Abstract

Designing photonic crystal cavities with high quality factors and low mode volumes is of great importance for maximizing interactions of light and matter in metamaterials. Previous work on photonic crystal cavities has revealed dramatic improvements in performance by fine-tuning the device design. In L3 cavities, slight shifts of the holes on the edge of the cavity have been found to greatly increase quality factors without significantly altering the mode volume. Here we demonstrate utilizing a nature inspired search algorithm to efficiently explore a large parameter space. The results converge upon a new cavity model with a high quality factor to mode volume ratio (Q/V = 798,000 (λ/n)−3).

© 2013 OSA

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2013 (1)

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-Resolved Two-Pulse Excitation of Quantum Dots Coupled to a Photonic Crystal Cavity in the Purcell Regime,” Phys. Rev. Lett.110(1), 013602 (2013).
[CrossRef] [PubMed]

2011 (3)

B. Jiang, Y. J. Zhang, W. J. Zhou, W. Chen, A. J. Liu, and W. H. Zheng, “Spontaneous-emission control by local density of states of photonic crystal cavity,” Chin. Phys. B20(2), 024208 (2011).
[CrossRef]

G. S. Hornby, J. D. Lohn, and D. S. Linden, “Computer-Automated Evolution of an X-Band Antenna for NASA’s Space Technology 5 Mission,” Evol. Comput.19(1), 1–23 (2011).
[CrossRef] [PubMed]

C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express19(S5Suppl 5), A1148–A1154 (2011).
[CrossRef] [PubMed]

2010 (2)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Z. Lin and J. Vučković, “Enhanced two-photon processes in single quantum dots inside photonic crystal nanocavities,” Phys. Rev. B81(3), 035301 (2010).
[CrossRef]

2009 (2)

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optim.41(4), 365–384 (2009).
[CrossRef]

E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, “GSA: A Gravitational Search Algorithm,” Inf. Sci.179(13), 2232–2248 (2009).
[CrossRef]

2008 (1)

2007 (1)

F. Römer, B. Witzigmann, O. Chinellato, and P. Arbenz, “Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver,” Opt. Quantum Electron.39(4-6), 341–352 (2007).
[CrossRef]

2005 (2)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express13(4), 1202–1214 (2005).
[CrossRef] [PubMed]

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett.86(6), 061111 (2005).
[CrossRef]

2004 (1)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

2003 (3)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett.83(8), 1512 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express13(4), 1202–1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett.83(8), 1512 (2003).
[CrossRef]

Arbenz, P.

F. Römer, B. Witzigmann, O. Chinellato, and P. Arbenz, “Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver,” Opt. Quantum Electron.39(4-6), 341–352 (2007).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express13(4), 1202–1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett.83(8), 1512 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Avniel, Y.

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optim.41(4), 365–384 (2009).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Boyd, S.

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optim.41(4), 365–384 (2009).
[CrossRef]

Chen, W.

B. Jiang, Y. J. Zhang, W. J. Zhou, W. Chen, A. J. Liu, and W. H. Zheng, “Spontaneous-emission control by local density of states of photonic crystal cavity,” Chin. Phys. B20(2), 024208 (2011).
[CrossRef]

Chinellato, O.

F. Römer, B. Witzigmann, O. Chinellato, and P. Arbenz, “Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver,” Opt. Quantum Electron.39(4-6), 341–352 (2007).
[CrossRef]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[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, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (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, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Farjadpour, A.

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optim.41(4), 365–384 (2009).
[CrossRef]

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, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Gondarenko, A.

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Hornby, G. S.

G. S. Hornby, J. D. Lohn, and D. S. Linden, “Computer-Automated Evolution of an X-Band Antenna for NASA’s Space Technology 5 Mission,” Evol. Comput.19(1), 1–23 (2011).
[CrossRef] [PubMed]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Jiang, B.

B. Jiang, Y. J. Zhang, W. J. Zhou, W. Chen, A. J. Liu, and W. H. Zheng, “Spontaneous-emission control by local density of states of photonic crystal cavity,” Chin. Phys. B20(2), 024208 (2011).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optim.41(4), 365–384 (2009).
[CrossRef]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Lee, J.

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-Resolved Two-Pulse Excitation of Quantum Dots Coupled to a Photonic Crystal Cavity in the Purcell Regime,” Phys. Rev. Lett.110(1), 013602 (2013).
[CrossRef] [PubMed]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Lin, C.

Lin, Z.

Z. Lin and J. Vučković, “Enhanced two-photon processes in single quantum dots inside photonic crystal nanocavities,” Phys. Rev. B81(3), 035301 (2010).
[CrossRef]

Linden, D. S.

G. S. Hornby, J. D. Lohn, and D. S. Linden, “Computer-Automated Evolution of an X-Band Antenna for NASA’s Space Technology 5 Mission,” Evol. Comput.19(1), 1–23 (2011).
[CrossRef] [PubMed]

Lipson, H.

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett.86(6), 061111 (2005).
[CrossRef]

Lipson, M.

A. Gondarenko and M. Lipson, “Low modal volume dipole-like dielectric slab resonator,” Opt. Express16(22), 17689–17694 (2008).
[CrossRef] [PubMed]

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett.86(6), 061111 (2005).
[CrossRef]

Liu, A. J.

B. Jiang, Y. J. Zhang, W. J. Zhou, W. Chen, A. J. Liu, and W. H. Zheng, “Spontaneous-emission control by local density of states of photonic crystal cavity,” Chin. Phys. B20(2), 024208 (2011).
[CrossRef]

Lohn, J. D.

G. S. Hornby, J. D. Lohn, and D. S. Linden, “Computer-Automated Evolution of an X-Band Antenna for NASA’s Space Technology 5 Mission,” Evol. Comput.19(1), 1–23 (2011).
[CrossRef] [PubMed]

Martin, A. J.

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-Resolved Two-Pulse Excitation of Quantum Dots Coupled to a Photonic Crystal Cavity in the Purcell Regime,” Phys. Rev. Lett.110(1), 013602 (2013).
[CrossRef] [PubMed]

Millunchick, J. M.

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-Resolved Two-Pulse Excitation of Quantum Dots Coupled to a Photonic Crystal Cavity in the Purcell Regime,” Phys. Rev. Lett.110(1), 013602 (2013).
[CrossRef] [PubMed]

Mutapcic, A.

A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Eng. Optim.41(4), 365–384 (2009).
[CrossRef]

Nezamabadi-pour, H.

E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, “GSA: A Gravitational Search Algorithm,” Inf. Sci.179(13), 2232–2248 (2009).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express13(4), 1202–1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett.83(8), 1512 (2003).
[CrossRef]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Povinelli, M. L.

Preble, S.

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett.86(6), 061111 (2005).
[CrossRef]

Rashedi, E.

E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, “GSA: A Gravitational Search Algorithm,” Inf. Sci.179(13), 2232–2248 (2009).
[CrossRef]

Römer, F.

F. Römer, B. Witzigmann, O. Chinellato, and P. Arbenz, “Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver,” Opt. Quantum Electron.39(4-6), 341–352 (2007).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Saryazdi, S.

E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, “GSA: A Gravitational Search Algorithm,” Inf. Sci.179(13), 2232–2248 (2009).
[CrossRef]

Saucer, T. W.

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-Resolved Two-Pulse Excitation of Quantum Dots Coupled to a Photonic Crystal Cavity in the Purcell Regime,” Phys. Rev. Lett.110(1), 013602 (2013).
[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, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[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, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Sih, V.

J. Lee, T. W. Saucer, A. J. Martin, J. M. Millunchick, and V. Sih, “Time-Resolved Two-Pulse Excitation of Quantum Dots Coupled to a Photonic Crystal Cavity in the Purcell Regime,” Phys. Rev. Lett.110(1), 013602 (2013).
[CrossRef] [PubMed]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express13(4), 1202–1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett.83(8), 1512 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

Z. Lin and J. Vučković, “Enhanced two-photon processes in single quantum dots inside photonic crystal nanocavities,” Phys. Rev. B81(3), 035301 (2010).
[CrossRef]

Witzigmann, B.

F. Römer, B. Witzigmann, O. Chinellato, and P. Arbenz, “Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver,” Opt. Quantum Electron.39(4-6), 341–352 (2007).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Yoshie, T.

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[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Photonic crystal cavity design parameters. The basic L3 design is modified by shifting the edge holes labeled “A” symmetrically along the x direction. Holes B and C are allowed to shift in both the x and y directions. All labeled holes are allowed to vary in radius.

Fig. 2
Fig. 2

Evolution of the hole radius, rA, and Q/V ratio through the simulation. After approximately 200 iterations results begin to converge upon optimized solution. Horizontal line in Q/V represents benchmark for comparison.

Fig. 3
Fig. 3

a) Electric field (Ey) mode profile for our final design parameters and b) the L3 cavity with 0.15a shift, which is our benchmark.

Tables (1)

Tables Icon

Table 1 Optimized design parameters for cavity with Q/V = 798,000 (λ/n)−3

Equations (4)

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s i,1 r A r min r max r min , s i,2 r B r min r max r min
m i = f( s i ) f min j [ f( s j ) f min ] +δm
s ¨ i = ji G m j | s j s i | ( s j s i )
V mode = ϵ (r) | E(r) | 2 dr max( ϵ(r) | E(r) | 2 )

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