Abstract

A photonic nanocavity with a high Q factor of 100,000 and a modal volume V of 0.71 cubic wavelengths, is demonstrated. According to the cavity design rule that we discovered recently, we further improve a point-defect cavity in a two-dimensional (2D) photonic crystal (PC) slab, where the arrangement of six air holes near the cavity edges is fine-tuned. We demonstrate that the measured Q factor for the designed cavity increases by a factor of 20 relative to that for a cavity without displaced air holes, while the calculated modal volume remains almost constant.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. 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).
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    [CrossRef]
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  17. 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]
  18. B. Gayral, J. M. Gérard, A. Lemaître, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908-1910 (1999).
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Appl. Phys. Lett. (8)

H. Takano, Y. Akahane, T. Asano, and S. Noda, “In-plane-type channel drop filter in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 84, 2226-2228 (2004).
[CrossRef]

M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648-4650 (2003).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388-3390 (2001).
[CrossRef]

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294-4296 (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]

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]

B. Gayral, J. M. Gérard, A. Lemaître, C. Dupuis, L. Manin, and J. L. Pelouard, “High-Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75, 1908-1910 (1999).
[CrossRef]

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80, 2051-2053 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. Manalatou, 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]

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

Nature (2)

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]

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]

Nature Materials (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultrahigh-Q photonic double-heterostructure nanocavity,” Nature Materials (to be published).
[PubMed]

Opt. Express (1)

Phys. Rev. B (1)

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306 (2004).
[CrossRef]

Phys. Rev. E (1)

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Science (3)

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[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, 1819-1821 (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, 2282-2285 (2000).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic of the point-defect nanocavity in a 2D photonic crystal (PC) slab. The base cavity structure is composed of three missing air holes in a line. The PC structure has a triangular lattice of air holes with lattice constant a. The thickness of the slab and the radius of the air holes are 0.6a and 0.29a, respectively. (b)The designed cavity structure created by displacing two air holes at both edges in order to obtain high-Q factor (see Ref. 13). (c) The designed cavity structure created by fine-tuning the positions of six air holes near both edges to obtain an even higher Q factor.

Fig. 2.
Fig. 2.

(a) The electric field distribution (Ey ) of the fundamental mode for a cavity without air hole displacement at both edges. (b) The profile of (a) along the center line of the cavity and the fitted curve corresponding to the product of a fundamental sinusoidal wave and a Gaussian envelope function. (c) The 1D FT spectra of (b). The leaky region or light cone is indicated by the gray area. (d), (e), (f) The electric field distribution (Ey ), the Ey profile at the center line and the fitted curve, and the 1D FT spectra, respectively, for the cavity structure shown in Fig. 1(b). The displacement of air holes at the edges is set at 0.20a. (g), (h) The 2D FT spectra of (a) and (d), respectively. (i), (j) The 2D FT spectra of Ex for cavities of (a) and (d), respectively.

Fig. 3.
Fig. 3.

(a) Cavity Q factors and the modal volume (V) obtained theoretically for cavities with a range of displacements of air holes at position A (the nearest neighbors). (b) Those for cavities with a range of displacements of air holes at position B (the second nearest neighbors), whilst fixing the position of air holes A at their optimum value of 0.200a. (c) Those for the cavities with a range of displacements of air holes at position C (the third nearest neighbors), whilst fixing the positions of air holes A and B at their optimum values of 0.200a and 0.025a, respectively.

Fig. 4.
Fig. 4.

SEM images of one of the fabricated samples, including the point-defect cavity with displaced air holes A, B, and C. (a) Magnified view of the point-defect cavity. (b) Top view of the sample. A line-defect waveguide was introduced near the point-defect cavity.

Fig. 5.
Fig. 5.

An example of the measured spectra. (a), (b) Show transmission and radiation spectra, respectively. The insets in the figures show the geometry of the photon fluxes measured.

Fig. 6.
Fig. 6.

(a) Cavity Q factors (Qv) obtained experimentally for cavities with various displacements of air holes at position A. (b) Those for cavities with various displacements of air holes at position B, whilst fixing the position of air holes A at their optimum value of around 0.176a. (c) Those for the cavities with various displacements of air holes at position C, whilst fixing the positions of air holes A and B at their optimum values of around 0.176a and 0.024a, respectively.

Fig. 7.
Fig. 7.

The resonant (radiation) spectrum obtained for the optimum cavity with the maximum Qv (100,000). The linewidth is as narrow as 18 pm, which means that very high Q total (88,000) is obtained.

Fig. 8.
Fig. 8.

Schematic of 2D PC slab including a cavity and a waveguide.

Equations (12)

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Q ω 0 U ( t ) d U ( t ) dt ,
U ( t ) = U ( 0 ) exp [ ( ω 0 t ) Q ] ,
ln [ H ( t ) ] = ln [ H ( 0 ) ] [ ω 0 ( 2 Q ) ] t .
V = ε ( r ) E ( r ) 2 d 3 r max [ ε ( r ) E ( r ) 3 ] ,
Q v = Q total T ,
d a 1 dt = ( j ω 0 1 τ v 1 τ in ) a 1 + 1 τ in e i β d 1 S + 1
S 1 = 1 τ in e i β d 1 a 1
S 2 = e i β ( d 1 + d 2 ) ( S + 1 1 τ in e i β d 1 a 1 )
T = S 2 S + 1 2 = ( ω ω 0 ) 2 + ( ω 0 2 Q v ) 2 ( ω ω 0 ) 2 + ( ω 0 2 Q v + ω 0 2 Q in ) 2
T = ( 1 Q v ) 2 ( 1 Q v + 1 Q in ) 2
1 Q = 1 Q v + 1 Q in
T = ( Q Q v ) 2

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