Abstract

In a recent paper [J. Opt. Soc. Am. B 29, 1799 (2012)], to construct the electromagnetic fields of the confined point dipole inside a dielectric cavity, the scattering-superposition method is used incorrectly, and the boundary conditions also are not satisfied. Therefore, the Purcell factor obtained in this paper must be misleading.

© 2014 Optical Society of America

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References

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  1. V. Bordo, “Purcell factor for a cylindrical nanocavity: ab initio analytical approach,” J. Opt. Soc. Am. B 29, 1799–1809 (2012).
    [CrossRef]
  2. L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).
  3. R. L. Hartman, S. M. Cohen, P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110, 2189 (1999).
    [CrossRef]
  4. L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
    [CrossRef]
  5. C. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE, 1991).
  6. H. Nha, W. Jhe, “Cavity quantum electrodynamics for a cylinder: inside a hollow dielectric and near a solid dielectric cylinder,” Phys. Rev. A 56, 2213–2220 (1997).
    [CrossRef]
  7. S. A. Schelkunoff, “On diffraction and radiation of electromagnetic waves,” Phys. Rev. 56, 308–316 (1939).
    [CrossRef]
  8. S. R. Rengarajan, Y. Rahmat-Samii, “The field equivalence principle: illustration of the establishment of the non-intuitive null fields,” IEEE Trans. Antennas Propag. Mag. 42, 122–128 (2000).
  9. A. V. Maslov, C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
    [CrossRef]
  10. A. Henneghien, B. Gayral, Y. Désières, J. Gérard, “Simulation of waveguiding and emitting properties of semiconductor nanowires with hexagonal or circular sections,” J. Opt. Soc. Am. B 26, 2396–2403 (2009).
    [CrossRef]
  11. G. K. Svendsen, H. Weman, J. Skaar, “Model for reflection and transmission matrices of nanowire end facets,” J. Appl. Phys. 109, 103101 (2011).
    [CrossRef]
  12. H. Y. Yee, L. B. Felsen, J. B. Keller, “Ray theory of reflection from the open end of a waveguide,” SIAM J. Appl. Math. 16, 268–300 (1968).
    [CrossRef]
  13. J. Browman, “Comparison of ray theory with exact theory for scattering by open wave guides,” SIAM J. Appl. Math. 18, 818–829 (1970).
    [CrossRef]
  14. J. Boersma, “Ray-optical analysis of reflection in an open-ended parallel-plane waveguide. i: Tm case,” SIAM J. Appl. Math. 29, 164–195 (1975).
    [CrossRef]
  15. A. Fallahi, B. Oswald, “On the computation of electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 59, 1433–1440 (2011).
    [CrossRef]

2012 (1)

2011 (2)

G. K. Svendsen, H. Weman, J. Skaar, “Model for reflection and transmission matrices of nanowire end facets,” J. Appl. Phys. 109, 103101 (2011).
[CrossRef]

A. Fallahi, B. Oswald, “On the computation of electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 59, 1433–1440 (2011).
[CrossRef]

2009 (1)

2004 (1)

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

2003 (1)

A. V. Maslov, C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

2000 (1)

S. R. Rengarajan, Y. Rahmat-Samii, “The field equivalence principle: illustration of the establishment of the non-intuitive null fields,” IEEE Trans. Antennas Propag. Mag. 42, 122–128 (2000).

1999 (1)

R. L. Hartman, S. M. Cohen, P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110, 2189 (1999).
[CrossRef]

1997 (1)

H. Nha, W. Jhe, “Cavity quantum electrodynamics for a cylinder: inside a hollow dielectric and near a solid dielectric cylinder,” Phys. Rev. A 56, 2213–2220 (1997).
[CrossRef]

1994 (1)

L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).

1975 (1)

J. Boersma, “Ray-optical analysis of reflection in an open-ended parallel-plane waveguide. i: Tm case,” SIAM J. Appl. Math. 29, 164–195 (1975).
[CrossRef]

1970 (1)

J. Browman, “Comparison of ray theory with exact theory for scattering by open wave guides,” SIAM J. Appl. Math. 18, 818–829 (1970).
[CrossRef]

1968 (1)

H. Y. Yee, L. B. Felsen, J. B. Keller, “Ray theory of reflection from the open end of a waveguide,” SIAM J. Appl. Math. 16, 268–300 (1968).
[CrossRef]

1939 (1)

S. A. Schelkunoff, “On diffraction and radiation of electromagnetic waves,” Phys. Rev. 56, 308–316 (1939).
[CrossRef]

Boersma, J.

J. Boersma, “Ray-optical analysis of reflection in an open-ended parallel-plane waveguide. i: Tm case,” SIAM J. Appl. Math. 29, 164–195 (1975).
[CrossRef]

Bordo, V.

Browman, J.

J. Browman, “Comparison of ray theory with exact theory for scattering by open wave guides,” SIAM J. Appl. Math. 18, 818–829 (1970).
[CrossRef]

Cohen, S. M.

R. L. Hartman, S. M. Cohen, P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110, 2189 (1999).
[CrossRef]

Désières, Y.

Fallahi, A.

A. Fallahi, B. Oswald, “On the computation of electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 59, 1433–1440 (2011).
[CrossRef]

Felsen, L. B.

H. Y. Yee, L. B. Felsen, J. B. Keller, “Ray theory of reflection from the open end of a waveguide,” SIAM J. Appl. Math. 16, 268–300 (1968).
[CrossRef]

Gayral, B.

Gérard, J.

Hartman, R. L.

R. L. Hartman, S. M. Cohen, P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110, 2189 (1999).
[CrossRef]

Henneghien, A.

Jhe, W.

H. Nha, W. Jhe, “Cavity quantum electrodynamics for a cylinder: inside a hollow dielectric and near a solid dielectric cylinder,” Phys. Rev. A 56, 2213–2220 (1997).
[CrossRef]

Keller, J. B.

H. Y. Yee, L. B. Felsen, J. B. Keller, “Ray theory of reflection from the open end of a waveguide,” SIAM J. Appl. Math. 16, 268–300 (1968).
[CrossRef]

Koh, J.

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

Kooi, P.

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

Kooi, P.-S.

L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).

Leong, M.

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

Leong, M.-S.

L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).

Leung, P. T.

R. L. Hartman, S. M. Cohen, P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110, 2189 (1999).
[CrossRef]

Li, L.

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

Li, L.-W.

L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).

Maslov, A. V.

A. V. Maslov, C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

Nha, H.

H. Nha, W. Jhe, “Cavity quantum electrodynamics for a cylinder: inside a hollow dielectric and near a solid dielectric cylinder,” Phys. Rev. A 56, 2213–2220 (1997).
[CrossRef]

Ning, C. Z.

A. V. Maslov, C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

Oswald, B.

A. Fallahi, B. Oswald, “On the computation of electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 59, 1433–1440 (2011).
[CrossRef]

Rahmat-Samii, Y.

S. R. Rengarajan, Y. Rahmat-Samii, “The field equivalence principle: illustration of the establishment of the non-intuitive null fields,” IEEE Trans. Antennas Propag. Mag. 42, 122–128 (2000).

Rengarajan, S. R.

S. R. Rengarajan, Y. Rahmat-Samii, “The field equivalence principle: illustration of the establishment of the non-intuitive null fields,” IEEE Trans. Antennas Propag. Mag. 42, 122–128 (2000).

Schelkunoff, S. A.

S. A. Schelkunoff, “On diffraction and radiation of electromagnetic waves,” Phys. Rev. 56, 308–316 (1939).
[CrossRef]

Skaar, J.

G. K. Svendsen, H. Weman, J. Skaar, “Model for reflection and transmission matrices of nanowire end facets,” J. Appl. Phys. 109, 103101 (2011).
[CrossRef]

Svendsen, G. K.

G. K. Svendsen, H. Weman, J. Skaar, “Model for reflection and transmission matrices of nanowire end facets,” J. Appl. Phys. 109, 103101 (2011).
[CrossRef]

Tai, C.

C. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE, 1991).

Weman, H.

G. K. Svendsen, H. Weman, J. Skaar, “Model for reflection and transmission matrices of nanowire end facets,” J. Appl. Phys. 109, 103101 (2011).
[CrossRef]

Yee, H. Y.

H. Y. Yee, L. B. Felsen, J. B. Keller, “Ray theory of reflection from the open end of a waveguide,” SIAM J. Appl. Math. 16, 268–300 (1968).
[CrossRef]

Yee, T.-S.

L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).

Yeo, T.

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

A. V. Maslov, C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

L. Li, J. Koh, T. Yeo, M. Leong, P. Kooi, “Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four-layered forest,” IEEE Trans. Antennas Propag. 52, 466–477 (2004).
[CrossRef]

IEEE Trans. Antennas Propag. Mag. (1)

S. R. Rengarajan, Y. Rahmat-Samii, “The field equivalence principle: illustration of the establishment of the non-intuitive null fields,” IEEE Trans. Antennas Propag. Mag. 42, 122–128 (2000).

IEEE Trans. Microw. Theory Tech. (2)

L.-W. Li, P.-S. Kooi, M.-S. Leong, T.-S. Yee, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).

A. Fallahi, B. Oswald, “On the computation of electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 59, 1433–1440 (2011).
[CrossRef]

J. Appl. Phys. (1)

G. K. Svendsen, H. Weman, J. Skaar, “Model for reflection and transmission matrices of nanowire end facets,” J. Appl. Phys. 109, 103101 (2011).
[CrossRef]

J. Chem. Phys. (1)

R. L. Hartman, S. M. Cohen, P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110, 2189 (1999).
[CrossRef]

J. Opt. Soc. Am. B (2)

Phys. Rev. (1)

S. A. Schelkunoff, “On diffraction and radiation of electromagnetic waves,” Phys. Rev. 56, 308–316 (1939).
[CrossRef]

Phys. Rev. A (1)

H. Nha, W. Jhe, “Cavity quantum electrodynamics for a cylinder: inside a hollow dielectric and near a solid dielectric cylinder,” Phys. Rev. A 56, 2213–2220 (1997).
[CrossRef]

SIAM J. Appl. Math. (3)

H. Y. Yee, L. B. Felsen, J. B. Keller, “Ray theory of reflection from the open end of a waveguide,” SIAM J. Appl. Math. 16, 268–300 (1968).
[CrossRef]

J. Browman, “Comparison of ray theory with exact theory for scattering by open wave guides,” SIAM J. Appl. Math. 18, 818–829 (1970).
[CrossRef]

J. Boersma, “Ray-optical analysis of reflection in an open-ended parallel-plane waveguide. i: Tm case,” SIAM J. Appl. Math. 29, 164–195 (1975).
[CrossRef]

Other (1)

C. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE, 1991).

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Figures (1)

Fig. 1.
Fig. 1.

Electric field intensity for a point dipole located at the center of an infinite dielectric slab ( ϵ = 4 ϵ 0 ). Figures are plotted in the cross section through the point dipole. (a) Calculated according to [1]. (b) Calculated after [25].

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

G 2 α 0 ( R , R 0 ; ω ) = G 0 ( R , R 0 ; ω ) e α + Ψ 2 e ( R ; ω ) e z + Ψ 2 m ( R ; ω ) e z .
G 2 α = G 2 α 0 ( R , R 0 ; ω ) + Φ 2 e ( R ; ω ) + Φ 2 e + ( R ; ω ) + Φ 2 m ( R ; ω ) + Φ 2 m + ( R ; ω ) ,
Ψ ˜ 1 σ ( r , θ , z ) = 1 q 1 2 n = a 1 n σ ( β ) H n ( 1 ) ( q 1 r ) e i n θ ,
Ψ ˜ 2 σ ( r , θ , z ) = 1 q 2 2 n = a 2 n σ ( β ) J n ( q 2 r ) e i n θ ,
M ^ n ( β ) A⃗ n α ( β ) 1 2 π C [ e i ( β β ) ( L / 2 z 0 ) e i ( β β ) ( L / 2 + z 0 ) ] × N ^ m ( β , β ) A⃗ n α ( β ) d β = B⃗ n α ( β ) .
E r + = e x E 0 η 0 η η 0 + η e i k L e i k z ,
E t + = e x E 0 2 η 0 η 0 + η e i ( k 0 k ) L / 2 e i k 0 z ,
E r = e x E 0 e i k z ,
E t = 0 ,

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