Abstract

We investigated the characteristics of an ultra-high-Q photonic nanocavity (Q = ~230,000 and modal volume = ~1.2 cubic wavelengths) at various input light powers. The cavity characteristics were red-shifted as the input power increased. This nonlinearity could be explained by coupled-mode theory, taking into account two-photon absorption, the associated free-carrier absorption, plasma effect, thermo-optic effect, and a Kerr effect. Nonlinear cavity characteristics were observed at an extremely low input light power of 10 μW. We confirmed that these low-power nonlinear optical effects could be attributed to the ultra-high Q factor of the nanocavity.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  5. T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Optical nonlinear phenomenon in point-defect cavity in two-dimensional photonic crystal slab," Ext. Abstr. 65th Meet. Jpn. Soc. Appl. Phys. 65, 942 (2004).
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  8. 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, 1512-1514 (2003).
    [CrossRef]
  9. A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, "Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 79, 2690-2692 (2001).
    [CrossRef]
  10. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
    [CrossRef]
  11. 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]
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  13. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. We confirmed that the FCA exceeded the TPA when we used the different value of free-carriers relaxation time in Ref. 6 (where it is described as free-carriers cross-section) for the calculation. However, the cavity characteristics remained similar, because the contributions of both the TPA and the FCA to the cavity characteristics occurred via a thermo-optic effect. It was therefore difficult to experimentally distinguish between these factors in the current work. We think that the TPA was larger than the FCA in this case because FCA is optical absorption consequent from TPA and also because free-carriers recombination time is as short as 0.5 ns.

Appl. Phys. Lett.

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]

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, 1512-1514 (2003).
[CrossRef]

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, "Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 79, 2690-2692 (2001).
[CrossRef]

G. Cocorullo, F. G. Della Corte, and I. Rendina, "Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm," Appl. Phys. Lett. 74, 3338-3340 (1999).
[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]

IEEE J. Quantum Electron.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

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

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004).
[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] [PubMed]

Opt. Express

Opt. Lett.

Phys. Lett.

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Soc. Appl. Phys.

T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Optical nonlinear phenomenon in point-defect cavity in two-dimensional photonic crystal slab," Ext. Abstr. 65th Meet. Jpn. Soc. Appl. Phys. 65, 942 (2004).

Other

K. H. Hellwege, O. Madelung, M. Schultz, and H. Weiss, LANDORT-BORNSTEIN New Series 17 (Springer-Verlag Berlin, Heidelberg, New York, 1982).

We confirmed that the FCA exceeded the TPA when we used the different value of free-carriers relaxation time in Ref. 6 (where it is described as free-carriers cross-section) for the calculation. However, the cavity characteristics remained similar, because the contributions of both the TPA and the FCA to the cavity characteristics occurred via a thermo-optic effect. It was therefore difficult to experimentally distinguish between these factors in the current work. We think that the TPA was larger than the FCA in this case because FCA is optical absorption consequent from TPA and also because free-carriers recombination time is as short as 0.5 ns.

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Figures (6)

Fig. 1.
Fig. 1.

Scanning electron microscope (SEM) image of the fabricated sample and schematic diagram of the measuring apparatus.

Fig. 2.
Fig. 2.

Radiation characteristics of the cavity at various input powers.

Fig. 3.
Fig. 3.

CMT calculation of radiation characteristics of the cavity with Q in = 3.7 × 105 and Q v = 6 × 105 at various input powers. Inset is the experimental results.

Fig. 4.
Fig. 4.

CMT calculation of radiation characteristics of a low-Q factor cavity (Q in = Q v = 5 × 104) at various input powers.

Fig. 5.
Fig. 5.

Calculated optical absorption rates within the cavity at shifted resonant wavelengths.

Fig. 6.
Fig. 6.

Calculated refractive index changes of the cavity material at shifted resonant wavelengths.

Tables (1)

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Table 1. Physical parameters used for calculations

Equations (18)

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a = 1 2 τ in S 1 j ( ω ω ' 0 ) + 1 2 τ total ,
ω ' 0 = 2 πc ( λ 0 + Δ λ free + Δ λ thermal + Δ λ Kerr ) .
1 τ total = 1 τ v + 1 τ in + 1 τ TPA + 1 τ FCA ,
α TPA = βc ε 0 n E eff 2 2 ,
a 2 = 1 2 ε 0 n 2 E eff 2 . V TPA ,
α TPA = βc n V TPA a 2 .
N = a 2 τ TPA × 1 2 ħ ω × 1 V cavity × τ recon ,
ε ' = ε 1 + j ε 2 = ε ω p 2 ω 2 + j ω p 2 ω 3 τ relax ,
ω p 2 = e 2 N ε 0 m * ,
n ' ε 1 = ( ε ω p 2 ω 2 ) 1 / 2 ~ n 0 ω p 2 2 n ω 2 = n 0 + Δ n free
Δ T ~ a 2 ( 1 τ TPA + 1 τ FCA ) × R ,
Δ n Kerr = n 2 c n V Kerr a 2 ,
du dt = u τ = 1 4 ε 0 2 c 2 n ( r ) 2 E ( r ) 4 .
cavity du dt d r = 1 4 ε 0 2 c 2 cavity n ( r ) 2 β ( r ) E ( r ) 4 d r .
1 τ TPA eff = cavity du dt d r cavity u d r = 1 4 ε 0 2 c 2 cavity n ( r ) 2 β ( r ) E ( r ) 4 d r 1 2 ε 0 cavity n ( r ) 2 E ( r ) 2 d r .
1 τ TPA eff = 1 2 ε 0 c 2 β E eff 2 .
1 2 ε 0 n 2 E eff 2 V TPA = 1 2 ε 0 cavity n ( r ) 2 E ( r ) 2 d r .
V TPA = β n 2 [ cavity n ( r ) 2 E ( r ) 2 d r ] 2 cavity n ( r ) 2 β ( r ) E ( r ) 4 d r .

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