Abstract

The waveguide-length sensitivity on modified spontaneous emission in finite-size planar photonic crystal (PC) waveguides is investigated by numerically computing the exact Purcell (enhanced emission) factor. An unusual dependence on the number of waveguide unit cells and on the waveguide facet truncation is found, allowing one to nanoengineer large Purcell factors in excess of several hundred. Besides having important applications for single-photon sources, these results offer physical insight into the nature of light–matter interactions in miniaturized finite-size PC waveguides, where periodic Bloch-wave analysis breaks down.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. M. Purcell, Phys. Rev. 69, 681 (1946).
    [Crossref]
  2. D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
    [Crossref]
  3. K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
    [Crossref] [PubMed]
  4. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
    [Crossref] [PubMed]
  5. S. Hughes, Opt. Lett. 29, 2659 (2004).
    [Crossref] [PubMed]
  6. E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
    [Crossref] [PubMed]
  7. V. S. C. Manga Rao and S. Hughes, Phys. Rev. B 75, 205437 (2007).
    [Crossref]
  8. G. Lecamp, P. Lalanne, and J. P. Hugonin, Phys. Rev. Lett. 99, 023902 (2007).
    [Crossref] [PubMed]
  9. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
    [Crossref] [PubMed]
  10. V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
    [Crossref]
  11. For this work, we have used “FDTD solutions,” see www.lumerical.com.
  12. L. Ramunno (University of Ottawa, Canada) and S. Hughes are preparing a manuscript entitled “Disorder-induced resonance shifts in photonic crystal nanocavities.”

2007 (4)

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

V. S. C. Manga 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]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

2005 (2)

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

2004 (2)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

S. Hughes, Opt. Lett. 29, 2659 (2004).
[Crossref] [PubMed]

1981 (1)

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[Crossref]

1946 (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[Crossref]

Atatüre, A.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Benisty, H.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Falt, S.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Houdre, R.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Hughes, S.

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

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

S. Hughes, Opt. Lett. 29, 2659 (2004).
[Crossref] [PubMed]

L. Ramunno (University of Ottawa, Canada) and S. Hughes are preparing a manuscript entitled “Disorder-induced resonance shifts in photonic crystal nanocavities.”

Hugonin, J. P.

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

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Kleppner, D.

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[Crossref]

Lalanne, P.

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

Lecamp, G.

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

Manga Rao, V. S. C.

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

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

Olivier, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[Crossref]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

L. Ramunno (University of Ottawa, Canada) and S. Hughes are preparing a manuscript entitled “Disorder-induced resonance shifts in photonic crystal nanocavities.”

Robert-Philip, I.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Smith, C. J. M.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Varoutsis, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Viasnoff-Schwoob, E.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Weisbuch, C.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

Winger, M.

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Nature (2)

K. Hennessy, A. Badolato, M. Winger, A. Atatüre, S. Falt, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).
[Crossref] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[Crossref]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (5)

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

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, S. Varoutsis, I. Robert-Philip, R. Houdre, and C. J. M. Smith, Phys. Rev. Lett. 95, 183901 (2005).
[Crossref] [PubMed]

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[Crossref]

Other (2)

For this work, we have used “FDTD solutions,” see www.lumerical.com.

L. Ramunno (University of Ottawa, Canada) and S. Hughes are preparing a manuscript entitled “Disorder-induced resonance shifts in photonic crystal nanocavities.”

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Dielectric profile of a finite-size planar PC waveguide (W1), where propagation is along the x axis and a single QD (filled circle) is embedded near the center of the slab. The propagation mode is bound by total internal reflection in the z direction by the slab. The structure parameters used in the simulations are as follows: hole radius r = 0.275 a , slab thickness 0.5 a , refractive index n = 12 , and lattice constant a = 420 nm . (b) Band structure of modes (solid and dashed curves) corresponding to an infinite-length planar PC waveguide shown within the TE-like bandgap [parameters as in (a)]. The gray shaded region above the light line represents the continuum of radiation modes.

Fig. 2
Fig. 2

Enhanced SE (Purcell) factors as a function of frequency (relative to a homogeneous medium) for four different unit-cell numbers in a finite-size PC waveguide: 5, 10, 15, and 20 (with the longer waveguides producing the largest Purcell factors and the narrower peaks). (a) Surrounded by air on either side. (b) As in (a) but with one side of the waveguide surrounded by five layers of regular PC acting as a mirror [see also Fig. 3b].

Fig. 3
Fig. 3

(a) Enhanced SE factor versus number of unit cells in a finite-size PC waveguide with air on either side. These are computed at the peak value over the frequency range shown in Fig. 2 and for the peak antinode position in the slab (see contour plots). The filled circles at the left are for the case when the truncation of the waveguide end is in between the nearest airholes on either side of the line-defect, and the filled squares at the left are the truncation of the waveguide end across the nearest airholes on either side of the line defect. The two insets show examples of the seven unit-cell guides for the peak Purcell factors, which are proportional to the E y 2 field distribution, at the center of the slab in the x y plane for two different truncation ends in the seven unit-cell sized waveguide. (b) Similar to (a) but with a five-layer PC at one end.

Equations (1)

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

F ( r d , ω ) = d Im [ G PC ( r d , r d ; ω ) ] d d Im [ G hom ( ω ) ] d ,

Metrics