Abstract

In this letter, we show that the Q factors of the latest high-Q cavities in two dimensional photonic crystals, measured experimentally to be ~1000000, are determined by losses due to imperfections in the fabricated structures, and not by the cavity design. Quantitative analysis shows that the dominant sources of loss include the tilt of air-holes within the cavity, the roughness of the inner walls of the air-holes, variation in the radii of the air-holes, and optical absorption by adsorbed material. We believe that cavities with experimental Q factors of the order of several millions will be obtained in the future by reducing the losses due to imperfections through improved fabrication techniques.

© 2006 Optical Society of America

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  1. B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
    [CrossRef]
  2. O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
    [CrossRef] [PubMed]
  3. O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
    [CrossRef]
  4. S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
    [CrossRef] [PubMed]
  5. T. Yoshie, J. Vuckovic, and A. Scherer, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
    [CrossRef]
  6. 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]
  7. We believe that it is necessary to reveal the measurement method in detail since the FWHM of the spectrum is of the order of picometers, almost at the limit of resolution. An external cavity, tunable wavelength, semiconductor laser was used (SANTEC, TSL-210). The emission wavelength was changed by controlling the cavity length with a piezo actuator. The width of the laser line was < 1MHz (~ 8 fm at 1570 nm). Each time the emission wavelength was altered, it was measured using a wavelength meter (Agilent 86122-A-opt-002: with high precision option). The differential accuracy of the wavelength meter was ± 0.15 pm. The best Lorentzian fit to the resonant spectrum had a FWHM value of 1.95 pm. We evaluated the range of FWHM value as 1.8-2.1 pm by adding an error value of ± 0.15 pm to the best fit value. (In addition to the accuracy of the measurement system, there is a problem of temperature fluctuation since temperature dependence of the cavity resonant wavelength is as large as 80 pm/K [14]. This might widen the evaluation range of FWHM further, namely, the FWHM value might be smaller than 1.8pm or larger than 2.1pm.)
  8. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
    [CrossRef]
  9. Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
    [CrossRef]
  10. D. G. Hall, "In-plane scattering in planar optical waveguides: refractive index fluctuations and surface roughness," J. Opt. Soc. Am. A 2, 747-751 (1985).
    [CrossRef]
  11. For Example: M Chaplin. Water Structure and Behavior. Personal Homepage, URL: http://www.lsbu.ac.uk/water/ (accessed 5/12/05).
  12. D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
    [CrossRef] [PubMed]
  13. M. Borselli, T. J. Johnson, and O. Painter, "Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment," Opt. Express 13, 1515-1530 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1515
    [CrossRef] [PubMed]
  14. T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
    [CrossRef]

2005

B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
[CrossRef]

D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
[CrossRef] [PubMed]

M. Borselli, T. J. Johnson, and O. Painter, "Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment," Opt. Express 13, 1515-1530 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1515
[CrossRef] [PubMed]

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

2003

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

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]

2001

T. Yoshie, J. Vuckovic, and A. Scherer, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
[CrossRef]

2000

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

1999

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

1985

Akahane, Y.

B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

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]

Allen, H. C.

D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
[CrossRef] [PubMed]

Asano, T.

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
[CrossRef]

B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

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]

Borselli, M.

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Dapkus, P. D.

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

Hall, D. G.

Husain, A.

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Johnson, T. J.

Kim, I.

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Kunishi, W.

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

Lee, R. K.

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Liu, D.

D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
[CrossRef] [PubMed]

Ma, G.

D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
[CrossRef] [PubMed]

Nakamura, M.

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

Noda, S.

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

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]

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

O’Brien, J. D.

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

O'Brien, J. D.

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

Painter, O.

Painter, O. J.

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Scherer, A.

T. Yoshie, J. Vuckovic, and A. Scherer, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
[CrossRef]

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

Song, B. S.

B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
[CrossRef]

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

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]

Tanaka, Y.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

Vuckovic, J.

T. Yoshie, J. Vuckovic, and A. Scherer, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
[CrossRef]

Xu, M.

D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
[CrossRef] [PubMed]

Yariv, A.

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Yoshie, T.

T. Yoshie, J. Vuckovic, and A. Scherer, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
[CrossRef]

Appl Phys Lett.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl Phys Lett. 82, 1661-1663 (2003).
[CrossRef]

Appl. Phys. Lett.

T. Yoshie, J. Vuckovic, and A. Scherer, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
[CrossRef]

Electron. Lett.

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005).
[CrossRef]

Environ. Sci. Technol.

D. Liu, G. Ma, M. Xu, and H. C. Allen, "Adsorption of Ethylene Glycol vapor on r-Al2O3 (0001) and amorphous SiO2 surfaces: observation of molecular orientation and surface hydroxyl groups as sorption sites," Environ. Sci. Technol. 39, 206-212 (2005).
[CrossRef] [PubMed]

J. Lightwave. Technol.

O. J. Painter, A. Husain, A. Scherer, J. D. O'Brien, I. Kim, and P. D. Dapkus, "Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP," J. Lightwave. Technol. 17, 2082-2088 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Mater.

B. S. Song, S. Noda, T. Asano and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Nature

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

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]

Opt Express

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt Express,  13, 1202-1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202.
[CrossRef]

Opt. Express

Science

O. J. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Other

We believe that it is necessary to reveal the measurement method in detail since the FWHM of the spectrum is of the order of picometers, almost at the limit of resolution. An external cavity, tunable wavelength, semiconductor laser was used (SANTEC, TSL-210). The emission wavelength was changed by controlling the cavity length with a piezo actuator. The width of the laser line was < 1MHz (~ 8 fm at 1570 nm). Each time the emission wavelength was altered, it was measured using a wavelength meter (Agilent 86122-A-opt-002: with high precision option). The differential accuracy of the wavelength meter was ± 0.15 pm. The best Lorentzian fit to the resonant spectrum had a FWHM value of 1.95 pm. We evaluated the range of FWHM value as 1.8-2.1 pm by adding an error value of ± 0.15 pm to the best fit value. (In addition to the accuracy of the measurement system, there is a problem of temperature fluctuation since temperature dependence of the cavity resonant wavelength is as large as 80 pm/K [14]. This might widen the evaluation range of FWHM further, namely, the FWHM value might be smaller than 1.8pm or larger than 2.1pm.)

For Example: M Chaplin. Water Structure and Behavior. Personal Homepage, URL: http://www.lsbu.ac.uk/water/ (accessed 5/12/05).

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Figures (2)

Fig. 1.
Fig. 1.

SEM image of the heterostructure photonic crystal cavity designed to have a Q factor of 16,000,000.

Fig. 2.
Fig. 2.

Measured cavity characteristics: Emission spectrum of the cavity (filled circles), fitted by Lorentzian functions with full width half maximum values of 1.8 pm (red line) and 2.1 pm (blue line); and transmission spectrum of the excitation waveguide (open circles).

Tables (1)

Tables Icon

Table 1. Summary of the origins, measured quantities, and calculated Q factors for each loss. Lc: Correlation length, σ: Standard deviation, nc: Carrier density , ρ: Resistivity, σ: Absorption coefficient.

Equations (3)

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

1 Q exp = 1 Q design + 1 Q imperfect .
Q exp = Q loaded T ,
Q = 2 π n 0 αλ ,

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