Abstract

Accounting for material absorption is very important for developing high quality factor (Q) photonic crystal cavities. However, to our knowledge, there have been very few systematic experimental investigations of its role in such cavities. In this paper, we present detailed experiments to reveal the relationship between Q, material absorption coefficient and field pattern. Modes with different field patterns and materials with different absorption coefficients were tested. We have developed a simple formula to describe the relationship, which can be used to replace time-consuming numerical calculations. The experimental and numerical data agree well with this formula.

© 2009 Optical Society of America

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  1. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
    [CrossRef] [PubMed]
  2. K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
    [CrossRef]
  3. T. Asano, B.-S. Song and S. Noda, "Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities," Opt. Express 14, 1996-2002 (2006).
    [CrossRef] [PubMed]
  4. C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
    [CrossRef]
  5. C. Kreuzer, J. Riedrich-Moller, E. Neu, and C. Becher, "Design of photonic crystal microcavities in diamond films," Opt. Express 16, 1632-1644 (2008).
    [CrossRef] [PubMed]
  6. E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, "Ultracompact biochemical sensor built with twodimensional photonic crystal microcavity," Opt. Lett. 29, 1093-1095 (2004).
    [CrossRef] [PubMed]
  7. M. Lee and P. M. Fauchet, "Two-dimensional silicon photonic crystal based biosensing platform for protein detection," Opt. Express 15, 4530-4535 (2007).
    [CrossRef] [PubMed]
  8. I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6402 (2002).
    [CrossRef]
  9. T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
    [CrossRef]
  10. T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
    [CrossRef]
  11. T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
    [CrossRef]

2008 (2)

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

C. Kreuzer, J. Riedrich-Moller, E. Neu, and C. Becher, "Design of photonic crystal microcavities in diamond films," Opt. Express 16, 1632-1644 (2008).
[CrossRef] [PubMed]

2007 (3)

M. Lee and P. M. Fauchet, "Two-dimensional silicon photonic crystal based biosensing platform for protein detection," Opt. Express 15, 4530-4535 (2007).
[CrossRef] [PubMed]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

2006 (1)

2005 (1)

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
[CrossRef]

2004 (1)

2003 (2)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

2002 (1)

I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6402 (2002).
[CrossRef]

Aitchison, J. S.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Alvarado-Rodriguez, I.

I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6402 (2002).
[CrossRef]

Asano, Takashi

Awschalom, D. D.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Barclay, Paul E.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Becher, C.

Butler, J. E.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Chen, Jianxin

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Cho, Alfred Y.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Chow, E.

Feygelson, T.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Girolami, G.

Gmachl, Claire

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Grot, A.

Hanson, R.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Hu, E. L.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Kreuzer, C.

Mirkarimi, L. W.

Mojahedi, M.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Nair, S. V.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
[CrossRef]

Neu, E.

Painter, Oskar

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Riedrich-Moller, J.

Ruda, H. E.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
[CrossRef]

Sigalas, M.

Srinivasan, Kartik

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Wang, C. F.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Wheeler, M. S.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Xu, T.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
[CrossRef]

Yablonovitch, E.

I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6402 (2002).
[CrossRef]

Yang, J.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

Yang, S.

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, "Highly confined mode above the light line in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

J. Appl. Phys. (1)

I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6402 (2002).
[CrossRef]

Nature (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (2)

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, "Confined modes in finite-size photonic crystals," Phys. Rev. B 72, 045126 (2005).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) The 2D bandstructure of a periodic rod array. The refractive index of the rods is 3.122 and the diameter is 0.4a,where a is the period. (b) A 9 × 9 array of rods confining M 1 mode. In the microwave experiments, two kinds of dielectric rods are used. In the experiment employing alumina rods, the period a is 4.1 mm and the rods have a diameter D of 1.62 mm and height h of 34.8 mm. When using sapphire rods, a = 4.4 mm, D = 1.74 mm, and h = 35 mm. (c) A heterostructure confining Γ2 mode. Along the direction perpendicular to the interfaces, the period in the core region a 1 is smaller than the period in the wall region a 2. In the experiment employing alumina rods, a 1 is 8.1 mm, a 2 is 9.7 mm, D is 2.4 mm and h is 47 mm. In (b) and (c), the black circles sketch the outlines of the rods and the Ez field of the confined mode calculated with 3D Finite-Difference Time-Domain (FDTD) overlaps with the structure.

Fig. 2.
Fig. 2.

The comparison between the microwave measurements and 3D FDTD simulation for the confined M 1 mode (a) and Γ2 mode (b). (Top) Frequency spectrum; (Bottom Left) Field distribution along z direction at Point1(a) and Point2(b); (Bottom Right) Field distribution along Line1(a) and Line2(b), where the dotted columns show the outlines of the rods neighboring the sampling lines. In the frequency spectrum, the simulation curve is shifted to compare with experimental data. Point1, Point2, Line1 and Line2 are marked in Fig. 1(b) and (c). For the data in this figure, alumina rods (Anderman Ceramics) are used in the experiments. In the field distribution figures, a in the axis is the period of the PhC.

Fig. 3.
Fig. 3.

(a) The comparison between the prediction of Eq. 4 and the numerical and experimental data for the Q of a confined M 1 and Γ2 mode in dielectric rod cavities. (b) The vertical cross section and (c) the horizontal cross section of the M 1 mode confined in a 9×9 dielectric rod array with different loss levels. For (b) and (c), the geometric data of the cavity and the position of the cross sections are given in Fig. 2(a).

Equations (4)

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

1Qtot=1Qrad+1Qabs,
1Qabs=Fk/α=2Fni/nr,
F=Vabs1/2×εr(r)E(r)2dVV1/2×εr(r)E(r)2dV,
1Qtot=1Qrad+2Fni/nr.

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