Abstract

We identify two physical mechanisms which drastically increase the Q/V factor of photonic crystal microcavities. Both mechanisms rely on a fine tuning the geometry of the holes around the cavity defect. The first mechanism relies on engineering the mirrors in order to reduce the out-of-plane far field radiation. The second mechanism is less intuitive and relies on a pure electromagnetism effect based on transient fields at the subwavelength scale, namely a recycling of the mirror losses by radiation modes. The recycling mechanism enables the design of high-performance microresonators with moderate requirements on the mirror reflectivity. Once the geometry around the defect is optimised, both mechanisms are shown to strongly impact the Q and the Purcell factors of the microcavity.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett. (3)

D. Peyrade, E. Silberstein, P. Lalanne, A. Talneau, Y. Chen, "Short Bragg mirrors with adiabatic modal conversion," Appl. Phys. Lett. 81, 829-831 (2002).
[CrossRef] [PubMed]

M. Palamaru and Ph. Lalanne, "Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion," Appl. Phys. Lett. 78, 1466-69 (2001).
[CrossRef]

Steven G. Johnson, Shanhui Fan, Attila 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, 3388-00 (2001).
[CrossRef]

Electron. Lett. (1)

A.S. Jugessur, P. Pottier, R.M. De La Rue, "One-dimensional periodic photonic crystal microcavity filters with transition mode-matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-369 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

Ph. Lalanne and J. P. Hugonin, "Bloch-wave engineering for high Q�??s, small V�??s microcavities," IEEE J. Quantum Electron. 39, 1430-38 (2003)
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J.P. Zhang, D.Y. Chu, S.L. Wu, W.G. Bi, R.C. Tiberio, R.M. Joseph, A. Taflove, C.W. Tu, S.T. Ho, �??Nanofabrication of 1-D Photonic Bandgap Structures Along Photonic Wire,�?? IEEE Photon. Technol. Lett. 8, 491 (1996).
[CrossRef]

J. Appl. Phys. (1)

D.J. Ripin, K.Y. Lim, G.S. Petrich, P.R. Villeneuve, S. Fan, E.R. Thoen, J.D. Joannopoulos, E.P. Ippen and L.A. Kolodziejski, �??Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,�?? J. Appl. Phys. 87, 1578-80 (2000).
[CrossRef]

J. Computational. Phys. (1)

J.P Bérenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational. Phys. 114, 185 (1994).

J. Lightwave Technol. (1)

J. Opt. Soc. Am A. (1)

E. Silberstein, Ph. Lalanne, J.P. Hugonin and Q. Cao, "On the use of grating theory in integrated optics," J. Opt. Soc. Am. A. 18, 2865 (2001).
[CrossRef]

Nature (3)

J.S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J.D. Joannopoulos, L.C. Kimerling, H.I. Smith and E.P. Ippen, �??Photonic-bandgap microcavities in optical waveguides,�?? Nature 390, 143 (1997).
[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]

Y. Akahane, T. Asano, B-S Song and S. Noda, �??High-Q photonic nanocavity in two-dimensional photonic crystal,�?? Nature 425, 944-47 (2003).

Opt. Commun. (1)

P. Benech and D. Khalil, "Rigorous spectral analysis of leaky structures: application to the prism coupling problem," Opt. Commun. 118, 220 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (1)

E.M. Purcell, �??Spontaneous emission probabilities at radio frequencies�??, Phys. Rev. 69, 681 (1946)

Phys. Rev. E (1)

J. Vuckovic, M. Loncar, H. Mabuchi and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, art. #016608 (2002).

Other (2)

H. Yokoyama and K. Ujihara, Spontaneous emission and laser oscillation in microcavities, (FL: CRC Press, 1995)

A.W. Snyder and J.D. Love, Optical Waveguide theory (Chapman and Hall, NY, 1983).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Air-bridge cavity geometry. The cavity is defined by two sets of four holes (diameter 250 nm, lattice constant 450 nm) separated by a defect of length h. The holes are assumed to be fully etched into a semiconductor (n=3.48) air-bridge waveguide 340-nm thick and 500-nm wide. (b) Red curve : calculated modal mirror reflectivity spectrum. Blue curve : cavity transmission spectrum for h=0.3 µm. (c) Calculated modal transmission as a function of wavelength and geometric cavity length h.

Fig. 2.
Fig. 2.

Minimal model for recycling radiation in microcavities. Black and red arrows correspond to the fundamental and leaky modes, respectively. The cavity being symmetrical, the coupling coefficients rm and r’ are the same for both mirrors.

Fig. 3.
Fig. 3.

Validation of the model. (a) Comparison between calculated data (black) and model predictions (blue) for the modulus of the cavity transmission coefficients |t| for six different wavelengths covering the full band-gap region. The t values for λ=1.45, 1.6 and 1.75 µm values are vertically shifted by 1 and the model predictions are horizontally shifted by 0.05 (otherwise undistinguishable). The inset in the top center shows an enlarged view of the second resonance (h=0.5 µm) (b) Q’s as a function of the number N of holes for λ=1.56 µm; black circles : calculated data, bold blue curve: model predictions. The horizontal dashed line represents the intrinsic QFP factor in the absence of recycling. For all curves, the model parameters are θ=0.82π, f=0.5 and n’+in”=0.5+i0.1.

Fig. 4.
Fig. 4.

Calculated modal transmission as a function of wavelength and cavity length h for the engineered cavity (N=4).

Fig. 5.
Fig. 5.

Q factor as a function of the number of holes for the cavity with optimised recycling. Circles represent calculated data. The horizontal dashed line represents the cavity intrinsic QFP factor in the absence of recycling.

Fig. 6.
Fig. 6.

Engineered mirrors. (a) Cavity with engineered mirrors. (b) Comparaison between the modal reflectivity spectra of a classical mirror (dotted curve) and that of the engineered mirror (solid curve). Vertical lines indicate the bandgap edges.

Tables (1)

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Table 1. Cavity performance

Equations (10)

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α 1 = t m + r m β 1 + r β 2
α 2 = r β 1
r = r m + t m β 1
t = t m α 1 exp ( i ϕ 1 )
β 1 exp ( i ϕ 1 ) = r m α 1 exp ( i ϕ 1 ) + r α 2 exp ( i ϕ 2 )
β 2 exp ( i ϕ 2 ) = r α 1 exp ( i ϕ 1 ) ,
r eff = r m [ 1 + 2 ( r r m ) 2 exp ( i ϕ 2 i ϕ 1 ) ] 1 2 .
t = t m 2 exp ( i ϕ 1 ) 1 r eff 2 exp ( 2 i ϕ 1 ) ,
r eff r m = 1 + f L r m 2 exp ( k 0 n h ) exp [ i k 0 ( n n eff ) h + 2 i θ ] ,
Q = m π r eff ( 1 r eff 2 ) ,

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