Abstract

We propose a novel geometry in a silicon planar resonator with an ultra-small modal volume of 0.01(λ/2n)3. The geometry induces strong electric field discontinuities to decrease the modal volume of the cavity below 1(λ/2n)3 The proposed structure and other common resonators such as 1D and 2D photonic crystal resonators are compared for tradeoffs in confinement and quality factors.

© 2008 Optical Society of America

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  1. E. M. Purcell, H. C. Torrey, and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev. 69, 37 (1946).
    [CrossRef]
  2. R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
    [CrossRef]
  3. 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," Science 284,1819 (1999).
    [CrossRef] [PubMed]
  4. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
    [CrossRef] [PubMed]
  5. S. Maier, "Effective Mode Volume of Nanoscale Plasmon Cavities," Opt. Quantum Electron. 38, 257 (2006).
    [CrossRef]
  6. E. Feigenbaum and M. Orenstein, "Optical 3D cavity modes below the diffraction-limit using slow-wave surface-plasmon-polaritons," Opt. Express 15, 2607-2612 (2007).
    [CrossRef] [PubMed]
  7. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202 (2005).
    [CrossRef] [PubMed]
  8. T. J. M. Borselli and O. Painter, "Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment," Opt. Express 13, 1515 (2005).
    [CrossRef] [PubMed]
  9. E. P. P. Velha, T. Charvolin, E. Hadji, J. C. Rodier, P. Lalanne, and D. Peyrade, "Ultra-High Q/V Fabry-Perot microcavity on SOI substrate," Opt. Express 15, 16090 (2007).
    [CrossRef] [PubMed]
  10. T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826 (2007).
    [CrossRef] [PubMed]
  11. T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
    [CrossRef]
  12. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultrasmall Mode Volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
    [CrossRef] [PubMed]
  13. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and Confining Light in Void Nanostructure," Opt. Lett. 29, 1209 (2004).
    [CrossRef] [PubMed]
  14. V. R. Almeida, Q. Xu, R. R. Panepucci, C. A. Barrios, and M. Lipson, "Light Guiding in Low Index Materials using High-Index-Contrast Waveguides," Proc. Mat. Res. Soc. Fall Meeting (2003).
    [CrossRef]
  15. A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
    [CrossRef] [PubMed]
  16. M. Lončar, A. Scherer, and Y. Qiu, "Photonic crystal laser sources for chemical detection," Appl. Phys. Lett. 82, 4648 (2003).
    [CrossRef]
  17. S. Kwon, T. Sünner, M. Kamp, and A. Forchel, "Optimization of photonic crystal cavity for chemical sensing," Opt. Express 16, 11709 (2008).
    [CrossRef] [PubMed]

2008

2007

2006

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

S. Maier, "Effective Mode Volume of Nanoscale Plasmon Cavities," Opt. Quantum Electron. 38, 257 (2006).
[CrossRef]

2005

2004

2003

M. Lončar, A. Scherer, and Y. Qiu, "Photonic crystal laser sources for chemical detection," Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

2000

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

1999

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," Science 284,1819 (1999).
[CrossRef] [PubMed]

1998

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[CrossRef]

1946

E. M. Purcell, H. C. Torrey, and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev. 69, 37 (1946).
[CrossRef]

Akahane, Y.

Almeida, V. R.

Asano, T.

Barrios, C. A.

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Boroditsky, M.

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[CrossRef]

Borselli, T. J. M.

Charvolin, T.

Chen, L.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultrasmall Mode Volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Cocciol, R.

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Feigenbaum, E.

Forchel, A.

Gondarenko, A.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Hadji, E.

Hu, E.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Imamoglu, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Kamp, M.

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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Kim, K. W.

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[CrossRef]

Kiraz, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Kondo, S.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

Kuramochi, E.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826 (2007).
[CrossRef] [PubMed]

Kwon, S.

Lalanne, P.

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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Lipson, H.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Lipson, M.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultrasmall Mode Volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and Confining Light in Void Nanostructure," Opt. Lett. 29, 1209 (2004).
[CrossRef] [PubMed]

Loncar, M.

M. Lončar, A. Scherer, and Y. Qiu, "Photonic crystal laser sources for chemical detection," Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

Maier, S.

S. Maier, "Effective Mode Volume of Nanoscale Plasmon Cavities," Opt. Quantum Electron. 38, 257 (2006).
[CrossRef]

Manolatou, C.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultrasmall Mode Volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Michler, P.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Noda, S.

Notomi, M.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826 (2007).
[CrossRef] [PubMed]

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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Orenstein, M.

Painter, O.

T. J. M. Borselli and O. Painter, "Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment," Opt. Express 13, 1515 (2005).
[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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Petroff, P. M.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Peyrade, D.

Pound, R. V.

E. M. Purcell, H. C. Torrey, and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev. 69, 37 (1946).
[CrossRef]

Preble, S.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, H. C. Torrey, and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev. 69, 37 (1946).
[CrossRef]

Qiu, Y.

M. Lončar, A. Scherer, and Y. Qiu, "Photonic crystal laser sources for chemical detection," Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

Rahmat-Samii, Y.

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[CrossRef]

Robinson, J.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Robinson, J. T.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultrasmall Mode Volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

Rodier, J. C.

Scherer, A.

M. Lončar, A. Scherer, and Y. Qiu, "Photonic crystal laser sources for chemical detection," Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Schoenfeld, W. V.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Shinya, A.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

Song, B. S.

Sünner, T.

Tanabe, T.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826 (2007).
[CrossRef] [PubMed]

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826 (2007).
[CrossRef] [PubMed]

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

Torrey, H. C.

E. M. Purcell, H. C. Torrey, and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev. 69, 37 (1946).
[CrossRef]

Velha, E. P. P.

Xu, Q.

Yablonovitch, E.

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[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," Science 284,1819 (1999).
[CrossRef] [PubMed]

Zhang, L.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, "Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode," Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

M. Lončar, A. Scherer, and Y. Qiu, "Photonic crystal laser sources for chemical detection," Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

IEE Proc. Opto.

R. Cocciol, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc. Opto. 145, 391-397 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

S. Maier, "Effective Mode Volume of Nanoscale Plasmon Cavities," Opt. Quantum Electron. 38, 257 (2006).
[CrossRef]

Phys. Rev.

E. M. Purcell, H. C. Torrey, and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev. 69, 37 (1946).
[CrossRef]

Phys. Rev. Lett.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, "Ultrasmall Mode Volumes in Dielectric Optical Microcavities," Phys. Rev. Lett. 95, 143901 (2005).
[CrossRef] [PubMed]

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, "Spontaneous Emergence of Periodic Patterns in a Biologically Inspired Simulation of Photonic Structures," Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Science

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," Science 284,1819 (1999).
[CrossRef] [PubMed]

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoğlu, "A quantum dot single-photon turnstile device," Science 290, 2282 (2000).
[CrossRef] [PubMed]

Other

V. R. Almeida, Q. Xu, R. R. Panepucci, C. A. Barrios, and M. Lipson, "Light Guiding in Low Index Materials using High-Index-Contrast Waveguides," Proc. Mat. Res. Soc. Fall Meeting (2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Evolution of a planar resonator in an evolutionary algorithm; (a) 1st generation, completely random device; (b) 100th generation, the bowtie shape is defined, (c) 200th generation, the bowtie shape is well defined and grating like structure begins to emerge; (d) 800th generation, the bowtie and the grating like structure are cleanly defined; each image is 120×120 pixels, each pixel represents 40×40nm square peg 250nm high in a 3D finite difference time domain simulation.

Fig. 2.
Fig. 2.

(a) Resonant mode amplitude (Ey) in a planar bowtie cavity; (b) radiative mode amplitude (E) in a bowtie, the dotted line represents the curvature of radiating field; insets, dielectric geometry of the respective devices, white: low index oxide 1.45, black: high index silicon 3.45.

Fig. 3.
Fig. 3.

Mode intensity in the bowtie cavity: blue, along the length and green in the transverse direction. The inset shows intensity distribution of a resonant mode in a bowtie cavity.

Fig. 4.
Fig. 4.

(a–d), Resonant modes in various categories of planar cavities; (e) Q vs V values of the above cavities; (a) holey waveguide; (b) holey waveguide with slot; (c) photonic crystal heterostructure; (d) bowtie cavity;

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