μe˜θrˆ,ω2+e˜ϕrˆ,ω2.
eθrˆ,t=μ4πctopdσ-Eϕsin ϕ+Eρcos ϕ+μ/Hϕcos θ cos ϕ+Hρcos θ sin ϕ+μ4πcsidedσ-Ezcos ϕ+μ/-Hzcos θ sin ϕ+Hϕsin θ,
Sωrˆ,ω=cω2/μe˜θθ,ω2 cos2 ϕ+e˜ϕθ,ω2 sin2 ϕ.

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