Abstract

We analyze the influence of the dielectric constant of the slab on the quality factor (Q) in slab photonic crystal cavities with a minimized vertical losses model. The higher value of Q in high-ε cavity is attributed to the lower mode frequency. The Q ratio in a high-ε (silicon) vs. low-ε (diamond) slab is examined as a function of mode volume (Vm). The mode volume compensation technique is discussed. Finally, diamond cavity design is addressed. The analytical results are compared to 3D FDTD calculations. In a double heterostructure design, a Q2.6×105 is obtained. The highest Q≈1.3×106 with Vm=1.77×(λ/n)3 in a local width modulation design is derived.

© 2008 Optical Society of America

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  1. S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke, and J. Salzman, "Diamond Based Photonic Crystal Microcavities," 11th Micro-optics Conference (MOC’05), Tokyo, Oct 30- Nov 2, 2005.
  2. A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
    [CrossRef]
  3. S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke, and J. Salzman, "Diamond based photonic crystal microcavities," Opt. Express 14, 3556 (2006).
    [CrossRef] [PubMed]
  4. I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for Quantum Electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (2007).
    [CrossRef]
  5. 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]
  6. C. Kreuzer, J. Riedrich-Möller, E. Neu, and C. Becher, "Design of Photonic Crystal Microcavities in Diamond Films," Opt. Express 16, 1632-1644 (2008).
    [CrossRef] [PubMed]
  7. B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
    [CrossRef]
  8. D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 12, 5961 (2005).
    [CrossRef]
  9. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
  10. J. Salzman, "Photonic Crystals in Diamond for Quantum Information Technology," PIERS Proceedings, 1331-1334, March 26-30, Beijing, China, 2007.
  11. I. Bayn, B. Meyler, A. Lahav, J. Salzman, P. Olivero, B. Fairchild, and S. Prawer, "First photonic crystal devices on single crystal diamond," Ib-2, IMEC-13, 9-10 on December, Haifa Israel.
  12. In the waveguide based cavities, the number of PC periods required for a similar Ql in slabs of different ε’s is different in the x and z directions (different confinement mechanism). Qualitatively, a diamond-based PC will reach a Ql similar to that of Si with 1.5-2 times more PC periods than that of a Si-based PC, In the x - z direction, respectively.
  13. These calculations are based on the characteristic mode frequencies and widths of DH cavities with refractive index n.
  14. M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: determing resonant frequencies and quality factor accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
    [CrossRef]
  15. D. Englund and J Vuckovic, "A direct analysis of photonic nanostructures," Opt. Express 14, 3472 (2006).
    [CrossRef] [PubMed]
  16. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

2008 (1)

2007 (2)

I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for Quantum Electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (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 (4)

A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
[CrossRef]

S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke, and J. Salzman, "Diamond based photonic crystal microcavities," Opt. Express 14, 3556 (2006).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

D. Englund and J Vuckovic, "A direct analysis of photonic nanostructures," Opt. Express 14, 3472 (2006).
[CrossRef] [PubMed]

2005 (3)

M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: determing resonant frequencies and quality factor accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
[CrossRef]

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 12, 5961 (2005).
[CrossRef]

2002 (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

Akahane, Y.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
[CrossRef]

Asano, T.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
[CrossRef]

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]

Bayn, I.

I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for Quantum Electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (2007).
[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]

de Sterke, C. M.

Englund, D.

D. Englund and J Vuckovic, "A direct analysis of photonic nanostructures," Opt. Express 14, 3472 (2006).
[CrossRef] [PubMed]

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 12, 5961 (2005).
[CrossRef]

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]

Fushman, I.

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 12, 5961 (2005).
[CrossRef]

Greentre, A. D.

A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
[CrossRef]

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]

Hollenberg, L. C.

A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
[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.

Kuramochi, E.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Neu, E.

Noda, S.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
[CrossRef]

Notomi, M.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Prawer, S.

A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
[CrossRef]

Qiu, M.

M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: determing resonant frequencies and quality factor accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

Riedrich-Möller, J.

Salzman, J.

I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for Quantum Electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (2007).
[CrossRef]

A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
[CrossRef]

S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke, and J. Salzman, "Diamond based photonic crystal microcavities," Opt. Express 14, 3556 (2006).
[CrossRef] [PubMed]

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Song, B.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
[CrossRef]

Steel, M. J.

Tanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Tomljenovic-Hanic, S.

Vuckovic, J

Vuckovic, J.

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 12, 5961 (2005).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

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]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[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]

Appl. Phys. Lett. (2)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[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]

Eur. Phys. J. Appl. Phys. (1)

I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for Quantum Electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (2007).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: determing resonant frequencies and quality factor accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005).
[CrossRef]

Nat. Mater. (1)

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double heterostructure nanocavity," Nat. Mater. 4, 207 (2005).
[CrossRef]

Opt. Express (4)

Phys. Rev. A (1)

A. D. Greentre, J. Salzman, S. Prawer, and L. C. Hollenberg, "Quantum gate for Q-switching photonic band-gap cavities containing two level atoms" Phys. Rev. A 73, 013818 (2006).
[CrossRef]

Phys. Rev. E (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016, 608 (2002).

Other (5)

S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke, and J. Salzman, "Diamond Based Photonic Crystal Microcavities," 11th Micro-optics Conference (MOC’05), Tokyo, Oct 30- Nov 2, 2005.

J. Salzman, "Photonic Crystals in Diamond for Quantum Information Technology," PIERS Proceedings, 1331-1334, March 26-30, Beijing, China, 2007.

I. Bayn, B. Meyler, A. Lahav, J. Salzman, P. Olivero, B. Fairchild, and S. Prawer, "First photonic crystal devices on single crystal diamond," Ib-2, IMEC-13, 9-10 on December, Haifa Israel.

In the waveguide based cavities, the number of PC periods required for a similar Ql in slabs of different ε’s is different in the x and z directions (different confinement mechanism). Qualitatively, a diamond-based PC will reach a Ql similar to that of Si with 1.5-2 times more PC periods than that of a Si-based PC, In the x - z direction, respectively.

These calculations are based on the characteristic mode frequencies and widths of DH cavities with refractive index n.

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Figures (6)

Fig. 1.
Fig. 1.

The notation of the linear PC waveguide in relation to the reciprocal lattice directions. In the inset the 1st Brillouin zone of the triangular lattice (blue) and the first irreducible Brillouin zone (cyan) with high symmetry points are depicted.

Fig. 2.
Fig. 2.

The mode width σx influence in silicon and diamond: QvSi/QvD vs. σx , while Vmx .

Fig. 3.
Fig. 3.

Mode volume compensation: σxn vs. σxSi , σxn is mode width along x direction for slab refractive index n, that provides QvSi xSi)/Qvn (σxn)≈1 and σxSi is mode width in silicon. In solid lines the calculated σxn is shown. Hollow circles denote the analytic fit of the form σxn 2=A+B(σxSi -C)2, where A, B and C are functions of ε=n 2. The x marks denote linear fit of the form σxn ασxSi +β. The green line is diamond (n=2.4).

Fig. 4.
Fig. 4.

Modified Double Heterostructure cavity: (a) Geometrical parameters for N21 =4 cavity, with schematic of waveguide confinement drawn below. (b) Q, Vm vs. N21 .

Fig. 5.
Fig. 5.

Local width modulation cavities (A1): (a) A1 cavity computational domain. (b) Detailed geometry. The holes A, B, C are shifted by DA , DB , DC . (c) Hy in the plane y=0 (d) Q, Vm vs. DA . The detailed holes shifts are summarized in Table 2.

Fig. 6.
Fig. 6.

log(|FT(Hy)|2 ) in a.u. for the A1 cavities with different DA shifts (see Table. 2).

Tables (2)

Tables Icon

Table 1. Modified/simple Double Heterostructure cavity parameters.

Tables Icon

Table 2. Local width modulation summary for the type A1 cavities in a units.

Equations (2)

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P ν η 2 λ 0 2 k k l k d k x d k z k l 2 k z F T 2 ( H y ) 2
F T 2 ( H y ) = k x 0 , k z 0 sign ( k x 0 ) exp ( ( k x k x 0 ) σ x 2 ) 2 exp ( ( k z k z 0 ) σ z 2 ) 2

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